add issequence function to data and plot functions and examples for geometry

docs/build/html/.buildinfo

@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 2cbc17343901b023dfef01a2244f3120
+config: caf5792fd17da2c604992977d35f1f60
 tags: 645f666f9bcd5a90fca523b33c5a78b7

docs/build/html/_modules/index.html

@@ -40,6 +40,7 @@
 <li><a href="pylib/geometry.html">pylib.geometry</a></li>
 <li><a href="pylib/geometry2d.html">pylib.geometry2d</a></li>
 <li><a href="pylib/geometry2d_plot.html">pylib.geometry2d_plot</a></li>
+<li><a href="pylib/geometry_plot_pylab.html">pylib.geometry_plot_pylab</a></li>
 <li><a href="pylib/mathematics.html">pylib.mathematics</a></li>
 <li><a href="pylib/numerical/fit.html">pylib.numerical.fit</a></li>
 <li><a href="pylib/numerical/integration.html">pylib.numerical.integration</a></li>

docs/build/html/_modules/pylib/data.html

@@ -47,6 +47,36 @@
 <span class="sd">&quot;&quot;&quot;</span>
 <span class="kn">import</span> <span class="nn">math</span>
 <span class="kn">import</span> <span class="nn">pickle</span>
+<span class="kn">import</span> <span class="nn">collections</span>
+
+<div class="viewcode-block" id="issequence"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.issequence">[docs]</a><span class="k">def</span> <span class="nf">issequence</span><span class="p">(</span><span class="n">obj</span><span class="p">):</span>
+  <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">  True for tuple, list, str</span>
+<span class="sd">  False for int, dict, set</span>
+
+<span class="sd">  :Example:</span>
+
+<span class="sd">  &gt;&gt;&gt; issequence(())</span>
+<span class="sd">  True</span>
+<span class="sd">  &gt;&gt;&gt; issequence((3, ))</span>
+<span class="sd">  True</span>
+<span class="sd">  &gt;&gt;&gt; issequence([])</span>
+<span class="sd">  True</span>
+<span class="sd">  &gt;&gt;&gt; issequence([1])</span>
+<span class="sd">  True</span>
+<span class="sd">  &gt;&gt;&gt; issequence([1, 2])</span>
+<span class="sd">  True</span>
+<span class="sd">  &gt;&gt;&gt; issequence(&#39;&#39;)</span>
+<span class="sd">  True</span>
+
+<span class="sd">  &gt;&gt;&gt; issequence((3))</span>
+<span class="sd">  False</span>
+<span class="sd">  &gt;&gt;&gt; issequence({})</span>
+<span class="sd">  False</span>
+<span class="sd">  &gt;&gt;&gt; issequence(set())</span>
+<span class="sd">  False</span>
+<span class="sd">  &quot;&quot;&quot;</span>
+  <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">)</span></div>
 
 <div class="viewcode-block" id="read"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.read">[docs]</a><span class="k">def</span> <span class="nf">read</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">x_column</span><span class="p">,</span> <span class="n">y_column</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
   <span class="sd">&quot;&quot;&quot;Read ascii data file.</span>

docs/build/html/_modules/pylib/function.html

@@ -235,7 +235,7 @@
 <span class="sd">  &gt;&gt;&gt; x, y, theta_end = hyotrochoid(20, 6, 6)</span>
 
 <span class="sd">  .. seealso::</span>
-<span class="sd">    :meth:`mathematics.lcm`</span>
+<span class="sd">    :meth:`pylib.mathematics.lcm`</span>
 <span class="sd">  &quot;&quot;&quot;</span>
   <span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">((</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
   <span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">((</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
@@ -412,7 +412,7 @@
 
 
 <span class="sd">  .. seealso::</span>
-<span class="sd">    :meth:`pylib.function.transformation`</span>
+<span class="sd">    :meth:`transformation`</span>
 <span class="sd">  &quot;&quot;&quot;</span>
   <span class="c1"># scale function to used chars and dots/pixel in y direction (4 for braille characters): from [0, 1] to [0, chars*4-1]</span>
   <span class="c1"># negate the function because the y axis is pointing downwards: from [0, 1] to [-1, 0] or from [0, chars*4-1] to [-(chars*4-1), 0]</span>
@@ -437,7 +437,7 @@
     <span class="c1">#frame = canvas.frame(min_x=a*pixel_per_char, min_y=1, max_x=b*pixel_per_char, max_y=21)</span>
     <span class="n">frame</span> <span class="o">=</span> <span class="n">canvas</span><span class="o">.</span><span class="n">frame</span><span class="p">()</span>
   <span class="k">elif</span> <span class="n">char_set</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;histogram&quot;</span><span class="p">,</span> <span class="s2">&quot;block&quot;</span><span class="p">]:</span>
-    <span class="kn">import</span> <span class="nn">drawblock</span>
+    <span class="kn">from</span> <span class="nn">.drawblock</span> <span class="kn">import</span> <span class="n">histogram</span>
 
     <span class="n">pixels_horizontal</span> <span class="o">=</span> <span class="mi">1</span>
     <span class="n">pixels_vertical</span> <span class="o">=</span> <span class="mi">8</span>
@@ -447,7 +447,7 @@
     <span class="n">density</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">density</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># density max 1!</span>
     <span class="n">x</span> <span class="o">=</span> <span class="n">seq</span><span class="p">(</span><span class="n">x_0</span><span class="o">*</span><span class="n">window_factor</span><span class="p">,</span> <span class="n">x_1</span><span class="o">*</span><span class="n">window_factor</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">pixels_horizontal</span><span class="o">/</span><span class="n">density</span><span class="p">)</span>
     <span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f</span><span class="p">(</span><span class="n">xi</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">xi</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]</span>
-    <span class="n">frame</span> <span class="o">=</span> <span class="n">drawblock</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
+    <span class="n">frame</span> <span class="o">=</span> <span class="n">histogram</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
 
   <span class="k">return</span> <span class="n">frame</span></div>
 </pre></div>

docs/build/html/_modules/pylib/geometry.html

@@ -35,7 +35,7 @@
   <h1>Source code for pylib.geometry</h1><div class="highlight"><pre>
 <span></span><span class="ch">#!/usr/bin/env python</span>
 <span class="c1"># -*- coding: utf-8 -*-</span>
-<span class="sd">&quot;&quot;&quot;2D geometry objects.</span>
+<span class="sd">&quot;&quot;&quot;Geometry objects.</span>
 
 <span class="sd">:Date: 2019-12-21</span>
 
@@ -44,26 +44,37 @@
 <span class="sd">  :synopsis: Geometry objects.</span>
 
 <span class="sd">.. moduleauthor:: Daniel Weschke &lt;daniel.weschke@directbox.de&gt;</span>
+
+<span class="sd">Affine transforms</span>
+<span class="sd">-----------------</span>
+
+<span class="sd">Functions in augmented space, in homogenous coordinates.</span>
+<span class="sd">Points are augment to 4 dimensions, by adding a dummy coordinate.</span>
+<span class="sd">For points the dummy coordinate is always normalized to 1.</span>
+<span class="sd">With homogenous coordinates translation of points is repesentable</span>
+<span class="sd">as a linear transformation.</span>
 <span class="sd">&quot;&quot;&quot;</span>
 <span class="kn">import</span> <span class="nn">math</span>
 <span class="kn">import</span> <span class="nn">copy</span>
-<span class="kn">from</span> <span class="nn">mathematics</span> <span class="kn">import</span> <span class="n">vector</span><span class="p">,</span> <span class="n">matrix</span>
+<span class="kn">from</span> <span class="nn">.mathematics</span> <span class="kn">import</span> <span class="n">vector</span><span class="p">,</span> <span class="n">matrix</span>
 
 <div class="viewcode-block" id="Direction"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Direction">[docs]</a><span class="k">class</span> <span class="nc">Direction</span><span class="p">(</span><span class="n">vector</span><span class="p">):</span>
   <span class="sd">&quot;&quot;&quot;Direction in local coordinate system&quot;&quot;&quot;</span>
   <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
-    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span></div>
-
-  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span></div>
 
 <div class="viewcode-block" id="Point"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Point">[docs]</a><span class="k">class</span> <span class="nc">Point</span><span class="p">(</span><span class="n">vector</span><span class="p">):</span>
   <span class="sd">&quot;&quot;&quot;Point in local coordinate system&quot;&quot;&quot;</span>
   <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
     <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
 
-  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+  <span class="c1"># TODO</span>
-    <span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span></div>
+<div class="viewcode-block" id="Point.projection"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Point.projection">[docs]</a>  <span class="k">def</span> <span class="nf">projection</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Orthographic projection to the xy-plane</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="c1"># P = matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])</span>
+    <span class="c1">#return (P*self)[:2]</span>
+    <span class="k">return</span> <span class="bp">self</span><span class="p">[:</span><span class="mi">2</span><span class="p">]</span></div></div>
 
 <div class="viewcode-block" id="CS"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS">[docs]</a><span class="k">class</span> <span class="nc">CS</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
   <span class="sd">&quot;&quot;&quot;Coordinate system</span>
@@ -71,9 +82,6 @@
   <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">y</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">z</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]):</span>
     <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([[</span><span class="o">*</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">*</span><span class="n">y</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">*</span><span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
 
-  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="s1">&#39;[&#39;</span> <span class="o">+</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_coordinates</span><span class="p">()])</span> <span class="o">+</span> <span class="s1">&#39;]&#39;</span>
-
 <div class="viewcode-block" id="CS.x90"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS.x90">[docs]</a>  <span class="nd">@staticmethod</span>
   <span class="k">def</span> <span class="nf">x90</span><span class="p">():</span>
     <span class="k">return</span> <span class="n">CS</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
@@ -94,7 +102,133 @@
     <span class="sd">&quot;&quot;&quot;Get coordinates in 3d space&quot;&quot;&quot;</span>
     <span class="k">return</span> <span class="bp">self</span><span class="p">[:</span><span class="mi">3</span><span class="p">,:</span><span class="mi">3</span><span class="p">]</span></div></div>
 
-<div class="viewcode-block" id="World"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World">[docs]</a><span class="k">class</span> <span class="nc">World</span><span class="p">():</span>
+<span class="c1"># TODO: Wireframe(list) or Wireframe(matrix) ?</span>
+<span class="c1"># list of Points</span>
+<div class="viewcode-block" id="Wireframe"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe">[docs]</a><span class="k">class</span> <span class="nc">Wireframe</span><span class="p">:</span>
+  <span class="sd">&quot;&quot;&quot;Open and closed wireframe object in local coordinate system</span>
+
+<span class="sd">  This class create its own points (copy).</span>
+<span class="sd">  &quot;&quot;&quot;</span>
+  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">points</span><span class="p">,</span> <span class="n">closed</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">copy</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">points</span><span class="p">]</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">closed</span> <span class="o">=</span> <span class="n">closed</span>
+
+<div class="viewcode-block" id="Wireframe.__str__"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.__str__">[docs]</a>  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">return</span> <span class="s1">&#39;[&#39;</span> <span class="o">+</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">point</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">])</span> <span class="o">+</span> <span class="s1">&#39;]&#39;</span></div>
+
+<div class="viewcode-block" id="Wireframe.__iter__"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.__iter__">[docs]</a>  <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Returns the Iterator object&quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">())</span></div>
+
+<div class="viewcode-block" id="Wireframe.points"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.points">[docs]</a>  <span class="k">def</span> <span class="nf">points</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Get coordinates in 3d space&quot;&quot;&quot;</span>
+    <span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="n">result</span> <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">closed</span> <span class="k">else</span> <span class="n">result</span> <span class="o">+</span> <span class="p">[</span><span class="n">result</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span></div>
+
+<div class="viewcode-block" id="Wireframe.xy"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.xy">[docs]</a>  <span class="k">def</span> <span class="nf">xy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Get coordinates in 3d space&quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="p">[</span><span class="n">i</span><span class="p">[:</span><span class="mi">2</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">()]))</span></div>
+
+<div class="viewcode-block" id="Wireframe.xyz"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.xyz">[docs]</a>  <span class="k">def</span> <span class="nf">xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Get coordinates in 3d space&quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="p">[</span><span class="n">i</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">()]))</span></div>
+
+<div class="viewcode-block" id="Wireframe.rotate_x"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_x">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Wireframe.rotate_y"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_y">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Wireframe.rotate_z"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_z">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_z</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Wireframe.translate"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.translate">[docs]</a>  <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="k">for</span>
+                    <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Wireframe.scale"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.scale">[docs]</a>  <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+    <span class="c1"># if not sy is not suitable because 0 is also false</span>
+    <span class="k">if</span> <span class="n">sy</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+      <span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
+      <span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="k">for</span>
+                    <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Wireframe.ch_cs"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.ch_cs">[docs]</a>  <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">(</span><span class="n">cs</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div></div>
+
+<div class="viewcode-block" id="Line"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Line">[docs]</a><span class="k">class</span> <span class="nc">Line</span><span class="p">(</span><span class="n">Wireframe</span><span class="p">):</span>
+  <span class="sd">&quot;&quot;&quot;Line a open wireframe object in local coordinate system&quot;&quot;&quot;</span>
+  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">point1</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">point2</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)):</span>
+    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Polygon"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Polygon">[docs]</a><span class="k">class</span> <span class="nc">Polygon</span><span class="p">(</span><span class="n">Wireframe</span><span class="p">):</span>
+  <span class="sd">&quot;&quot;&quot;Polygon as closed wireframe object in local coordinate system&quot;&quot;&quot;</span>
+  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">points</span><span class="p">):</span>
+    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">,</span> <span class="n">closed</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Circle"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Circle">[docs]</a><span class="k">class</span> <span class="nc">Circle</span><span class="p">(</span><span class="n">Polygon</span><span class="p">):</span>
+  <span class="sd">&quot;&quot;&quot;Circle a closed wireframe object in local coordinate system&quot;&quot;&quot;</span>
+  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
+    <span class="n">points</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+      <span class="n">x</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
+      <span class="n">y</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
+      <span class="n">points</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Point</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
+    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Solid"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Solid">[docs]</a><span class="k">class</span> <span class="nc">Solid</span><span class="p">:</span>
+  <span class="sd">&quot;&quot;&quot;Solid object in local coordinate system</span>
+
+<span class="sd">  This class lists Wireframe objects.</span>
+<span class="sd">  The Wireframe class create its own points (copy).</span>
+<span class="sd">  &quot;&quot;&quot;</span>
+  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">wireframes</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span> <span class="o">=</span> <span class="n">wireframes</span>
+
+<div class="viewcode-block" id="Solid.wireframes"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Solid.wireframes">[docs]</a>  <span class="k">def</span> <span class="nf">wireframes</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span></div>
+
+<div class="viewcode-block" id="Solid.translate"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Solid.translate">[docs]</a>  <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span> <span class="o">=</span> <span class="p">[</span><span class="n">wireframe</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="k">for</span>
+                        <span class="n">wireframe</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Solid.scale"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Solid.scale">[docs]</a>  <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+    <span class="c1"># if not sy is not suitable because 0 is also false</span>
+    <span class="k">if</span> <span class="n">sy</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+      <span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
+      <span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span> <span class="o">=</span> <span class="p">[</span><span class="n">wireframe</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="k">for</span>
+                        <span class="n">wireframe</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Solid.ch_cs"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Solid.ch_cs">[docs]</a>  <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span> <span class="o">=</span> <span class="p">[</span><span class="n">wireframe</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">(</span><span class="n">cs</span><span class="p">)</span> <span class="k">for</span>
+                        <span class="n">wireframe</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_wireframes</span><span class="p">]</span>
+    <span class="k">return</span> <span class="bp">self</span></div></div>
+
+<div class="viewcode-block" id="Hexahedron"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Hexahedron">[docs]</a><span class="k">class</span> <span class="nc">Hexahedron</span><span class="p">(</span><span class="n">Solid</span><span class="p">):</span>
+  <span class="sd">&quot;&quot;&quot;Line a open wireframe object in local coordinate system&quot;&quot;&quot;</span>
+  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+               <span class="n">point1</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">point2</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span>
+               <span class="n">point3</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">point4</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span>
+               <span class="n">point5</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">point6</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>
+               <span class="n">point7</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">point8</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)):</span>
+    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span>
+      <span class="n">Polygon</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">point3</span><span class="p">,</span> <span class="n">point4</span><span class="p">),</span>
+      <span class="n">Polygon</span><span class="p">(</span><span class="n">point5</span><span class="p">,</span> <span class="n">point6</span><span class="p">,</span> <span class="n">point7</span><span class="p">,</span> <span class="n">point8</span><span class="p">),</span>
+      <span class="n">Polygon</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">point6</span><span class="p">,</span> <span class="n">point5</span><span class="p">),</span>
+      <span class="n">Polygon</span><span class="p">(</span><span class="n">point3</span><span class="p">,</span> <span class="n">point4</span><span class="p">,</span> <span class="n">point8</span><span class="p">,</span> <span class="n">point7</span><span class="p">)</span>
+      <span class="p">)</span></div>
+
+<div class="viewcode-block" id="World"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World">[docs]</a><span class="k">class</span> <span class="nc">World</span><span class="p">:</span>
   <span class="sd">&quot;&quot;&quot;World-space with world-space coordinates</span>
 <span class="sd">  &quot;&quot;&quot;</span>
   <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
@@ -102,12 +236,13 @@
     <span class="bp">self</span><span class="o">.</span><span class="n">_objects</span> <span class="o">=</span> <span class="p">[]</span>
     <span class="bp">self</span><span class="o">.</span><span class="n">_store_init</span><span class="p">()</span>
 
-  <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="World.__iter__"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.__iter__">[docs]</a>  <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Returns the Iterator object&quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">objects</span><span class="p">())</span>
+    <span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">objects</span><span class="p">())</span></div>
 
   <span class="k">def</span> <span class="nf">_store_init</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;Initialize or reset calculated values, because a new object was added.</span>
+    <span class="sd">&quot;&quot;&quot;Initialize or reset calculated values, because a new object</span>
+<span class="sd">    was added.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="bp">self</span><span class="o">.</span><span class="n">_bb</span> <span class="o">=</span> <span class="kc">None</span>
     <span class="bp">self</span><span class="o">.</span><span class="n">_sd</span> <span class="o">=</span> <span class="kc">None</span>
@@ -141,6 +276,33 @@
     <span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span>
     <span class="k">return</span> <span class="bp">self</span></div>
 
+<div class="viewcode-block" id="World.wireframes"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.wireframes">[docs]</a>  <span class="k">def</span> <span class="nf">wireframes</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">objects</span><span class="p">():</span>
+      <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">Wireframe</span><span class="p">):</span>
+        <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">points</span><span class="p">())</span>
+      <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">Solid</span><span class="p">):</span>
+        <span class="p">[</span><span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">j</span><span class="o">.</span><span class="n">points</span><span class="p">())</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">i</span><span class="o">.</span><span class="n">wireframes</span><span class="p">()]</span>
+    <span class="k">return</span> <span class="n">result</span></div>
+
+<div class="viewcode-block" id="World.wireframes_xy"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.wireframes_xy">[docs]</a>  <span class="k">def</span> <span class="nf">wireframes_xy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">objects</span><span class="p">():</span>
+      <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">Wireframe</span><span class="p">):</span>
+        <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">xy</span><span class="p">())</span>
+      <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">Solid</span><span class="p">):</span>
+        <span class="p">[</span><span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">j</span><span class="o">.</span><span class="n">xy</span><span class="p">())</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">i</span><span class="o">.</span><span class="n">wireframes</span><span class="p">()]</span>
+    <span class="k">return</span> <span class="n">result</span></div>
+
+<div class="viewcode-block" id="World.wireframes_xyz"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.wireframes_xyz">[docs]</a>  <span class="k">def</span> <span class="nf">wireframes_xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">objects</span><span class="p">():</span>
+      <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">Wireframe</span><span class="p">):</span>
+        <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span>
+      <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">Solid</span><span class="p">):</span>
+        <span class="p">[</span><span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">j</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">i</span><span class="o">.</span><span class="n">wireframes</span><span class="p">()]</span>
+    <span class="k">return</span> <span class="n">result</span></div>
+
 <div class="viewcode-block" id="World.objects"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.objects">[docs]</a>  <span class="k">def</span> <span class="nf">objects</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
     <span class="k">return</span> <span class="p">[</span><span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_objects</span><span class="p">]</span></div>
 
@@ -159,10 +321,9 @@
     <span class="n">xmax</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">inf</span>
     <span class="n">ymax</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">inf</span>
     <span class="n">zmax</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">inf</span>
-    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_objects</span><span class="p">:</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">wireframes_xyz</span><span class="p">():</span>
-      <span class="n">xi</span><span class="p">,</span> <span class="n">yi</span><span class="p">,</span> <span class="n">zi</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">min</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span>
+      <span class="n">xi</span><span class="p">,</span> <span class="n">yi</span><span class="p">,</span> <span class="n">zi</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">min</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
-      <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">zs</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">max</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span>
+      <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">zs</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">max</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
-      <span class="c1">#xmax = x if x &gt; xmax: xmax = x</span>
       <span class="n">xmin</span> <span class="o">=</span> <span class="n">xi</span> <span class="k">if</span> <span class="n">xi</span> <span class="o">&lt;</span> <span class="n">xmin</span> <span class="k">else</span> <span class="n">xmin</span>
       <span class="n">ymin</span> <span class="o">=</span> <span class="n">yi</span> <span class="k">if</span> <span class="n">yi</span> <span class="o">&lt;</span> <span class="n">ymin</span> <span class="k">else</span> <span class="n">ymin</span>
       <span class="n">zmin</span> <span class="o">=</span> <span class="n">zi</span> <span class="k">if</span> <span class="n">zi</span> <span class="o">&lt;</span> <span class="n">zmin</span> <span class="k">else</span> <span class="n">zmin</span>
@@ -183,81 +344,11 @@
 
 <div class="viewcode-block" id="World.center"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.center">[docs]</a>  <span class="k">def</span> <span class="nf">center</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
     <span class="n">bb</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounding_box</span><span class="p">()</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">]])</span>
+    <span class="bp">self</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">bb</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
+                <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">bb</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
+                <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">+</span><span class="n">bb</span><span class="p">[</span><span class="mi">5</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],</span>
+                <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
     <span class="k">return</span> <span class="bp">self</span></div></div>
-
-<span class="c1"># TODO: Wireframe(list) or Wireframe(matrix) ?</span>
-<span class="c1"># list of Points</span>
-<div class="viewcode-block" id="Wireframe"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe">[docs]</a><span class="k">class</span> <span class="nc">Wireframe</span><span class="p">():</span>
-  <span class="sd">&quot;&quot;&quot;Open and closed wireframe object in local coordinate system</span>
-
-<span class="sd">  This class create its own points (copy).</span>
-<span class="sd">  &quot;&quot;&quot;</span>
-  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">points</span><span class="p">,</span> <span class="n">closed</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">copy</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">points</span><span class="p">]</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">closed</span> <span class="o">=</span> <span class="n">closed</span>
-
-  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="s1">&#39;[&#39;</span> <span class="o">+</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">point</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">])</span> <span class="o">+</span> <span class="s1">&#39;]&#39;</span>
-
-  <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;Returns the Iterator object&quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">())</span>
-
-<div class="viewcode-block" id="Wireframe.points"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.points">[docs]</a>  <span class="k">def</span> <span class="nf">points</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;Get coordinates in 3d space&quot;&quot;&quot;</span>
-    <span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="n">result</span> <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">closed</span> <span class="k">else</span> <span class="n">result</span> <span class="o">+</span> <span class="p">[</span><span class="n">result</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span></div>
-
-<div class="viewcode-block" id="Wireframe.xyz"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.xyz">[docs]</a>  <span class="k">def</span> <span class="nf">xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="p">[</span><span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">()</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">()])</span></div>
-
-<div class="viewcode-block" id="Wireframe.rotate_x"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_x">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="bp">self</span></div>
-
-<div class="viewcode-block" id="Wireframe.rotate_y"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_y">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="bp">self</span></div>
-
-<div class="viewcode-block" id="Wireframe.rotate_z"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_z">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_z</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="bp">self</span></div>
-
-<div class="viewcode-block" id="Wireframe.translate"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.translate">[docs]</a>  <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="bp">self</span></div>
-
-<div class="viewcode-block" id="Wireframe.scale"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.scale">[docs]</a>  <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">sy</span><span class="p">:</span>
-      <span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
-      <span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="bp">self</span></div>
-
-<div class="viewcode-block" id="Wireframe.ch_cs"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.ch_cs">[docs]</a>  <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
-    <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">(</span><span class="n">cs</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
-    <span class="k">return</span> <span class="bp">self</span></div></div>
-
-<div class="viewcode-block" id="Line"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Line">[docs]</a><span class="k">class</span> <span class="nc">Line</span><span class="p">(</span><span class="n">Wireframe</span><span class="p">):</span>
-  <span class="sd">&quot;&quot;&quot;Line a open wireframe object in local coordinate system&quot;&quot;&quot;</span>
-  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">point1</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">point2</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)):</span>
-    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">)</span></div>
-
-<div class="viewcode-block" id="Polygon"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Polygon">[docs]</a><span class="k">class</span> <span class="nc">Polygon</span><span class="p">(</span><span class="n">Wireframe</span><span class="p">):</span>
-  <span class="sd">&quot;&quot;&quot;Polygon as closed wireframe object in local coordinate system&quot;&quot;&quot;</span>
-  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">points</span><span class="p">):</span>
-    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">,</span> <span class="n">closed</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
-
-<div class="viewcode-block" id="Circle"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Circle">[docs]</a><span class="k">class</span> <span class="nc">Circle</span><span class="p">(</span><span class="n">Polygon</span><span class="p">):</span>
-  <span class="sd">&quot;&quot;&quot;Circle a closed wireframe object in local coordinate system&quot;&quot;&quot;</span>
-  <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-    <span class="n">points</span> <span class="o">=</span> <span class="p">[]</span>
-    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-      <span class="n">x</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
-      <span class="n">y</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
-      <span class="n">points</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Point</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
-    <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">)</span></div>
 </pre></div>
 
           </div>

docs/build/html/_modules/pylib/geometry2d_plot.html

@@ -46,7 +46,7 @@
 <span class="sd">.. moduleauthor:: Daniel Weschke &lt;daniel.weschke@directbox.de&gt;</span>
 <span class="sd">&quot;&quot;&quot;</span>
 <span class="kn">import</span> <span class="nn">pylab</span>
-<span class="kn">from</span> <span class="nn">geometry2d</span> <span class="kn">import</span> <span class="p">(</span>
+<span class="kn">from</span> <span class="nn">.geometry2d</span> <span class="kn">import</span> <span class="p">(</span>
   <span class="n">distance</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">line</span><span class="p">,</span> <span class="n">interpolate_hermite</span><span class="p">,</span> <span class="n">rotate_xy</span><span class="p">,</span> <span class="n">translate_xy</span>
 <span class="p">)</span>
 

docs/build/html/_modules/pylib/geometry_plot_pylab.html

@@ -0,0 +1,346 @@
+
+<!DOCTYPE html>
+
+<html xmlns="http://www.w3.org/1999/xhtml">
+  <head>
+    <meta charset="utf-8" />
+    <title>pylib.geometry_plot_pylab &#8212; pylib 2019.12.21 documentation</title>
+    <link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
+    <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
+    <link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
+    <script type="text/javascript" id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
+    <script type="text/javascript" src="../../_static/jquery.js"></script>
+    <script type="text/javascript" src="../../_static/underscore.js"></script>
+    <script type="text/javascript" src="../../_static/doctools.js"></script>
+    <script type="text/javascript" src="../../_static/language_data.js"></script>
+    <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
+    <link rel="index" title="Index" href="../../genindex.html" />
+    <link rel="search" title="Search" href="../../search.html" />
+   
+  <link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
+  
+  
+  <meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
+
+  </head><body>
+  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          
+
+          <div class="body" role="main">
+            
+  <h1>Source code for pylib.geometry_plot_pylab</h1><div class="highlight"><pre>
+<span></span><span class="ch">#!/usr/bin/env python</span>
+<span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;Geometry plotter using pylab (matplotlib).</span>
+
+<span class="sd">:Date: 2019-12-23</span>
+
+<span class="sd">.. module:: geometry_plot_pylab</span>
+<span class="sd">  :platform: *nix, Windows</span>
+<span class="sd">  :synopsis: Geometry plotting (pylab).</span>
+
+<span class="sd">.. moduleauthor:: Daniel Weschke &lt;daniel.weschke@directbox.de&gt;</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="c1"># This import registers the 3D projection, but is otherwise unused.</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
+<span class="k">assert</span> <span class="n">Axes3D</span>  <span class="c1"># silence pyflakes</span>
+<span class="kn">import</span> <span class="nn">pylab</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s1">&#39;dark_background&#39;</span><span class="p">)</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;text.color&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;grey&#39;</span>      <span class="c1"># lightgrey</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;axes.edgecolor&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;grey&#39;</span>  <span class="c1"># lightgrey</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;grid.color&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;grey&#39;</span>      <span class="c1"># lightgrey</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;xtick.color&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;grey&#39;</span>     <span class="c1"># lightgrey</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;ytick.color&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;grey&#39;</span>     <span class="c1"># lightgrey</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;axes3d.grid&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
+<span class="c1"># default for dark_background cycler(</span>
+<span class="c1"># &#39;color&#39;, [&#39;#1f77b4&#39;, &#39;#ff7f0e&#39;, &#39;#2ca02c&#39;, &#39;#d62728&#39;, &#39;#9467bd&#39;,</span>
+<span class="c1">#           &#39;#8c564b&#39;, &#39;#e377c2&#39;, &#39;#7f7f7f&#39;, &#39;#bcbd22&#39;, &#39;#17becf&#39;])</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;axes.prop_cycle&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">cycler</span><span class="p">(</span>
+  <span class="s2">&quot;color&quot;</span><span class="p">,</span> <span class="p">[</span><span class="s1">&#39;#3498DB&#39;</span><span class="p">,</span> <span class="s1">&#39;#ff7f0e&#39;</span><span class="p">,</span> <span class="s1">&#39;#2ca02c&#39;</span><span class="p">,</span> <span class="s1">&#39;#d62728&#39;</span><span class="p">,</span> <span class="s1">&#39;#9467bd&#39;</span><span class="p">,</span>
+            <span class="s1">&#39;#8c564b&#39;</span><span class="p">,</span> <span class="s1">&#39;#e377c2&#39;</span><span class="p">,</span> <span class="s1">&#39;#7f7f7f&#39;</span><span class="p">,</span> <span class="s1">&#39;#bcbd22&#39;</span><span class="p">,</span> <span class="s1">&#39;#17becf&#39;</span><span class="p">])</span>
+
+<span class="c1"># remove f for fullscreen toggle, default [&#39;f&#39;, &#39;ctrl+f&#39;]</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;keymap.fullscreen&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;ctrl+f&#39;</span><span class="p">]</span>
+<span class="c1"># remove L for log/lin toggle, default [&#39;k&#39;, &#39;L&#39;]</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;keymap.xscale&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;k&#39;</span><span class="p">]</span>
+<span class="c1"># remove l for log/lin toggle, default [&#39;l&#39;]</span>
+<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;keymap.yscale&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+
+<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">mean</span>
+<span class="kn">from</span> <span class="nn">.geometry</span> <span class="kn">import</span> <span class="n">CS</span>
+
+<span class="c1"># type of ax</span>
+<span class="c1"># - matplotlib.axes._subplots.Axes3DSubplot)</span>
+<span class="c1"># - matplotlib.axes.Axes</span>
+<span class="c1"># - pylab.Axes</span>
+
+<div class="viewcode-block" id="set_aspect_equal"><a class="viewcode-back" href="../../pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.set_aspect_equal">[docs]</a><span class="k">def</span> <span class="nf">set_aspect_equal</span><span class="p">(</span><span class="n">ax</span><span class="p">):</span>
+  <span class="sd">&#39;&#39;&#39;Make axes of 3D plot have equal scale so that spheres appear as</span>
+<span class="sd">  spheres, cubes as cubes, etc..  This is one possible solution to</span>
+<span class="sd">  Matplotlib&#39;s ax.set_aspect(&#39;equal&#39;) and ax.axis(&#39;equal&#39;) not</span>
+<span class="sd">  working for 3D.</span>
+
+<span class="sd">  :param ax: a pylab axis</span>
+<span class="sd">  :type ax: pylab.Axes</span>
+
+<span class="sd">  Source: https://stackoverflow.com/a/35126679</span>
+<span class="sd">  &#39;&#39;&#39;</span>
+  <span class="k">if</span> <span class="n">ax</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="s1">&#39;3d&#39;</span><span class="p">:</span>
+
+    <span class="n">xlim</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_xlim3d</span><span class="p">()</span>
+    <span class="n">ylim</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_ylim3d</span><span class="p">()</span>
+    <span class="n">zlim</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_zlim3d</span><span class="p">()</span>
+
+    <span class="n">xmean</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">xlim</span><span class="p">)</span>
+    <span class="n">ymean</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">ylim</span><span class="p">)</span>
+    <span class="n">zmean</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">zlim</span><span class="p">)</span>
+
+    <span class="n">plot_radius</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="nb">abs</span><span class="p">(</span><span class="n">lim</span> <span class="o">-</span> <span class="n">mean_</span><span class="p">)</span>
+                       <span class="k">for</span> <span class="n">lims</span><span class="p">,</span> <span class="n">mean_</span> <span class="ow">in</span> <span class="p">((</span><span class="n">xlim</span><span class="p">,</span> <span class="n">xmean</span><span class="p">),</span>
+                                           <span class="p">(</span><span class="n">ylim</span><span class="p">,</span> <span class="n">ymean</span><span class="p">),</span>
+                                           <span class="p">(</span><span class="n">zlim</span><span class="p">,</span> <span class="n">zmean</span><span class="p">))</span>
+                       <span class="k">for</span> <span class="n">lim</span> <span class="ow">in</span> <span class="n">lims</span><span class="p">])</span>
+
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_xlim3d</span><span class="p">([</span><span class="n">xmean</span> <span class="o">-</span> <span class="n">plot_radius</span><span class="p">,</span> <span class="n">xmean</span> <span class="o">+</span> <span class="n">plot_radius</span><span class="p">])</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim3d</span><span class="p">([</span><span class="n">ymean</span> <span class="o">-</span> <span class="n">plot_radius</span><span class="p">,</span> <span class="n">ymean</span> <span class="o">+</span> <span class="n">plot_radius</span><span class="p">])</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_zlim3d</span><span class="p">([</span><span class="n">zmean</span> <span class="o">-</span> <span class="n">plot_radius</span><span class="p">,</span> <span class="n">zmean</span> <span class="o">+</span> <span class="n">plot_radius</span><span class="p">])</span>
+  <span class="k">else</span><span class="p">:</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">&#39;equal&#39;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="plot_post"><a class="viewcode-back" href="../../pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.plot_post">[docs]</a><span class="k">def</span> <span class="nf">plot_post</span><span class="p">(</span><span class="n">ax</span><span class="p">):</span>
+  <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">pylab</span><span class="o">.</span><span class="n">Axes</span><span class="p">):</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="p">[</span><span class="n">ax</span><span class="p">]</span>
+  <span class="k">for</span> <span class="n">axi</span> <span class="ow">in</span> <span class="n">ax</span><span class="p">:</span>
+    <span class="k">if</span> <span class="n">axi</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="s1">&#39;3d&#39;</span><span class="p">:</span>
+      <span class="c1">#axi.w_xaxis.set_pane_color((0, 0, 0, 0))</span>
+      <span class="c1">#axi.w_yaxis.set_pane_color((0, 0, 0, 0))</span>
+      <span class="c1">#axi.w_zaxis.set_pane_color((0, 0, 0, 0))</span>
+      <span class="n">axi</span><span class="o">.</span><span class="n">w_xaxis</span><span class="o">.</span><span class="n">pane</span><span class="o">.</span><span class="n">fill</span> <span class="o">=</span> <span class="kc">False</span>
+      <span class="n">axi</span><span class="o">.</span><span class="n">w_yaxis</span><span class="o">.</span><span class="n">pane</span><span class="o">.</span><span class="n">fill</span> <span class="o">=</span> <span class="kc">False</span>
+      <span class="n">axi</span><span class="o">.</span><span class="n">w_zaxis</span><span class="o">.</span><span class="n">pane</span><span class="o">.</span><span class="n">fill</span> <span class="o">=</span> <span class="kc">False</span>
+    <span class="n">set_aspect_equal</span><span class="p">(</span><span class="n">axi</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="wireframe3d"><a class="viewcode-back" href="../../pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.wireframe3d">[docs]</a><span class="k">def</span> <span class="nf">wireframe3d</span><span class="p">(</span><span class="n">world</span><span class="p">):</span>
+  <span class="n">fig</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+  <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+  <span class="p">[</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">*</span><span class="n">i</span><span class="p">,</span> <span class="s1">&#39;C0&#39;</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">world</span><span class="o">.</span><span class="n">wireframes_xyz</span><span class="p">()]</span>
+  <span class="n">plot_post</span><span class="p">(</span><span class="n">ax</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="cad_wireframe"><a class="viewcode-back" href="../../pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.cad_wireframe">[docs]</a><span class="k">def</span> <span class="nf">cad_wireframe</span><span class="p">(</span><span class="n">world</span><span class="p">,</span> <span class="n">centering</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+  <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">  Graphical projections</span>
+
+<span class="sd">  * Parallel projections</span>
+
+<span class="sd">    * Orthographic</span>
+
+<span class="sd">      * Multiview</span>
+
+<span class="sd">        * \* First-angle</span>
+<span class="sd">        * Third-angle</span>
+<span class="sd">        * Plan Elevation</span>
+
+<span class="sd">      * Axonometric</span>
+
+<span class="sd">        * \* Isometric</span>
+<span class="sd">        * Dimetric</span>
+<span class="sd">        * Trimetri</span>
+
+<span class="sd">    * Oblique</span>
+
+<span class="sd">      * Carbinet</span>
+<span class="sd">      * Cavalier</span>
+<span class="sd">      * Military</span>
+<span class="sd">      * Top-down</span>
+
+<span class="sd">  * Perspective projections</span>
+
+<span class="sd">    * 1-point</span>
+<span class="sd">    * 2-point</span>
+<span class="sd">    * 3-point</span>
+<span class="sd">    * Curvilinear</span>
+
+<span class="sd">  &quot;&quot;&quot;</span>
+  <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+    <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+
+  <span class="n">fig</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="s1">&#39;geometry-cad&#39;</span><span class="p">)</span>
+  <span class="n">fig</span><span class="o">.</span><span class="n">clf</span><span class="p">()</span>
+  <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
+
+  <span class="n">pylab</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">&#39;off&#39;</span><span class="p">)</span>
+  <span class="n">pylab</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">left</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+
+  <span class="n">lps</span> <span class="o">=</span> <span class="p">[</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">*</span><span class="n">i</span><span class="p">,</span> <span class="s1">&#39;C0&#39;</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">world</span><span class="o">.</span><span class="n">wireframes_xy</span><span class="p">()]</span>
+
+  <span class="n">plot_post</span><span class="p">(</span><span class="n">ax</span><span class="p">)</span>
+
+  <span class="k">def</span> <span class="nf">press</span><span class="p">(</span><span class="n">event</span><span class="p">,</span> <span class="n">world</span><span class="p">,</span> <span class="n">lps</span><span class="p">):</span>
+    <span class="c1">#print(&#39;key pressed:&#39;, event.key)</span>
+    <span class="c1">#sys.stdout.flush()</span>
+    <span class="k">if</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="ow">in</span> <span class="p">[</span>
+        <span class="s1">&#39;left&#39;</span><span class="p">,</span> <span class="s1">&#39;right&#39;</span><span class="p">,</span> <span class="s1">&#39;up&#39;</span><span class="p">,</span> <span class="s1">&#39;down&#39;</span><span class="p">,</span>
+        <span class="s1">&#39;f&#39;</span><span class="p">,</span> <span class="s1">&#39;t&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;l&#39;</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">,</span> <span class="s1">&#39;i&#39;</span><span class="p">,</span> <span class="s1">&#39;d&#39;</span><span class="p">,</span>
+        <span class="s1">&#39;shift+left&#39;</span><span class="p">,</span> <span class="s1">&#39;shift+right&#39;</span><span class="p">,</span> <span class="s1">&#39;shift+up&#39;</span><span class="p">,</span> <span class="s1">&#39;shift+down&#39;</span><span class="p">,</span>
+        <span class="s1">&#39;ctrl+up&#39;</span><span class="p">,</span> <span class="s1">&#39;ctrl+down&#39;</span><span class="p">,</span> <span class="s1">&#39;ctrl+left&#39;</span><span class="p">,</span> <span class="s1">&#39;ctrl+right&#39;</span><span class="p">]:</span>
+      <span class="n">d</span> <span class="o">=</span> <span class="n">world</span><span class="o">.</span><span class="n">space_diagonal</span><span class="p">()</span>
+      <span class="k">if</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;left&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="o">*</span><span class="mi">10</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;right&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="o">*</span><span class="mi">10</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;up&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="o">*</span><span class="mi">10</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;down&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="o">*</span><span class="mi">10</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;f&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="p">())</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;t&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="o">.</span><span class="n">x90</span><span class="p">())</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;b&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="o">.</span><span class="n">xm90</span><span class="p">())</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;l&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="o">.</span><span class="n">y90</span><span class="p">())</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;r&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="o">.</span><span class="n">ym90</span><span class="p">())</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;i&#39;</span><span class="p">:</span>
+        <span class="c1">#theta_y = -math.pi/2/3</span>
+        <span class="c1">#theta_x = math.pi/2/3</span>
+        <span class="n">theta_y</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span><span class="o">/</span><span class="mi">2</span>
+        <span class="n">theta_x</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">asin</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span><span class="o">/</span><span class="mi">3</span><span class="p">))</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="p">()</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="n">theta_y</span><span class="p">)</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="n">theta_x</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;d&#39;</span><span class="p">:</span>
+        <span class="c1">#theta_x = math.asin(math.tan(math.pi/2/3/2))</span>
+        <span class="n">theta_y</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span><span class="o">/</span><span class="mi">2</span>
+        <span class="n">theta_x</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">atan</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">cs</span><span class="p">(</span><span class="n">CS</span><span class="p">()</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="n">theta_y</span><span class="p">)</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="n">theta_x</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">centering</span><span class="p">:</span>
+          <span class="n">world</span><span class="o">.</span><span class="n">center</span><span class="p">()</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;shift+left&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="o">-</span><span class="mf">0.1</span><span class="o">*</span><span class="n">d</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;shift+right&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mf">0.1</span><span class="o">*</span><span class="n">d</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;shift+up&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="o">*</span><span class="n">d</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;shift+down&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="o">*</span><span class="n">d</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;ctrl+left&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">rotate_z</span><span class="p">(</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="o">*</span><span class="mi">10</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;ctrl+right&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">rotate_z</span><span class="p">(</span><span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="o">*</span><span class="mi">10</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;ctrl+up&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mf">1.1</span><span class="p">)</span>
+      <span class="k">elif</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">&#39;ctrl+down&#39;</span><span class="p">:</span>
+        <span class="n">world</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mf">0.9</span><span class="p">)</span>
+      <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">lps</span><span class="p">,</span> <span class="n">world</span><span class="o">.</span><span class="n">wireframes_xy</span><span class="p">()):</span>
+        <span class="n">i</span><span class="o">.</span><span class="n">set_data</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
+    <span class="n">fig</span><span class="o">.</span><span class="n">canvas</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
+
+  <span class="k">def</span> <span class="nf">onresize</span><span class="p">(</span><span class="n">event</span><span class="p">,</span> <span class="n">w</span><span class="p">):</span>
+    <span class="n">r</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">w</span><span class="o">.</span><span class="n">space_diagonal</span><span class="p">()</span><span class="o">/</span><span class="mi">2</span>
+    <span class="n">pylab</span><span class="o">.</span><span class="n">xlim</span><span class="p">((</span><span class="o">-</span><span class="n">r</span><span class="p">,</span> <span class="n">r</span><span class="p">))</span>
+    <span class="n">pylab</span><span class="o">.</span><span class="n">ylim</span><span class="p">((</span><span class="o">-</span><span class="n">r</span><span class="p">,</span> <span class="n">r</span><span class="p">))</span>
+
+  <span class="n">fig</span><span class="o">.</span><span class="n">canvas</span><span class="o">.</span><span class="n">mpl_connect</span><span class="p">(</span><span class="s1">&#39;key_press_event&#39;</span><span class="p">,</span>
+                         <span class="k">lambda</span> <span class="n">event</span><span class="p">:</span> <span class="n">press</span><span class="p">(</span><span class="n">event</span><span class="p">,</span> <span class="n">world</span><span class="p">,</span> <span class="n">lps</span><span class="p">))</span>
+  <span class="n">fig</span><span class="o">.</span><span class="n">canvas</span><span class="o">.</span><span class="n">mpl_connect</span><span class="p">(</span><span class="s1">&#39;resize_event&#39;</span><span class="p">,</span>
+                         <span class="k">lambda</span> <span class="n">event</span><span class="p">:</span> <span class="n">onresize</span><span class="p">(</span><span class="n">event</span><span class="p">,</span> <span class="n">world</span><span class="p">))</span>
+
+  <span class="n">pylab</span><span class="o">.</span><span class="n">text</span><span class="p">(</span>
+    <span class="mi">0</span><span class="o">+.</span><span class="mi">01</span><span class="p">,</span> <span class="mi">1</span><span class="o">-.</span><span class="mi">015</span><span class="p">,</span>
+    <span class="s1">&#39;rotate: left, right, up, down, ctrl+left, ctrl+right</span><span class="se">\n</span><span class="s1">&#39;</span> <span class="o">+</span>
+    <span class="s1">&#39;pan: shift+left, shift+right, shift+up, shift+down</span><span class="se">\n</span><span class="s1">&#39;</span> <span class="o">+</span>
+    <span class="s1">&#39;zoom: ctrl+up, ctrl+down</span><span class="se">\n</span><span class="s1">&#39;</span> <span class="o">+</span>
+    <span class="s1">&#39;view: f (front), l (left), r (right), t (top), b (bottom)</span><span class="se">\n</span><span class="s1">&#39;</span> <span class="o">+</span>
+    <span class="s1">&#39;      i (isometric), d (dimetric)&#39;</span><span class="p">,</span>
+    <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;left&#39;</span><span class="p">,</span>
+    <span class="n">verticalalignment</span><span class="o">=</span><span class="s1">&#39;top&#39;</span><span class="p">,</span>
+    <span class="n">transform</span><span class="o">=</span><span class="n">fig</span><span class="o">.</span><span class="n">transFigure</span><span class="p">,</span>
+    <span class="n">bbox</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">),</span>
+    <span class="n">family</span><span class="o">=</span><span class="s1">&#39;monospace&#39;</span>
+    <span class="p">)</span>
+  <span class="n">pylab</span><span class="o">.</span><span class="n">show</span><span class="p">()</span></div>
+</pre></div>
+
+          </div>
+          
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<h1 class="logo"><a href="../../index.html">pylib</a></h1>
+
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+<h3>Navigation</h3>
+<p class="caption"><span class="caption-text">Contents:</span></p>
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+</ul>
+</div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" />
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+<script type="text/javascript">$('#searchbox').show(0);</script>
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+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="footer">
+      &copy;2019, Daniel Weschke.
+      
+      |
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 2.2.1</a>
+      &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
+      
+    </div>
+
+    
+
+    
+  </body>
+</html>

docs/build/html/_modules/pylib/mathematics.html

@@ -56,69 +56,68 @@
 <div class="viewcode-block" id="vector"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector">[docs]</a><span class="k">class</span> <span class="nc">vector</span><span class="p">(</span><span class="nb">list</span><span class="p">):</span>
   <span class="sd">&quot;&quot;&quot;Use/create vector like lists</span>
 
-<span class="sd">  * size  -&gt; len(a)</span>
+<span class="sd">  * size, length of a vector use len(a)</span>
-<span class="sd">  * abs   -&gt; abs(a)</span>
+<span class="sd">  * absolute, magntude, norm of a vector use abs(a), see</span>
-<span class="sd">  * dot   -&gt; a * b</span>
+<span class="sd">    :meth:`__abs__`</span>
-<span class="sd">  * outer -&gt; a @ b</span>
+<span class="sd">  * dot product use a * b, see :meth:`__mul__` and  :meth:`__rmul__`</span>
+<span class="sd">  * outer product use a @ b, see :meth:`__matmul__`</span>
 
-<span class="sd">  use super constructor</span>
+<span class="sd">  :__iter__:</span>
 
-<span class="sd">  use super __iter__</span>
+<span class="sd">  &gt;&gt;&gt; [i*2 for i in vector([1, 2, 3])]</span>
+<span class="sd">  [2, 4, 6]</span>
 
-<span class="sd">  use super __setitem__</span>
+<span class="sd">  :__setitem__:</span>
 
-<span class="sd">  &gt;&gt;&gt; v = vector([1,2,3,4,5])</span>
+<span class="sd">  &gt;&gt;&gt; v = vector([1, 2, 3, 4, 5])</span>
-<span class="sd">  &gt;&gt;&gt; v[3:5] = [1,2]</span>
+<span class="sd">  &gt;&gt;&gt; v[3:5] = [1, 2]</span>
 <span class="sd">  &gt;&gt;&gt; print(v)</span>
 <span class="sd">  [1, 2, 3, 1, 2]</span>
 <span class="sd">  &gt;&gt;&gt; isinstance(v, vector)</span>
 <span class="sd">  True</span>
 
-<span class="sd">  use super __lt__(a, b)</span>
+<span class="sd">  :__eq__(a, b):</span>
 
-<span class="sd">  use super __le__(a, b)</span>
+<span class="sd">  &gt;&gt;&gt; vector([1, 2, 3, 1, 2]) == vector([1, 2, 3, 1, 2])</span>
+<span class="sd">  True</span>
+<span class="sd">  &gt;&gt;&gt; vector([1, 2, 3, 1, 2]) == vector([1, 2, 3, 2, 1])</span>
+<span class="sd">  False</span>
 
-<span class="sd">  use super __eq__(a, b)</span>
+<span class="sd">  :__ne__(a, b):</span>
 
-<span class="sd">  &gt;&gt;&gt; v = vector([1,2,3,1,2])</span>
+<span class="sd">  &gt;&gt;&gt; vector([1, 2, 3, 1, 2]) != vector([1, 2, 3, 1, 2])</span>
-<span class="sd">  &gt;&gt;&gt; v2 = vector([1,2,3,1,2])</span>
+<span class="sd">  False</span>
-<span class="sd">  &gt;&gt;&gt; v == v2</span>
+<span class="sd">  &gt;&gt;&gt; vector([1, 2, 3, 1, 2]) != vector([1, 2, 3, 2, 1])</span>
 <span class="sd">  True</span>
 
-<span class="sd">  use super __ne__(a, b)</span>
+<span class="sd">  :__contains__:</span>
 
-<span class="sd">  use super __ge__(a, b)</span>
+<span class="sd">  &gt;&gt;&gt; 2 in vector([1, 2, 3])</span>
-
-<span class="sd">  use super __gt__(a, b)</span>
-
-<span class="sd">  use super __contains__</span>
-
-<span class="sd">  &gt;&gt;&gt; 2 in vector([1,2,3])</span>
 <span class="sd">  True</span>
 
-<span class="sd">  __isub__</span>
+<span class="sd">  :__isub__:</span>
 
-<span class="sd">  &gt;&gt;&gt; v = vector([1,2,3])</span>
+<span class="sd">  &gt;&gt;&gt; v = vector([1, 2, 3])</span>
-<span class="sd">  &gt;&gt;&gt; v -= vector([3,3,3])</span>
+<span class="sd">  &gt;&gt;&gt; v -= vector([3, 3, 3])</span>
 <span class="sd">  &gt;&gt;&gt; print(v)</span>
 <span class="sd">  [-2, -1, 0]</span>
 
-<span class="sd">  __imul__</span>
+<span class="sd">  :__imul__:</span>
 
-<span class="sd">  &gt;&gt;&gt; v = vector([1,2,3])</span>
+<span class="sd">  &gt;&gt;&gt; v = vector([1, 2, 3])</span>
-<span class="sd">  &gt;&gt;&gt; v *= vector([3,3,3])</span>
+<span class="sd">  &gt;&gt;&gt; v *= vector([3, 3, 3])</span>
 <span class="sd">  &gt;&gt;&gt; print(v)</span>
 <span class="sd">  18</span>
 
-<span class="sd">  __imatmul__</span>
+<span class="sd">  :__imatmul__:</span>
 
-<span class="sd">  &gt;&gt;&gt; m = vector([1,2,3])</span>
+<span class="sd">  &gt;&gt;&gt; m = vector([1, 2, 3])</span>
-<span class="sd">  &gt;&gt;&gt; m *= vector([3,3,3])</span>
+<span class="sd">  &gt;&gt;&gt; m *= vector([3, 3, 3])</span>
 <span class="sd">  &gt;&gt;&gt; print(v)</span>
 <span class="sd">  [[3, 3, 3], [6, 6, 6], [9, 9, 9]]</span>
 <span class="sd">  &quot;&quot;&quot;</span>
 
-  <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__getitem__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__getitem__">[docs]</a>  <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    For index return value, for range return new vector object.</span>
 
@@ -133,57 +132,68 @@
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="c1"># use the list.__getslice__ method and convert result to vector</span>
     <span class="n">item</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">vector</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="k">else</span> <span class="n">item</span>
+    <span class="k">return</span> <span class="n">vector</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="k">else</span> <span class="n">item</span></div>
 
-  <span class="k">def</span> <span class="fm">__pos__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__pos__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__pos__">[docs]</a>  <span class="k">def</span> <span class="fm">__pos__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;+ a (new object)</span>
+    <span class="sd">&quot;&quot;&quot;\+ a (new object)</span>
+
+<span class="sd">    .. math::</span>
+<span class="sd">      \mathbf{b} = +\mathbf{a}</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="o">*</span><span class="bp">self</span><span class="p">])</span>
+    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="o">*</span><span class="bp">self</span><span class="p">])</span></div>
 
-  <span class="k">def</span> <span class="fm">__neg__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__neg__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__neg__">[docs]</a>  <span class="k">def</span> <span class="fm">__neg__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;- a (new object)</span>
+    <span class="sd">&quot;&quot;&quot;\- a (new object)</span>
+
+<span class="sd">    .. math::</span>
+<span class="sd">      \mathbf{b} = -\mathbf{a}</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="o">-</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
+    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="o">-</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span></div>
 
-  <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__add__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__add__">[docs]</a>  <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;a + b (new object)</span>
 
+<span class="sd">    .. math::</span>
+<span class="sd">      \mathbf{c} = \mathbf{a} + \mathbf{b}</span>
+
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; v = vector([1,2,3]) + vector([1,2,3])</span>
+<span class="sd">    &gt;&gt;&gt; v = vector([1, 2, 3]) + vector([1, 2, 3])</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [2, 4, 6]</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">+</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span>
+    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">+</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span></div>
 
-  <span class="k">def</span> <span class="fm">__iadd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+  <span class="c1"># overwrite because [1, 2] + [5, 8] = [1, 2, 5, 8]</span>
+<div class="viewcode-block" id="vector.__iadd__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__iadd__">[docs]</a>  <span class="k">def</span> <span class="fm">__iadd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;a += b (new object)</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; v = vector([1,2,3])</span>
+<span class="sd">    &gt;&gt;&gt; v = vector([1, 2, 3])</span>
-<span class="sd">    &gt;&gt;&gt; v += vector([3,3,3])</span>
+<span class="sd">    &gt;&gt;&gt; v += vector([3, 3, 3])</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [4, 5, 6]</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">+</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span>
+    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">+</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span></div>
 
-  <span class="k">def</span> <span class="fm">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__sub__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__sub__">[docs]</a>  <span class="k">def</span> <span class="fm">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;a - b (new object)</span>
 
+<span class="sd">    .. math::</span>
+<span class="sd">      \mathbf{c} = \mathbf{a} - \mathbf{b}</span>
+
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; v = vector([1,2,3]) - vector([1,2,3])</span>
+<span class="sd">    &gt;&gt;&gt; v = vector([1, 2, 3]) - vector([1, 2, 3])</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [0, 0, 0]</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">-</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span>
+    <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">-</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span></div>
 
-  <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__mul__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__mul__">[docs]</a>  <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Scalar multiplication, dot product (inner product) or</span>
-<span class="sd">    vector-matrix multiplication.</span>
+<span class="sd">    vector-matrix multiplication. (new object)</span>
-
-<span class="sd">    a * b (new object)</span>
 
 <span class="sd">    :type other: scalar, vector (or 1d list), matrix (or 2d list)</span>
 
@@ -193,18 +203,18 @@
 <span class="sd">      \mathbf{c} &amp;= \mathbf{a} \cdot \mathbf{B}</span>
 
 <span class="sd">    .. note::</span>
-<span class="sd">      No size checking will be conducted, therefore no exceptions for</span>
+<span class="sd">      No size checking will be conducted, therefore no exceptions</span>
-<span class="sd">      wrong usage (result will be nonsense).</span>
+<span class="sd">      for wrong usage (result will be nonsense).</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; v = vector([1,2,3,4,5])*3</span>
+<span class="sd">    &gt;&gt;&gt; v = vector([1, 2, 3, 4, 5]) * 3</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [3, 6, 9, 12, 15]</span>
-<span class="sd">    &gt;&gt;&gt; v = vector([1,2,3,4,5])*3.</span>
+<span class="sd">    &gt;&gt;&gt; v = vector([1, 2, 3, 4, 5]) * 3.</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [3.0, 6.0, 9.0, 12.0, 15.0]</span>
-<span class="sd">    &gt;&gt;&gt; s = vector([1,2,3])*vector([1,2,3])</span>
+<span class="sd">    &gt;&gt;&gt; s = vector([1, 2, 3]) * vector([1, 2, 3])</span>
 <span class="sd">    &gt;&gt;&gt; print(s)</span>
 <span class="sd">    14</span>
 
@@ -215,15 +225,14 @@
       <span class="k">return</span> <span class="nb">sum</span><span class="p">([</span><span class="n">i</span><span class="o">*</span><span class="n">j</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)])</span>
     <span class="k">except</span><span class="p">:</span>
       <span class="k">try</span><span class="p">:</span>     <span class="c1"># vector * matrix</span>
-        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span> <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">other</span><span class="p">)])</span>
+        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span>
+                       <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">other</span><span class="p">)])</span>
       <span class="k">except</span><span class="p">:</span>  <span class="c1"># vector * scalar</span>
-        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">*</span><span class="n">other</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">*</span><span class="n">other</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span></div>
 
-  <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__rmul__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__rmul__">[docs]</a>  <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Scalar multiplication, dot product (inner product) or</span>
-<span class="sd">    matrix-vector multiplication.</span>
+<span class="sd">    matrix-vector multiplication. (new object)</span>
-
-<span class="sd">    a * b (new object)</span>
 
 <span class="sd">    :type other: scalar (or 1d list and 2d list)</span>
 
@@ -233,32 +242,32 @@
 <span class="sd">      \mathbf{c} &amp;= \mathbf{A} \cdot \mathbf{b}</span>
 
 <span class="sd">    .. note::</span>
-<span class="sd">      No size checking will be conducted, therefore no exceptions for</span>
+<span class="sd">      No size checking will be conducted, therefore no exceptions</span>
-<span class="sd">      wrong usage (result will be nonsense).</span>
+<span class="sd">      for wrong usage (result will be nonsense).</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; v = 3*vector([1,2,3,4,5])</span>
+<span class="sd">    &gt;&gt;&gt; v = 3 * vector([1, 2, 3, 4, 5])</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [3, 6, 9, 12, 15]</span>
-<span class="sd">    &gt;&gt;&gt; v = 3.*vector([1,2,3,4,5])</span>
+<span class="sd">    &gt;&gt;&gt; v = 3. * vector([1, 2, 3, 4, 5])</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [3.0, 6.0, 9.0, 12.0, 15.0]</span>
 
 <span class="sd">    .. seealso::</span>
-<span class="sd">      :meth:`__mul__`</span>
+<span class="sd">      :meth:`__mul__` and :meth:`matrix.__mul__` for matrix * vector</span>
-<span class="sd">      :meth:`matrix.__mul__` for matrix * vector</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">try</span><span class="p">:</span>     <span class="c1"># 2d list * vector (matrix * vector see matrix.__mul__)</span>
-      <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="bp">self</span><span class="p">))</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="n">other</span><span class="p">])</span>
+      <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="bp">self</span><span class="p">))</span> <span class="k">for</span>
+                     <span class="n">a_row</span> <span class="ow">in</span> <span class="n">other</span><span class="p">])</span>
     <span class="k">except</span><span class="p">:</span>  <span class="c1"># scalar * vector</span>
-      <span class="k">return</span> <span class="bp">self</span><span class="o">*</span><span class="n">other</span>
+      <span class="k">return</span> <span class="bp">self</span><span class="o">*</span><span class="n">other</span></div>
 
-  <span class="k">def</span> <span class="fm">__matmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__matmul__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__matmul__">[docs]</a>  <span class="k">def</span> <span class="fm">__matmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Outer product a @ b (new object)</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      \vec{a} \otimes \vec{b}</span>
+<span class="sd">      \mathbf{c} = \mathbf{a} \otimes \mathbf{b}</span>
 <span class="sd">      =</span>
 <span class="sd">      \begin{pmatrix}</span>
 <span class="sd">        a_{1}\\</span>
@@ -281,35 +290,98 @@
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; m = vector([1,2,3]) @ vector([1,2,4])</span>
+<span class="sd">    &gt;&gt;&gt; m = vector([1, 2, 3]) @ vector([1, 2, 4])</span>
 <span class="sd">    &gt;&gt;&gt; print(m)</span>
 <span class="sd">    [[1, 2, 4], [2, 4, 8], [3, 6, 12]]</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">try</span><span class="p">:</span>     <span class="c1"># vector * vector</span>
       <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="n">i</span><span class="o">*</span><span class="n">j</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">other</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
     <span class="k">except</span><span class="p">:</span>  <span class="c1"># vector * number</span>
-      <span class="k">return</span> <span class="bp">self</span><span class="o">*</span><span class="n">other</span>
+      <span class="k">return</span> <span class="bp">self</span><span class="o">*</span><span class="n">other</span></div>
 
-  <span class="k">def</span> <span class="fm">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__abs__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__abs__">[docs]</a>  <span class="k">def</span> <span class="fm">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Magnitude / norm of a vector</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      b = \sqrt{\sum a_i^2}</span>
+<span class="sd">      b = |\mathbf{a}| = \sqrt{\sum a_i^2} =</span>
+<span class="sd">      \sqrt{\mathbf{a} \cdot \mathbf{a}}</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; norm([3, 4])</span>
+<span class="sd">    &gt;&gt;&gt; v = vector([3, 4])</span>
-<span class="sd">    5</span>
+<span class="sd">    &gt;&gt;&gt; abs(v)</span>
-<span class="sd">    &gt;&gt;&gt; norm(vector([3, 4]))</span>
+<span class="sd">    5.0</span>
-<span class="sd">    5</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span> <span class="o">*</span> <span class="bp">self</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span> <span class="o">*</span> <span class="bp">self</span><span class="p">)</span></div>
 
-  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="vector.__lt__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__lt__">[docs]</a>  <span class="k">def</span> <span class="fm">__lt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">str</span><span class="p">([</span><span class="o">*</span><span class="bp">self</span><span class="p">])</span>
+    <span class="sd">&quot;&quot;&quot;Test if this object is lower (smaller) than the other object.</span>
 
-  <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="sd">    .. math::</span>
-    <span class="k">return</span> <span class="s2">&quot;vector(&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;)&quot;</span>
+<span class="sd">      |\mathbf{a}| \lt |\mathbf{b}|</span>
+
+<span class="sd">    :Example:</span>
+
+<span class="sd">    &gt;&gt;&gt; vector([3, 2, 1]) &lt; vector([1, 2, 3])</span>
+<span class="sd">    False</span>
+<span class="sd">    &gt;&gt;&gt; vector([3, 2, 1]) &lt; vector([1, 2, 4])</span>
+<span class="sd">    True</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">&lt;</span> <span class="nb">abs</span><span class="p">(</span><span class="n">other</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="vector.__le__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__le__">[docs]</a>  <span class="k">def</span> <span class="fm">__le__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Test if this object is lower (smaller) than or equal the</span>
+<span class="sd">    other object.</span>
+
+<span class="sd">    .. math::</span>
+<span class="sd">      |\mathbf{a}| \le |\mathbf{b}|</span>
+
+<span class="sd">    :Example:</span>
+
+<span class="sd">    &gt;&gt;&gt; vector([3, 2, 1]) &lt;= vector([1, 2, 3])</span>
+<span class="sd">    True</span>
+<span class="sd">    &gt;&gt;&gt; vector([3, 2, 1]) &lt;= vector([1, 2, 2])</span>
+<span class="sd">    False</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">other</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="vector.__gt__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__gt__">[docs]</a>  <span class="k">def</span> <span class="fm">__gt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Test if this object is greater (larger) than the other</span>
+<span class="sd">    object.</span>
+
+<span class="sd">    .. math::</span>
+<span class="sd">      |\mathbf{a}| \gt |\mathbf{b}|</span>
+
+<span class="sd">    :Example:</span>
+
+<span class="sd">    &gt;&gt;&gt; vector([1, 2, 3]) &gt; vector([3, 2, 1])</span>
+<span class="sd">    False</span>
+<span class="sd">    &gt;&gt;&gt; vector([1, 2, 3]) &gt; vector([2, 2, 1])</span>
+<span class="sd">    True</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">&gt;</span> <span class="nb">abs</span><span class="p">(</span><span class="n">other</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="vector.__ge__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__ge__">[docs]</a>  <span class="k">def</span> <span class="fm">__ge__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Test if this object is greater (larger) than or equal the</span>
+<span class="sd">    other object.</span>
+
+<span class="sd">    .. math::</span>
+<span class="sd">      |\mathbf{a}| \ge |\mathbf{b}|</span>
+
+<span class="sd">    :Example:</span>
+
+<span class="sd">    &gt;&gt;&gt; vector([1, 2, 3]) &gt;= vector([3, 2, 1])</span>
+<span class="sd">    True</span>
+<span class="sd">    &gt;&gt;&gt; vector([1, 2, 3]) &gt;= vector([4, 2, 1])</span>
+<span class="sd">    False</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">other</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="vector.__str__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__str__">[docs]</a>  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">return</span> <span class="nb">str</span><span class="p">([</span><span class="o">*</span><span class="bp">self</span><span class="p">])</span></div>
+
+<div class="viewcode-block" id="vector.__repr__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.__repr__">[docs]</a>  <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">return</span> <span class="s2">&quot;vector(&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;)&quot;</span></div>
 
 <div class="viewcode-block" id="vector.full"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.full">[docs]</a>  <span class="nd">@staticmethod</span>
   <span class="k">def</span> <span class="nf">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="n">fill_value</span><span class="p">):</span>
@@ -363,8 +435,8 @@
 
 <div class="viewcode-block" id="vector.random"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.random">[docs]</a>  <span class="nd">@staticmethod</span>
   <span class="k">def</span> <span class="nf">random</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="n">lmin</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">lmax</span><span class="o">=</span><span class="mf">1.0</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;Returns a random vector of length n or matrix of size m rows, n</span>
+    <span class="sd">&quot;&quot;&quot;Returns a random vector of length n or matrix of size m rows,</span>
-<span class="sd">    columns filled with random numbers.</span>
+<span class="sd">    n columns filled with random numbers.</span>
 
 <span class="sd">    :Example:</span>
 
@@ -386,10 +458,10 @@
 <span class="sd">    :type a: vector</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      \vec{e}_a = \frac{\vec{a}}{|\vec{a}|}</span>
+<span class="sd">      \mathbf{\hat{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}</span>
 
 <span class="sd">    .. seealso::</span>
-<span class="sd">      :meth:`norm` for a norm (magnitude) of a vector</span>
+<span class="sd">      :meth:`__abs__` for a norm (magnitude) of a vector</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="n">a_mag</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
     <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">/</span><span class="n">a_mag</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
@@ -450,15 +522,12 @@
 <span class="sd">    The direction of c can be found with the right-hand rule.</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      \vec{c} = \vec{a} \times \vec{b}</span>
+<span class="sd">      \mathbf{c} = \mathbf{a} \times \mathbf{b}</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">return</span> <span class="p">[</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
             <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span>
             <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span></div>
 
-<div class="viewcode-block" id="vector.xyz"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.xyz">[docs]</a>  <span class="k">def</span> <span class="nf">xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="bp">self</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span></div>
-
 <div class="viewcode-block" id="vector.rotate_x"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.rotate_x">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Rotation about the x dirction.</span>
 
@@ -528,10 +597,10 @@
 
 <span class="sd">    uniform scaling if sx=sy=sz=s.</span>
 <span class="sd">    Note that scaling happens around the origin, so objects not</span>
-<span class="sd">    centered at the origin will have their centers move. To avoid this,</span>
+<span class="sd">    centered at the origin will have their centers move. To avoid</span>
-<span class="sd">    either scale the object when it&#39;s located at the origin, or</span>
+<span class="sd">    this, either scale the object when it&#39;s located at the origin,</span>
-<span class="sd">    perform a translation afterwards to move the object back to where</span>
+<span class="sd">    or perform a translation afterwards to move the object back to</span>
-<span class="sd">    it should be.</span>
+<span class="sd">    where it should be.</span>
 
 <span class="sd">    .. math::</span>
 <span class="sd">      \begin{bmatrix}x&#39; \\ y&#39; \\ z&#39; \\ h&#39;\end{bmatrix} =</span>
@@ -543,16 +612,17 @@
 <span class="sd">      \end{bmatrix}</span>
 <span class="sd">      \begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">sy</span><span class="p">:</span>
+    <span class="c1"># if not sy is not suitable because 0 is also false</span>
+    <span class="k">if</span> <span class="n">sy</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
       <span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
       <span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
     <span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">s</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
     <span class="k">return</span> <span class="bp">self</span></div>
 
 <div class="viewcode-block" id="vector.ch_cs"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.ch_cs">[docs]</a>  <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
-    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Transform this vector from its defined coordinate system to a</span>
+    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Transform this vector from its defined coordinate system to</span>
-<span class="sd">    new coordinate system, defined by the given coordinate system (u,</span>
+<span class="sd">    a new coordinate system, defined by the given coordinate system</span>
-<span class="sd">    v and w direction vectors).</span>
+<span class="sd">    (u, v and w direction vectors).</span>
 
 <span class="sd">    .. math::</span>
 <span class="sd">      \begin{bmatrix}x&#39; \\ y&#39; \\ z&#39; \\ h&#39;\end{bmatrix} =</span>
@@ -571,30 +641,32 @@
   <span class="sd">&quot;&quot;&quot;Use/create matrix like list of lists</span>
 <span class="sd">  &quot;&quot;&quot;</span>
 
-  <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">):</span>
+<div class="viewcode-block" id="matrix.__getitem__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.__getitem__">[docs]</a>  <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    For index return value, for range return new vector object.</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], [0, 0, 0, 0]])</span>
+<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], \</span>
+<span class="sd">                    [0, 0, 0, 0]])</span>
 <span class="sd">    &gt;&gt;&gt; print(m[2])</span>
 <span class="sd">    [7, 8, 9, 0]</span>
-<span class="sd">    &gt;&gt;&gt; print(m[:,1:3])</span>
+<span class="sd">    &gt;&gt;&gt; print(m[:, 1:3])</span>
 <span class="sd">    [[2, 3], [5, 6], [8, 9], [0, 0]]</span>
-<span class="sd">    &gt;&gt;&gt; print(m[0:2,1:3])</span>
+<span class="sd">    &gt;&gt;&gt; print(m[0:2, 1:3])</span>
 <span class="sd">    [[2, 3], [5, 6]]</span>
-<span class="sd">    &gt;&gt;&gt; print(m[::2,::2])</span>
+<span class="sd">    &gt;&gt;&gt; print(m[::2, ::2])</span>
 <span class="sd">    [[1, 3], [7, 9]]</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="c1"># index: slice(stop), slice(start, stop[, step])</span>
-    <span class="c1"># for e. g. m[(1,3),:] -&gt; index = ((1, 3), slice(None, None, None))</span>
+    <span class="c1"># for m[(1,3),:] -&gt; index = ((1, 3), slice(None, None, None))</span>
     <span class="c1"># use the list.__getslice__ method and convert result to vector</span>
     <span class="k">try</span><span class="p">:</span>    <span class="c1"># 2d slicing (tuple of sclices)</span>
-      <span class="n">item</span> <span class="o">=</span> <span class="p">[</span><span class="n">row</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">[</span><span class="mi">0</span><span class="p">])]</span>
+      <span class="n">item</span> <span class="o">=</span> <span class="p">[</span><span class="n">row</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="k">for</span>
+              <span class="n">row</span> <span class="ow">in</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">[</span><span class="mi">0</span><span class="p">])]</span>
     <span class="k">except</span><span class="p">:</span> <span class="c1"># 1d slicing</span>
       <span class="n">item</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">matrix</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="k">else</span> <span class="n">item</span>
+    <span class="k">return</span> <span class="n">matrix</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="k">else</span> <span class="n">item</span></div>
 
 <div class="viewcode-block" id="matrix.rx"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rx">[docs]</a>  <span class="nd">@staticmethod</span>
   <span class="k">def</span> <span class="nf">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
@@ -603,7 +675,7 @@
 <span class="sd">    Rotates the coordinate system of vectors</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      R_{x}(\theta) =</span>
+<span class="sd">      \mathbf{R}_{x}(\theta) =</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        1 &amp; 0 &amp; 0 &amp; 0 \\</span>
 <span class="sd">        0 &amp; \cos \theta &amp; -\sin \theta &amp; 0 \\</span>
@@ -626,7 +698,7 @@
 <span class="sd">    Rotates the coordinate system of vectors</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      R_{y}(\theta) =</span>
+<span class="sd">      \mathbf{R}_{y}(\theta) =</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        \cos \theta &amp; 0 &amp; \sin \theta &amp; 0 \\</span>
 <span class="sd">        0 &amp; 1 &amp; 0 &amp; 0 \\</span>
@@ -649,7 +721,7 @@
 <span class="sd">    Rotates the coordinate system of vectors</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      R_{z}(\theta) =</span>
+<span class="sd">      \mathbf{R}_{z}(\theta) =</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        \cos \theta &amp; -\sin \theta &amp; 0 &amp; 0 \\</span>
 <span class="sd">        \sin \theta &amp; \cos \theta &amp; 0 &amp; 0 \\</span>
@@ -660,14 +732,17 @@
 <span class="sd">    :Example:</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      R_{z}(\theta) \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =</span>
+<span class="sd">      \mathbf{R}_{z}(\theta)</span>
+<span class="sd">      \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix}</span>
+<span class="sd">      &amp;=</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        \cos 90° &amp; -\sin 90° &amp; 0 &amp; 0 \\</span>
 <span class="sd">        \sin 90° &amp; \cos 90° &amp; 0 &amp; 0 \\</span>
 <span class="sd">        0 &amp; 0 &amp; 1 &amp; 0 \\</span>
 <span class="sd">        0 &amp; 0 &amp; 0 &amp; 1</span>
 <span class="sd">      \end{bmatrix}</span>
-<span class="sd">      \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =</span>
+<span class="sd">      \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} \\</span>
+<span class="sd">      &amp;=</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        0 &amp; -1 &amp; 0 &amp; 0 \\</span>
 <span class="sd">        1 &amp; 0 &amp; 0 &amp; 0 \\</span>
@@ -690,7 +765,7 @@
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Translation matrix</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      T =</span>
+<span class="sd">      \mathbf{T} =</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        1 &amp; 0 &amp; 0 &amp; t_x \\</span>
 <span class="sd">        0 &amp; 1 &amp; 0 &amp; t_y \\</span>
@@ -710,13 +785,13 @@
 
 <span class="sd">    uniform scaling if sx=sy=sz=s.</span>
 <span class="sd">    Note that scaling happens around the origin, so objects not</span>
-<span class="sd">    centered at the origin will have their centers move. To avoid this,</span>
+<span class="sd">    centered at the origin will have their centers move. To avoid</span>
-<span class="sd">    either scale the object when it&#39;s located at the origin, or</span>
+<span class="sd">    this, either scale the object when it&#39;s located at the origin,</span>
-<span class="sd">    perform a translation afterwards to move the object back to where</span>
+<span class="sd">    or perform a translation afterwards to move the object back to</span>
-<span class="sd">    it should be.</span>
+<span class="sd">    where it should be.</span>
 
 <span class="sd">    .. math::</span>
-<span class="sd">      S =</span>
+<span class="sd">      \mathbf{S} =</span>
 <span class="sd">      \begin{bmatrix}</span>
 <span class="sd">        s_x &amp; 0 &amp; 0 &amp; 0 \\</span>
 <span class="sd">        0 &amp; s_y &amp; 0 &amp; 0 \\</span>
@@ -724,7 +799,8 @@
 <span class="sd">        0 &amp; 0 &amp; 0 &amp; 1</span>
 <span class="sd">      \end{bmatrix}</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">sy</span><span class="p">:</span>
+    <span class="c1"># if not sy is not suitable because 0 is also false</span>
+    <span class="k">if</span> <span class="n">sy</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
       <span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
       <span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
     <span class="n">T</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">([[</span><span class="n">sx</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
@@ -733,11 +809,9 @@
                 <span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
     <span class="k">return</span> <span class="n">T</span></div>
 
-  <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="matrix.__mul__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.__mul__">[docs]</a>  <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Scalar multiplication, dot product (inner product) or</span>
-<span class="sd">    matrix-vector multiplication.</span>
+<span class="sd">    matrix-vector multiplication. (new object)</span>
-
-<span class="sd">    a * b (new object)</span>
 
 <span class="sd">    :type other: scalar, vector (or 1d list), matrix (or 2d list)</span>
 
@@ -747,21 +821,25 @@
 <span class="sd">      \mathbf{C} &amp;= \mathbf{A} \cdot \mathbf{B}</span>
 
 <span class="sd">    .. note::</span>
-<span class="sd">      No size checking will be conducted, therefore no exceptions for</span>
+<span class="sd">      No size checking will be conducted, therefore no exceptions</span>
-<span class="sd">      wrong usage (result will be nonsense).</span>
+<span class="sd">      for wrong usage (result will be nonsense).</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5</span>
+<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], \</span>
+<span class="sd">                    [0, 0, 0, 1]]) * 5</span>
 <span class="sd">    &gt;&gt;&gt; print(m)</span>
 <span class="sd">    [[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]</span>
-<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5.</span>
+<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], \</span>
+<span class="sd">                    [0, 0, 0, 1]]) * 5.</span>
 <span class="sd">    &gt;&gt;&gt; print(m)</span>
 <span class="sd">    [[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]</span>
-<span class="sd">    &gt;&gt;&gt; v = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * vector([12, 12, 13])</span>
+<span class="sd">    &gt;&gt;&gt; v = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * \</span>
+<span class="sd">        vector([12, 12, 13])</span>
 <span class="sd">    &gt;&gt;&gt; print(v)</span>
 <span class="sd">    [75, 186, 297]</span>
-<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])</span>
+<span class="sd">    &gt;&gt;&gt; m = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * \</span>
+<span class="sd">        matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])</span>
 <span class="sd">    &gt;&gt;&gt; print(m)</span>
 <span class="sd">    [[91, 96, 102], [220, 231, 246], [349, 366, 390]]</span>
 
@@ -769,18 +847,18 @@
 <span class="sd">      :meth:`__rmul__`</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">try</span><span class="p">:</span>       <span class="c1"># matrix * matrix</span>
-      <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span> <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">other</span><span class="p">)]</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
+      <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span>
+                      <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">other</span><span class="p">)]</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
     <span class="k">except</span><span class="p">:</span>
       <span class="k">try</span><span class="p">:</span>     <span class="c1"># matrix * vector</span>
-        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="n">other</span><span class="p">))</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="n">other</span><span class="p">))</span> <span class="k">for</span>
+                       <span class="n">a_row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
       <span class="k">except</span><span class="p">:</span>  <span class="c1"># matrix * scalar</span>
-        <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="n">a</span><span class="o">*</span><span class="n">other</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">a_row</span><span class="p">]</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="n">a</span><span class="o">*</span><span class="n">other</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">a_row</span><span class="p">]</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span></div>
 
-  <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<div class="viewcode-block" id="matrix.__rmul__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.__rmul__">[docs]</a>  <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Scalar multiplication, dot product (inner product) or</span>
-<span class="sd">    vector-matrix multiplication.</span>
+<span class="sd">    vector-matrix multiplication. (new object)</span>
-
-<span class="sd">    a * b (new object)</span>
 
 <span class="sd">    :type other: scalar (or 1d list and 2d list)</span>
 
@@ -790,35 +868,38 @@
 <span class="sd">      \mathbf{C} &amp;= \mathbf{A} \cdot \mathbf{B}</span>
 
 <span class="sd">    .. note::</span>
-<span class="sd">      No size checking will be conducted, therefore no exceptions for</span>
+<span class="sd">      No size checking will be conducted, therefore no exceptions</span>
-<span class="sd">      wrong usage (result will be nonsense).</span>
+<span class="sd">      for wrong usage (result will be nonsense).</span>
 
 <span class="sd">    :Example:</span>
 
-<span class="sd">    &gt;&gt;&gt; m = 5 * matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5</span>
+<span class="sd">    &gt;&gt;&gt; m = 5 * matrix([[1, 2, 3, 4], [5, 6, 7, 8], \</span>
+<span class="sd">                        [9, 10, 11, 12], [0, 0, 0, 1]])</span>
 <span class="sd">    &gt;&gt;&gt; print(m)</span>
 <span class="sd">    [[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]</span>
-<span class="sd">    &gt;&gt;&gt; m = 5. * matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]])</span>
+<span class="sd">    &gt;&gt;&gt; m = 5. * matrix([[1, 2, 3, 4], [5, 6, 7, 8], \</span>
+<span class="sd">                         [9, 10, 11, 12], [0, 0, 0, 1]])</span>
 <span class="sd">    &gt;&gt;&gt; print(m)</span>
 <span class="sd">    [[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]</span>
 
 <span class="sd">    .. seealso::</span>
-<span class="sd">      :meth:`__mul__`</span>
+<span class="sd">      :meth:`__mul__` and :meth:`vector.__mul__` for vector * matrix</span>
-<span class="sd">      :meth:`vector.__mul__` for vector * matrix</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">try</span><span class="p">:</span>       <span class="c1"># 2d list * matrix (matrix * matrix see matrix.__mul__)</span>
-      <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span> <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="bp">self</span><span class="p">)]</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="n">other</span><span class="p">])</span>
+      <span class="k">return</span> <span class="n">matrix</span><span class="p">([[</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">a_row</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span>
+                      <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="bp">self</span><span class="p">)]</span> <span class="k">for</span> <span class="n">a_row</span> <span class="ow">in</span> <span class="n">other</span><span class="p">])</span>
     <span class="k">except</span><span class="p">:</span>
       <span class="k">try</span><span class="p">:</span>     <span class="c1"># 1d list * matrix (vector * matrix see vector.__mul__)</span>
-        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span> <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="bp">self</span><span class="p">)])</span>
+        <span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">sum</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">d</span> <span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">b_col</span><span class="p">))</span> <span class="k">for</span>
+                       <span class="n">b_col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="bp">self</span><span class="p">)])</span>
       <span class="k">except</span><span class="p">:</span>  <span class="c1"># scalar * vector</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">*</span><span class="n">other</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">*</span><span class="n">other</span></div>
 
-  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="matrix.__str__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.__str__">[docs]</a>  <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">str</span><span class="p">([</span><span class="o">*</span><span class="bp">self</span><span class="p">])</span>
+    <span class="k">return</span> <span class="nb">str</span><span class="p">([</span><span class="o">*</span><span class="bp">self</span><span class="p">])</span></div>
 
-  <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="matrix.__repr__"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.__repr__">[docs]</a>  <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-    <span class="k">return</span> <span class="s2">&quot;matrix(&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;)&quot;</span>
+    <span class="k">return</span> <span class="s2">&quot;matrix(&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;)&quot;</span></div>
 
 <div class="viewcode-block" id="matrix.rotate_x"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rotate_x">[docs]</a>  <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
     <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Rotation about the x dirction.</span>
@@ -929,10 +1010,10 @@
 
 <span class="sd">    uniform scaling if sx=sy=sz=s.</span>
 <span class="sd">    Note that scaling happens around the origin, so objects not</span>
-<span class="sd">    centered at the origin will have their centers move. To avoid this,</span>
+<span class="sd">    centered at the origin will have their centers move. To avoid</span>
-<span class="sd">    either scale the object when it&#39;s located at the origin, or</span>
+<span class="sd">    this, either scale the object when it&#39;s located at the origin,</span>
-<span class="sd">    perform a translation afterwards to move the object back to where</span>
+<span class="sd">    or perform a translation afterwards to move the object back to</span>
-<span class="sd">    it should be.</span>
+<span class="sd">    where it should be.</span>
 
 <span class="sd">    .. math::</span>
 <span class="sd">      \begin{bmatrix}</span>
@@ -954,7 +1035,8 @@
 <span class="sd">        0 &amp; 0 &amp; 0 &amp; h</span>
 <span class="sd">      \end{bmatrix}</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">sy</span><span class="p">:</span>
+    <span class="c1"># if not sy is not suitable because 0 is also false</span>
+    <span class="k">if</span> <span class="n">sy</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
       <span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
       <span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
     <span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">s</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>

docs/build/html/_sources/pylib.geometry_plot.rst.txt

@@ -0,0 +1,7 @@
+pylib.geometry\_plot module
+===========================
+
+.. automodule:: pylib.geometry_plot
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/build/html/_sources/pylib.geometry_plot_pylab.rst.txt

@@ -0,0 +1,7 @@
+pylib.geometry\_plot\_pylab module
+==================================
+
+.. automodule:: pylib.geometry_plot_pylab
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/build/html/_sources/pylib.rst.txt

@@ -25,5 +25,7 @@ Submodules
    pylib.geometry
    pylib.geometry2d
    pylib.geometry2d_plot
+   pylib.geometry_plot
+   pylib.geometry_plot_pylab
    pylib.mathematics
    pylib.time_of_day

docs/build/html/_static/alabaster.css

@@ -295,8 +295,8 @@ div.important {
 }
 
 div.note {
-    background-color: #EEE;
+    background-color: #25272c;
-    border: 1px solid #CCC;
+    border: 1px solid #2C2C2C;
 }
 
 div.tip {

docs/build/html/_static/custom.css

@@ -7,7 +7,7 @@ table.indextable tr.cap {
 }
 /* move doc link a bit up */
 .viewcode-back {
-    float: right;
+  float: right;
-    position: relative;
+  position: relative;
-    top: -1.5em;
+  top: -1.5em;
 }

docs/build/html/genindex.html

@@ -37,7 +37,8 @@
 <h1 id="index">Index</h1>
 
 <div class="genindex-jumpbox">
- <a href="#A"><strong>A</strong></a>
+ <a href="#_"><strong>_</strong></a>
+ | <a href="#A"><strong>A</strong></a>
  | <a href="#B"><strong>B</strong></a>
  | <a href="#C"><strong>C</strong></a>
  | <a href="#D"><strong>D</strong></a>
@@ -62,6 +63,74 @@
  | <a href="#Z"><strong>Z</strong></a>
  
 </div>
+<h2 id="_">_</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__abs__">__abs__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__add__">__add__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__ge__">__ge__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.__getitem__">__getitem__() (matrix method)</a>
+
+      <ul>
+        <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__getitem__">(vector method)</a>
+</li>
+      </ul></li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__gt__">__gt__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__iadd__">__iadd__() (vector method)</a>
+</li>
+      <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.__iter__">__iter__() (Wireframe method)</a>
+
+      <ul>
+        <li><a href="pylib.geometry.html#pylib.geometry.World.__iter__">(World method)</a>
+</li>
+      </ul></li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__le__">__le__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__lt__">__lt__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__matmul__">__matmul__() (vector method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.__mul__">__mul__() (matrix method)</a>
+
+      <ul>
+        <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__mul__">(vector method)</a>
+</li>
+      </ul></li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__neg__">__neg__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__pos__">__pos__() (vector method)</a>
+</li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.__repr__">__repr__() (matrix method)</a>
+
+      <ul>
+        <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__repr__">(vector method)</a>
+</li>
+      </ul></li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.__rmul__">__rmul__() (matrix method)</a>
+
+      <ul>
+        <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__rmul__">(vector method)</a>
+</li>
+      </ul></li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.__str__">__str__() (matrix method)</a>
+
+      <ul>
+        <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__str__">(vector method)</a>
+</li>
+        <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.__str__">(Wireframe method)</a>
+</li>
+      </ul></li>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.__sub__">__sub__() (vector method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
 <h2 id="A">A</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -93,22 +162,26 @@
 <h2 id="C">C</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.cad_wireframe">cad_wireframe() (in module pylib.geometry_plot_pylab)</a>
+</li>
       <li><a href="pylib.geometry.html#pylib.geometry.World.center">center() (World method)</a>
 </li>
-      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.ch_cs">ch_cs() (vector method)</a>
+      <li><a href="pylib.geometry.html#pylib.geometry.Solid.ch_cs">ch_cs() (Solid method)</a>
 
       <ul>
+        <li><a href="pylib.mathematics.html#pylib.mathematics.vector.ch_cs">(vector method)</a>
+</li>
         <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.ch_cs">(Wireframe method)</a>
 </li>
         <li><a href="pylib.geometry.html#pylib.geometry.World.ch_cs">(World method)</a>
 </li>
       </ul></li>
       <li><a href="pylib.geometry.html#pylib.geometry.Circle">Circle (class in pylib.geometry)</a>
-</li>
-      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.conjugate">conjugate() (vector static method)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.conjugate">conjugate() (vector static method)</a>
+</li>
       <li><a href="pylib.function.html#pylib.function.cosine_wave">cosine_wave() (in module pylib.function)</a>
 </li>
       <li><a href="pylib.mathematics.html#pylib.mathematics.vector.cross">cross() (vector static method)</a>
@@ -205,11 +278,15 @@
 </li>
       <li><a href="pylib.geometry.html#module-geometry">geometry (module)</a>
 </li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="pylib.geometry2d.html#module-geometry2d">geometry2d (module)</a>
 </li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="pylib.geometry2d_plot.html#module-geometry2d_plot">geometry2d_plot (module)</a>
+</li>
+      <li><a href="pylib.geometry_plot.html#module-geometry_plot">geometry_plot (module)</a>
+</li>
+      <li><a href="pylib.geometry_plot_pylab.html#module-geometry_plot_pylab">geometry_plot_pylab (module)</a>
 </li>
       <li><a href="pylib.geometry.html#pylib.geometry.CS.get_coordinates">get_coordinates() (CS method)</a>
 </li>
@@ -221,12 +298,14 @@
 <h2 id="H">H</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="pylib.drawblock.html#pylib.drawblock.histogram">histogram() (in module pylib.drawblock)</a>
+      <li><a href="pylib.geometry.html#pylib.geometry.Hexahedron">Hexahedron (class in pylib.geometry)</a>
 </li>
-      <li><a href="pylib.time_of_day.html#pylib.time_of_day.hours">hours() (in module pylib.time_of_day)</a>
+      <li><a href="pylib.drawblock.html#pylib.drawblock.histogram">histogram() (in module pylib.drawblock)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="pylib.time_of_day.html#pylib.time_of_day.hours">hours() (in module pylib.time_of_day)</a>
+</li>
       <li><a href="pylib.time_of_day.html#pylib.time_of_day.hours_norm">hours_norm() (in module pylib.time_of_day)</a>
 </li>
       <li><a href="pylib.function.html#pylib.function.hypotrochoid">hypotrochoid() (in module pylib.function)</a>
@@ -241,13 +320,15 @@
 </li>
       <li><a href="pylib.mathematics.html#pylib.mathematics.vector.im">im() (vector static method)</a>
 </li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="pylib.time_of_day.html#pylib.time_of_day.in_seconds">in_seconds() (in module pylib.time_of_day)</a>
 </li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="pylib.numerical.integration.html#module-integration">integration (module)</a>
 </li>
       <li><a href="pylib.geometry2d.html#pylib.geometry2d.interpolate_hermite">interpolate_hermite() (in module pylib.geometry2d)</a>
+</li>
+      <li><a href="pylib.data.html#pylib.data.issequence">issequence() (in module pylib.data)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -324,12 +405,16 @@
       <li><a href="pylib.geometry2d_plot.html#pylib.geometry2d_plot.plot_cubic_lines">plot_cubic_lines() (in module pylib.geometry2d_plot)</a>
 </li>
       <li><a href="pylib.geometry2d_plot.html#pylib.geometry2d_plot.plot_lines">plot_lines() (in module pylib.geometry2d_plot)</a>
+</li>
+      <li><a href="pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.plot_post">plot_post() (in module pylib.geometry_plot_pylab)</a>
 </li>
       <li><a href="pylib.geometry.html#pylib.geometry.Point">Point (class in pylib.geometry)</a>
 </li>
       <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.points">points() (Wireframe method)</a>
 </li>
       <li><a href="pylib.geometry.html#pylib.geometry.Polygon">Polygon (class in pylib.geometry)</a>
+</li>
+      <li><a href="pylib.geometry.html#pylib.geometry.Point.projection">projection() (Point method)</a>
 </li>
       <li><a href="pylib.html#module-pylib">pylib (module)</a>
 </li>
@@ -348,6 +433,10 @@
       <li><a href="pylib.geometry2d.html#module-pylib.geometry2d">pylib.geometry2d (module)</a>
 </li>
       <li><a href="pylib.geometry2d_plot.html#module-pylib.geometry2d_plot">pylib.geometry2d_plot (module)</a>
+</li>
+      <li><a href="pylib.geometry_plot.html#module-pylib.geometry_plot">pylib.geometry_plot (module)</a>
+</li>
+      <li><a href="pylib.geometry_plot_pylab.html#module-pylib.geometry_plot_pylab">pylib.geometry_plot_pylab (module)</a>
 </li>
       <li><a href="pylib.mathematics.html#module-pylib.mathematics">pylib.mathematics (module)</a>
 </li>
@@ -432,6 +521,8 @@
       <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.scale">scale() (matrix method)</a>
 
       <ul>
+        <li><a href="pylib.geometry.html#pylib.geometry.Solid.scale">(Solid method)</a>
+</li>
         <li><a href="pylib.mathematics.html#pylib.mathematics.vector.scale">(vector method)</a>
 </li>
         <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.scale">(Wireframe method)</a>
@@ -446,8 +537,12 @@
       <li><a href="pylib.time_of_day.html#pylib.time_of_day.seconds_norm">seconds_norm() (in module pylib.time_of_day)</a>
 </li>
       <li><a href="pylib.data.html#pylib.data.seq">seq() (in module pylib.data)</a>
+</li>
+      <li><a href="pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.set_aspect_equal">set_aspect_equal() (in module pylib.geometry_plot_pylab)</a>
 </li>
       <li><a href="pylib.function.html#pylib.function.sine_wave">sine_wave() (in module pylib.function)</a>
+</li>
+      <li><a href="pylib.geometry.html#pylib.geometry.Solid">Solid (class in pylib.geometry)</a>
 </li>
       <li><a href="pylib.geometry.html#pylib.geometry.World.space_diagonal">space_diagonal() (World method)</a>
 </li>
@@ -475,6 +570,8 @@
 
       <ul>
         <li><a href="pylib.mathematics.html#pylib.mathematics.matrix.translate">(matrix method)</a>
+</li>
+        <li><a href="pylib.geometry.html#pylib.geometry.Solid.translate">(Solid method)</a>
 </li>
         <li><a href="pylib.mathematics.html#pylib.mathematics.vector.translate">(vector method)</a>
 </li>
@@ -513,8 +610,20 @@
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="pylib.geometry.html#pylib.geometry.Wireframe">Wireframe (class in pylib.geometry)</a>
 </li>
+      <li><a href="pylib.geometry_plot_pylab.html#pylib.geometry_plot_pylab.wireframe3d">wireframe3d() (in module pylib.geometry_plot_pylab)</a>
+</li>
+      <li><a href="pylib.geometry.html#pylib.geometry.Solid.wireframes">wireframes() (Solid method)</a>
+
+      <ul>
+        <li><a href="pylib.geometry.html#pylib.geometry.World.wireframes">(World method)</a>
+</li>
+      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="pylib.geometry.html#pylib.geometry.World.wireframes_xy">wireframes_xy() (World method)</a>
+</li>
+      <li><a href="pylib.geometry.html#pylib.geometry.World.wireframes_xyz">wireframes_xyz() (World method)</a>
+</li>
       <li><a href="pylib.geometry.html#pylib.geometry.World">World (class in pylib.geometry)</a>
 </li>
       <li><a href="pylib.data.html#pylib.data.write">write() (in module pylib.data)</a>
@@ -531,12 +640,10 @@
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="pylib.mathematics.html#pylib.mathematics.vector.xyz">xyz() (vector method)</a>
+      <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.xy">xy() (Wireframe method)</a>
-
+</li>
-      <ul>
+      <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.xyz">xyz() (Wireframe method)</a>
-        <li><a href="pylib.geometry.html#pylib.geometry.Wireframe.xyz">(Wireframe method)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 

docs/build/html/modules.html

@@ -51,9 +51,14 @@
 <li class="toctree-l3"><a class="reference internal" href="pylib.date.html">pylib.date module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="pylib.drawblock.html">pylib.drawblock module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="pylib.function.html">pylib.function module</a></li>
-<li class="toctree-l3"><a class="reference internal" href="pylib.geometry.html">pylib.geometry module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="pylib.geometry.html">pylib.geometry module</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="pylib.geometry.html#affine-transforms">Affine transforms</a></li>
+</ul>
+</li>
 <li class="toctree-l3"><a class="reference internal" href="pylib.geometry2d.html">pylib.geometry2d module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="pylib.geometry2d_plot.html">pylib.geometry2d_plot module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="pylib.geometry_plot.html">pylib.geometry_plot module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="pylib.geometry_plot_pylab.html">pylib.geometry_plot_pylab module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="pylib.mathematics.html">pylib.mathematics module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="pylib.time_of_day.html">pylib.time_of_day module</a></li>
 </ul>

docs/build/html/py-modindex.html

@@ -99,6 +99,16 @@
        <td>
        <a href="pylib.geometry2d_plot.html#module-geometry2d_plot"><code class="xref">geometry2d_plot</code></a> <em>(*nix, Windows)</em></td><td>
        <em>2D geometry plotting.</em></td></tr>
+     <tr>
+       <td></td>
+       <td>
+       <a href="pylib.geometry_plot.html#module-geometry_plot"><code class="xref">geometry_plot</code></a> <em>(*nix, Windows)</em></td><td>
+       <em>Geometry plotting.</em></td></tr>
+     <tr>
+       <td></td>
+       <td>
+       <a href="pylib.geometry_plot_pylab.html#module-geometry_plot_pylab"><code class="xref">geometry_plot_pylab</code></a> <em>(*nix, Windows)</em></td><td>
+       <em>Geometry plotting (pylab).</em></td></tr>
      <tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
      <tr class="cap" id="cap-i"><td></td><td>
        <strong>i</strong></td><td></td></tr>
@@ -172,6 +182,16 @@
        <td>&#160;&#160;&#160;
        <a href="pylib.geometry2d_plot.html#module-pylib.geometry2d_plot"><code class="xref">pylib.geometry2d_plot</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="pylib.geometry_plot.html#module-pylib.geometry_plot"><code class="xref">pylib.geometry_plot</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="pylib.geometry_plot_pylab.html#module-pylib.geometry_plot_pylab"><code class="xref">pylib.geometry_plot_pylab</code></a></td><td>
+       <em></em></td></tr>
      <tr class="cg-1">
        <td></td>
        <td>&#160;&#160;&#160;

docs/build/html/pylib.data.html

@@ -83,6 +83,39 @@ array. m = k / n</p>
 </dl>
 </dd></dl>
 
+<dl class="function">
+<dt id="pylib.data.issequence">
+<code class="sig-name descname">issequence</code><span class="sig-paren">(</span><em class="sig-param">obj</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#issequence"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.issequence" title="Permalink to this definition">¶</a></dt>
+<dd><p>True for tuple, list, str
+False for int, dict, set</p>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">(())</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="p">))</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">([])</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">([</span><span class="mi">1</span><span class="p">])</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
+<span class="go">True</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">((</span><span class="mi">3</span><span class="p">))</span>
+<span class="go">False</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">({})</span>
+<span class="go">False</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">issequence</span><span class="p">(</span><span class="nb">set</span><span class="p">())</span>
+<span class="go">False</span>
+</pre></div>
+</div>
+</dd></dl>
+
 <dl class="function">
 <dt id="pylib.data.load">
 <code class="sig-name descname">load</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">default=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#load"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.load" title="Permalink to this definition">¶</a></dt>

docs/build/html/pylib.function.html

@@ -172,7 +172,7 @@ y(\theta) = (R - r)\sin\theta - d\sin\left(\frac{R-r}{r}\theta\right) \\
 </div>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
-<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">mathematics.lcm()</span></code></p>
+<p><a class="reference internal" href="pylib.mathematics.html#pylib.mathematics.lcm" title="pylib.mathematics.lcm"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pylib.mathematics.lcm()</span></code></a></p>
 </div>
 </dd></dl>
 
@@ -359,7 +359,7 @@ Example of 3 columns and 3 rows (upside down view of ‘normal’ braille/drawil
 </dl>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pylib.function.transformation" title="pylib.function.transformation"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pylib.function.transformation()</span></code></a></p>
+<p><a class="reference internal" href="#pylib.function.transformation" title="pylib.function.transformation"><code class="xref py py-meth docutils literal notranslate"><span class="pre">transformation()</span></code></a></p>
 </div>
 </dd></dl>
 

docs/build/html/pylib.geometry.html

@@ -36,16 +36,23 @@
             
   <div class="section" id="module-pylib.geometry">
 <span id="pylib-geometry-module"></span><h1>pylib.geometry module<a class="headerlink" href="#module-pylib.geometry" title="Permalink to this headline">¶</a></h1>
-<p>2D geometry objects.</p>
+<p>Geometry objects.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Date</dt>
 <dd class="field-odd"><p>2019-12-21</p>
 </dd>
 </dl>
-<span class="target" id="module-geometry"></span><dl class="class">
+<span class="target" id="module-geometry"></span><div class="section" id="affine-transforms">
+<h2>Affine transforms<a class="headerlink" href="#affine-transforms" title="Permalink to this headline">¶</a></h2>
+<p>Functions in augmented space, in homogenous coordinates.
+Points are augment to 4 dimensions, by adding a dummy coordinate.
+For points the dummy coordinate is always normalized to 1.
+With homogenous coordinates translation of points is repesentable
+as a linear transformation.</p>
+<dl class="class">
 <dt id="pylib.geometry.CS">
 <em class="property">class </em><code class="sig-name descname">CS</code><span class="sig-paren">(</span><em class="sig-param">x=[1, 0, 0], y=[0, 1, 0], z=[0, 0, 1]</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">mathematics.matrix</span></code></p>
+<dd><p>Bases: <a class="reference internal" href="pylib.mathematics.html#pylib.mathematics.matrix" title="pylib.mathematics.matrix"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.mathematics.matrix</span></code></a></p>
 <p>Coordinate system</p>
 <dl class="method">
 <dt id="pylib.geometry.CS.get_coordinates">
@@ -85,13 +92,20 @@
 <dl class="class">
 <dt id="pylib.geometry.Direction">
 <em class="property">class </em><code class="sig-name descname">Direction</code><span class="sig-paren">(</span><em class="sig-param">x=1</em>, <em class="sig-param">y=0</em>, <em class="sig-param">z=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Direction"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Direction" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">mathematics.vector</span></code></p>
+<dd><p>Bases: <a class="reference internal" href="pylib.mathematics.html#pylib.mathematics.vector" title="pylib.mathematics.vector"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.mathematics.vector</span></code></a></p>
 <p>Direction in local coordinate system</p>
 </dd></dl>
 
+<dl class="class">
+<dt id="pylib.geometry.Hexahedron">
+<em class="property">class </em><code class="sig-name descname">Hexahedron</code><span class="sig-paren">(</span><em class="sig-param">point1=vector([-1</em>, <em class="sig-param">-1</em>, <em class="sig-param">-1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point2=vector([1</em>, <em class="sig-param">-1</em>, <em class="sig-param">-1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point3=vector([1</em>, <em class="sig-param">1</em>, <em class="sig-param">-1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point4=vector([-1</em>, <em class="sig-param">1</em>, <em class="sig-param">-1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point5=vector([-1</em>, <em class="sig-param">-1</em>, <em class="sig-param">1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point6=vector([1</em>, <em class="sig-param">-1</em>, <em class="sig-param">1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point7=vector([1</em>, <em class="sig-param">1</em>, <em class="sig-param">1</em>, <em class="sig-param">1])</em>, <em class="sig-param">point8=vector([-1</em>, <em class="sig-param">1</em>, <em class="sig-param">1</em>, <em class="sig-param">1])</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Hexahedron"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Hexahedron" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pylib.geometry.Solid" title="pylib.geometry.Solid"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.geometry.Solid</span></code></a></p>
+<p>Line a open wireframe object in local coordinate system</p>
+</dd></dl>
+
 <dl class="class">
 <dt id="pylib.geometry.Line">
-<em class="property">class </em><code class="sig-name descname">Line</code><span class="sig-paren">(</span><em class="sig-param">point1=vector([-1</em>, <em class="sig-param">0</em>, <em class="sig-param">0])</em>, <em class="sig-param">point2=vector([1</em>, <em class="sig-param">0</em>, <em class="sig-param">0])</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Line"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Line" title="Permalink to this definition">¶</a></dt>
+<em class="property">class </em><code class="sig-name descname">Line</code><span class="sig-paren">(</span><em class="sig-param">point1=vector([-1</em>, <em class="sig-param">0</em>, <em class="sig-param">0</em>, <em class="sig-param">1])</em>, <em class="sig-param">point2=vector([1</em>, <em class="sig-param">0</em>, <em class="sig-param">0</em>, <em class="sig-param">1])</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Line"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Line" title="Permalink to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#pylib.geometry.Wireframe" title="pylib.geometry.Wireframe"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.geometry.Wireframe</span></code></a></p>
 <p>Line a open wireframe object in local coordinate system</p>
 </dd></dl>
@@ -99,8 +113,14 @@
 <dl class="class">
 <dt id="pylib.geometry.Point">
 <em class="property">class </em><code class="sig-name descname">Point</code><span class="sig-paren">(</span><em class="sig-param">x=0</em>, <em class="sig-param">y=0</em>, <em class="sig-param">z=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Point"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Point" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">mathematics.vector</span></code></p>
+<dd><p>Bases: <a class="reference internal" href="pylib.mathematics.html#pylib.mathematics.vector" title="pylib.mathematics.vector"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.mathematics.vector</span></code></a></p>
 <p>Point in local coordinate system</p>
+<dl class="method">
+<dt id="pylib.geometry.Point.projection">
+<code class="sig-name descname">projection</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Point.projection"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Point.projection" title="Permalink to this definition">¶</a></dt>
+<dd><p>Orthographic projection to the xy-plane</p>
+</dd></dl>
+
 </dd></dl>
 
 <dl class="class">
@@ -110,12 +130,53 @@
 <p>Polygon as closed wireframe object in local coordinate system</p>
 </dd></dl>
 
+<dl class="class">
+<dt id="pylib.geometry.Solid">
+<em class="property">class </em><code class="sig-name descname">Solid</code><span class="sig-paren">(</span><em class="sig-param">*wireframes</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Solid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Solid" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Solid object in local coordinate system</p>
+<p>This class lists Wireframe objects.
+The Wireframe class create its own points (copy).</p>
+<dl class="method">
+<dt id="pylib.geometry.Solid.ch_cs">
+<code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Solid.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Solid.ch_cs" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="pylib.geometry.Solid.scale">
+<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Solid.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Solid.scale" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="pylib.geometry.Solid.translate">
+<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Solid.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Solid.translate" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="pylib.geometry.Solid.wireframes">
+<code class="sig-name descname">wireframes</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Solid.wireframes"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Solid.wireframes" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
 <dl class="class">
 <dt id="pylib.geometry.Wireframe">
 <em class="property">class </em><code class="sig-name descname">Wireframe</code><span class="sig-paren">(</span><em class="sig-param">*points</em>, <em class="sig-param">closed=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe" title="Permalink to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
 <p>Open and closed wireframe object in local coordinate system</p>
 <p>This class create its own points (copy).</p>
+<dl class="method">
+<dt id="pylib.geometry.Wireframe.__iter__">
+<code class="sig-name descname">__iter__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.__iter__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.__iter__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Returns the Iterator object</p>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.geometry.Wireframe.__str__">
+<code class="sig-name descname">__str__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.__str__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.__str__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return str(self).</p>
+</dd></dl>
+
 <dl class="method">
 <dt id="pylib.geometry.Wireframe.ch_cs">
 <code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.ch_cs" title="Permalink to this definition">¶</a></dt>
@@ -152,10 +213,17 @@
 <code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.translate" title="Permalink to this definition">¶</a></dt>
 <dd></dd></dl>
 
+<dl class="method">
+<dt id="pylib.geometry.Wireframe.xy">
+<code class="sig-name descname">xy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.xy" title="Permalink to this definition">¶</a></dt>
+<dd><p>Get coordinates in 3d space</p>
+</dd></dl>
+
 <dl class="method">
 <dt id="pylib.geometry.Wireframe.xyz">
 <code class="sig-name descname">xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.xyz" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Get coordinates in 3d space</p>
+</dd></dl>
 
 </dd></dl>
 
@@ -164,6 +232,12 @@
 <em class="property">class </em><code class="sig-name descname">World</code><a class="reference internal" href="_modules/pylib/geometry.html#World"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World" title="Permalink to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
 <p>World-space with world-space coordinates</p>
+<dl class="method">
+<dt id="pylib.geometry.World.__iter__">
+<code class="sig-name descname">__iter__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.__iter__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.__iter__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Returns the Iterator object</p>
+</dd></dl>
+
 <dl class="method">
 <dt id="pylib.geometry.World.add">
 <code class="sig-name descname">add</code><span class="sig-paren">(</span><em class="sig-param">*objects</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.add"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.add" title="Permalink to this definition">¶</a></dt>
@@ -224,8 +298,24 @@
 <code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.translate" title="Permalink to this definition">¶</a></dt>
 <dd></dd></dl>
 
+<dl class="method">
+<dt id="pylib.geometry.World.wireframes">
+<code class="sig-name descname">wireframes</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.wireframes"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.wireframes" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="pylib.geometry.World.wireframes_xy">
+<code class="sig-name descname">wireframes_xy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.wireframes_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.wireframes_xy" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="pylib.geometry.World.wireframes_xyz">
+<code class="sig-name descname">wireframes_xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.wireframes_xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.wireframes_xyz" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
 </dd></dl>
 
+</div>
 </div>
 
 

docs/build/html/pylib.geometry2d.html

@@ -276,7 +276,7 @@ decides what the left and the right end point of the line is.</p></li>
 </dl>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
-<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">plot_lines()</span></code> of the <code class="xref py py-mod docutils literal notranslate"><span class="pre">geometry_plot</span></code>
+<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">plot_lines()</span></code> of the <a class="reference internal" href="pylib.geometry_plot.html#module-geometry_plot" title="geometry_plot: Geometry plotting. (*nix, Windows)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">geometry_plot</span></code></a>
 module to plot the lines</p>
 </div>
 </dd></dl>

docs/build/html/pylib.geometry2d_plot.html

@@ -16,7 +16,7 @@
     <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
-    <link rel="next" title="pylib.mathematics module" href="pylib.mathematics.html" />
+    <link rel="next" title="pylib.geometry_plot module" href="pylib.geometry_plot.html" />
     <link rel="prev" title="pylib.geometry2d module" href="pylib.geometry2d.html" />
    
   <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -86,7 +86,7 @@
   <li><a href="modules.html">pylib</a><ul>
   <li><a href="pylib.html">pylib package</a><ul>
       <li>Previous: <a href="pylib.geometry2d.html" title="previous chapter">pylib.geometry2d module</a></li>
-      <li>Next: <a href="pylib.mathematics.html" title="next chapter">pylib.mathematics module</a></li>
+      <li>Next: <a href="pylib.geometry_plot.html" title="next chapter">pylib.geometry_plot module</a></li>
   </ul></li>
   </ul></li>
   </ul></li>

docs/build/html/pylib.geometry_plot.html

@@ -0,0 +1,123 @@
+
+<!DOCTYPE html>
+
+<html xmlns="http://www.w3.org/1999/xhtml">
+  <head>
+    <meta charset="utf-8" />
+    <title>pylib.geometry_plot module &#8212; pylib 2019.12.21 documentation</title>
+    <link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
+    <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
+    <link rel="stylesheet" href="_static/custom.css" type="text/css" />
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+    <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" />
+    <link rel="next" title="pylib.geometry_plot_pylab module" href="pylib.geometry_plot_pylab.html" />
+    <link rel="prev" title="pylib.geometry2d_plot module" href="pylib.geometry2d_plot.html" />
+   
+  <link rel="stylesheet" href="_static/custom.css" type="text/css" />
+  
+  
+  <meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
+
+  </head><body>
+  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          
+
+          <div class="body" role="main">
+            
+  <div class="section" id="module-pylib.geometry_plot">
+<span id="pylib-geometry-plot-module"></span><h1>pylib.geometry_plot module<a class="headerlink" href="#module-pylib.geometry_plot" title="Permalink to this headline">¶</a></h1>
+<p>Geometry plotter using  matplotlib (pylab).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Date</dt>
+<dd class="field-odd"><p>2019-12-23</p>
+</dd>
+</dl>
+<span class="target" id="module-geometry_plot"></span></div>
+
+
+          </div>
+          
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<h1 class="logo"><a href="index.html">pylib</a></h1>
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+
+<h3>Navigation</h3>
+<p class="caption"><span class="caption-text">Contents:</span></p>
+<ul class="current">
+<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
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+<h3>Related Topics</h3>
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docs/build/html/pylib.geometry_plot_pylab.html

@@ -0,0 +1,194 @@
+
+<!DOCTYPE html>
+
+<html xmlns="http://www.w3.org/1999/xhtml">
+  <head>
+    <meta charset="utf-8" />
+    <title>pylib.geometry_plot_pylab module &#8212; pylib 2019.12.21 documentation</title>
+    <link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
+    <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
+    <link rel="stylesheet" href="_static/custom.css" type="text/css" />
+    <script type="text/javascript" id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
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+    <script type="text/javascript" src="_static/doctools.js"></script>
+    <script type="text/javascript" src="_static/language_data.js"></script>
+    <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" />
+    <link rel="next" title="pylib.mathematics module" href="pylib.mathematics.html" />
+    <link rel="prev" title="pylib.geometry_plot module" href="pylib.geometry_plot.html" />
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+  <link rel="stylesheet" href="_static/custom.css" type="text/css" />
+  
+  
+  <meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
+
+  </head><body>
+  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          
+
+          <div class="body" role="main">
+            
+  <div class="section" id="module-pylib.geometry_plot_pylab">
+<span id="pylib-geometry-plot-pylab-module"></span><h1>pylib.geometry_plot_pylab module<a class="headerlink" href="#module-pylib.geometry_plot_pylab" title="Permalink to this headline">¶</a></h1>
+<p>Geometry plotter using pylab (matplotlib).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Date</dt>
+<dd class="field-odd"><p>2019-12-23</p>
+</dd>
+</dl>
+<span class="target" id="module-geometry_plot_pylab"></span><dl class="function">
+<dt id="pylib.geometry_plot_pylab.cad_wireframe">
+<code class="sig-name descname">cad_wireframe</code><span class="sig-paren">(</span><em class="sig-param">world</em>, <em class="sig-param">centering=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry_plot_pylab.html#cad_wireframe"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry_plot_pylab.cad_wireframe" title="Permalink to this definition">¶</a></dt>
+<dd><p>Graphical projections</p>
+<ul class="simple">
+<li><p>Parallel projections</p>
+<ul>
+<li><p>Orthographic</p>
+<ul>
+<li><p>Multiview</p>
+<ul>
+<li><p>* First-angle</p></li>
+<li><p>Third-angle</p></li>
+<li><p>Plan Elevation</p></li>
+</ul>
+</li>
+<li><p>Axonometric</p>
+<ul>
+<li><p>* Isometric</p></li>
+<li><p>Dimetric</p></li>
+<li><p>Trimetri</p></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><p>Oblique</p>
+<ul>
+<li><p>Carbinet</p></li>
+<li><p>Cavalier</p></li>
+<li><p>Military</p></li>
+<li><p>Top-down</p></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><p>Perspective projections</p>
+<ul>
+<li><p>1-point</p></li>
+<li><p>2-point</p></li>
+<li><p>3-point</p></li>
+<li><p>Curvilinear</p></li>
+</ul>
+</li>
+</ul>
+</dd></dl>
+
+<dl class="function">
+<dt id="pylib.geometry_plot_pylab.plot_post">
+<code class="sig-name descname">plot_post</code><span class="sig-paren">(</span><em class="sig-param">ax</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry_plot_pylab.html#plot_post"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry_plot_pylab.plot_post" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="function">
+<dt id="pylib.geometry_plot_pylab.set_aspect_equal">
+<code class="sig-name descname">set_aspect_equal</code><span class="sig-paren">(</span><em class="sig-param">ax</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry_plot_pylab.html#set_aspect_equal"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry_plot_pylab.set_aspect_equal" title="Permalink to this definition">¶</a></dt>
+<dd><p>Make axes of 3D plot have equal scale so that spheres appear as
+spheres, cubes as cubes, etc..  This is one possible solution to
+Matplotlib’s ax.set_aspect(‘equal’) and ax.axis(‘equal’) not
+working for 3D.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>ax</strong> (<em>pylab.Axes</em>) – a pylab axis</p>
+</dd>
+</dl>
+<p>Source: <a class="reference external" href="https://stackoverflow.com/a/35126679">https://stackoverflow.com/a/35126679</a></p>
+</dd></dl>
+
+<dl class="function">
+<dt id="pylib.geometry_plot_pylab.wireframe3d">
+<code class="sig-name descname">wireframe3d</code><span class="sig-paren">(</span><em class="sig-param">world</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry_plot_pylab.html#wireframe3d"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry_plot_pylab.wireframe3d" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</div>
+
+
+          </div>
+          
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<h1 class="logo"><a href="index.html">pylib</a></h1>
+
+
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+
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+
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+<h3>Navigation</h3>
+<p class="caption"><span class="caption-text">Contents:</span></p>
+<ul class="current">
+<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
+<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
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+<div class="relations">
+<h3>Related Topics</h3>
+<ul>
+  <li><a href="index.html">Documentation overview</a><ul>
+  <li><a href="modules.html">pylib</a><ul>
+  <li><a href="pylib.html">pylib package</a><ul>
+      <li>Previous: <a href="pylib.geometry_plot.html" title="previous chapter">pylib.geometry_plot module</a></li>
+      <li>Next: <a href="pylib.mathematics.html" title="next chapter">pylib.mathematics module</a></li>
+  </ul></li>
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+</div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
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+      <input type="text" name="q" aria-labelledby="searchlabel" />
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+      &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
+      
+      |
+      <a href="_sources/pylib.geometry_plot_pylab.rst.txt"
+          rel="nofollow">Page source</a>
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docs/build/html/pylib.html

@@ -61,9 +61,14 @@
 <li class="toctree-l1"><a class="reference internal" href="pylib.date.html">pylib.date module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="pylib.drawblock.html">pylib.drawblock module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="pylib.function.html">pylib.function module</a></li>
-<li class="toctree-l1"><a class="reference internal" href="pylib.geometry.html">pylib.geometry module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="pylib.geometry.html">pylib.geometry module</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="pylib.geometry.html#affine-transforms">Affine transforms</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="pylib.geometry2d.html">pylib.geometry2d module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="pylib.geometry2d_plot.html">pylib.geometry2d_plot module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="pylib.geometry_plot.html">pylib.geometry_plot module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="pylib.geometry_plot_pylab.html">pylib.geometry_plot_pylab module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="pylib.mathematics.html">pylib.mathematics module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="pylib.time_of_day.html">pylib.time_of_day module</a></li>
 </ul>

docs/build/html/pylib.mathematics.html

@@ -17,7 +17,7 @@
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="pylib.time_of_day module" href="pylib.time_of_day.html" />
-    <link rel="prev" title="pylib.geometry2d_plot module" href="pylib.geometry2d_plot.html" />
+    <link rel="prev" title="pylib.geometry_plot_pylab module" href="pylib.geometry_plot_pylab.html" />
    
   <link rel="stylesheet" href="_static/custom.css" type="text/css" />
   
@@ -53,6 +53,119 @@
 <em class="property">class </em><code class="sig-name descname">matrix</code><a class="reference internal" href="_modules/pylib/mathematics.html#matrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix" title="Permalink to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
 <p>Use/create matrix like list of lists</p>
+<dl class="method">
+<dt id="pylib.mathematics.matrix.__getitem__">
+<code class="sig-name descname">__getitem__</code><span class="sig-paren">(</span><em class="sig-param">index</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.__getitem__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.__getitem__" title="Permalink to this definition">¶</a></dt>
+<dd><p>For index return value, for range return new vector object.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>                     <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+<span class="go">[7, 8, 9, 0]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">])</span>
+<span class="go">[[2, 3], [5, 6], [8, 9], [0, 0]]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">])</span>
+<span class="go">[[2, 3], [5, 6]]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">[::</span><span class="mi">2</span><span class="p">,</span> <span class="p">::</span><span class="mi">2</span><span class="p">])</span>
+<span class="go">[[1, 3], [7, 9]]</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.matrix.__mul__">
+<code class="sig-name descname">__mul__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.__mul__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.__mul__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Scalar multiplication, dot product (inner product) or
+matrix-vector multiplication. (new object)</p>
+<dl class="field-list simple">
+</dl>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{C} &amp;= \mathbf{A} \cdot b \\
+\mathbf{c} &amp;= \mathbf{A} \cdot \mathbf{b} \\
+\mathbf{C} &amp;= \mathbf{A} \cdot \mathbf{B}\end{split}\]</div>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).</p>
+</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">],</span> \
+<span class="go">                [0, 0, 0, 1]]) * 5</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<span class="go">[[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">],</span> \
+<span class="go">                [0, 0, 0, 1]]) * 5.</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<span class="go">[[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]])</span> <span class="o">*</span> \
+<span class="go">    vector([12, 12, 13])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[75, 186, 297]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]])</span> <span class="o">*</span> \
+<span class="go">    matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<span class="go">[[91, 96, 102], [220, 231, 246], [349, 366, 390]]</span>
+</pre></div>
+</div>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pylib.mathematics.matrix.__rmul__" title="pylib.mathematics.matrix.__rmul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__rmul__()</span></code></a></p>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.matrix.__repr__">
+<code class="sig-name descname">__repr__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.__repr__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.__repr__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return repr(self).</p>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.matrix.__rmul__">
+<code class="sig-name descname">__rmul__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.__rmul__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.__rmul__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Scalar multiplication, dot product (inner product) or
+vector-matrix multiplication. (new object)</p>
+<dl class="field-list simple">
+</dl>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{C} &amp;= a \cdot \mathbf{B} \\
+\mathbf{c} &amp;= \mathbf{a} \cdot \mathbf{B} \\
+\mathbf{C} &amp;= \mathbf{A} \cdot \mathbf{B}\end{split}\]</div>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).</p>
+</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> \
+<span class="go">                    [9, 10, 11, 12], [0, 0, 0, 1]])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<span class="go">[[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="mf">5.</span> <span class="o">*</span> <span class="n">matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> \
+<span class="go">                     [9, 10, 11, 12], [0, 0, 0, 1]])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<span class="go">[[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]</span>
+</pre></div>
+</div>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pylib.mathematics.matrix.__mul__" title="pylib.mathematics.matrix.__mul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__mul__()</span></code></a> and <a class="reference internal" href="#pylib.mathematics.vector.__mul__" title="pylib.mathematics.vector.__mul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">vector.__mul__()</span></code></a> for vector * matrix</p>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.matrix.__str__">
+<code class="sig-name descname">__str__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.__str__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.__str__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return str(self).</p>
+</dd></dl>
+
 <dl class="method">
 <dt id="pylib.mathematics.matrix.rotate_x">
 <code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.rotate_x" title="Permalink to this definition">¶</a></dt>
@@ -134,7 +247,7 @@
 <dd><p>Rotation matrix about the x direction.</p>
 <p>Rotates the coordinate system of vectors</p>
 <div class="math notranslate nohighlight">
-\[\begin{split}R_{x}(\theta) =
+\[\begin{split}\mathbf{R}_{x}(\theta) =
 \begin{bmatrix}
   1 &amp; 0 &amp; 0 &amp; 0 \\
   0 &amp; \cos \theta &amp; -\sin \theta &amp; 0 \\
@@ -149,7 +262,7 @@
 <dd><p>Rotation matrix about the y direction.</p>
 <p>Rotates the coordinate system of vectors</p>
 <div class="math notranslate nohighlight">
-\[\begin{split}R_{y}(\theta) =
+\[\begin{split}\mathbf{R}_{y}(\theta) =
 \begin{bmatrix}
   \cos \theta &amp; 0 &amp; \sin \theta &amp; 0 \\
   0 &amp; 1 &amp; 0 &amp; 0 \\
@@ -164,7 +277,7 @@
 <dd><p>Rotation matrix about the z direction.</p>
 <p>Rotates the coordinate system of vectors</p>
 <div class="math notranslate nohighlight">
-\[\begin{split}R_{z}(\theta) =
+\[\begin{split}\mathbf{R}_{z}(\theta) =
 \begin{bmatrix}
   \cos \theta &amp; -\sin \theta &amp; 0 &amp; 0 \\
   \sin \theta &amp; \cos \theta &amp; 0 &amp; 0 \\
@@ -176,14 +289,17 @@
 <dd class="field-odd"><p></p></dd>
 </dl>
 <div class="math notranslate nohighlight">
-\[\begin{split}R_{z}(\theta) \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+\[\begin{split}\mathbf{R}_{z}(\theta)
+\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix}
+&amp;=
 \begin{bmatrix}
   \cos 90° &amp; -\sin 90° &amp; 0 &amp; 0 \\
   \sin 90° &amp; \cos 90° &amp; 0 &amp; 0 \\
   0 &amp; 0 &amp; 1 &amp; 0 \\
   0 &amp; 0 &amp; 0 &amp; 1
 \end{bmatrix}
-\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} \\
+&amp;=
 \begin{bmatrix}
   0 &amp; -1 &amp; 0 &amp; 0 \\
   1 &amp; 0 &amp; 0 &amp; 0 \\
@@ -200,12 +316,12 @@
 <dd><p>Scaling matrix</p>
 <p>uniform scaling if sx=sy=sz=s.
 Note that scaling happens around the origin, so objects not
-centered at the origin will have their centers move. To avoid this,
+centered at the origin will have their centers move. To avoid
-either scale the object when it’s located at the origin, or
+this, either scale the object when it’s located at the origin,
-perform a translation afterwards to move the object back to where
+or perform a translation afterwards to move the object back to
-it should be.</p>
+where it should be.</p>
 <div class="math notranslate nohighlight">
-\[\begin{split}S =
+\[\begin{split}\mathbf{S} =
 \begin{bmatrix}
   s_x &amp; 0 &amp; 0 &amp; 0 \\
   0 &amp; s_y &amp; 0 &amp; 0 \\
@@ -220,10 +336,10 @@ it should be.</p>
 <dd><p>Scaling</p>
 <p>uniform scaling if sx=sy=sz=s.
 Note that scaling happens around the origin, so objects not
-centered at the origin will have their centers move. To avoid this,
+centered at the origin will have their centers move. To avoid
-either scale the object when it’s located at the origin, or
+this, either scale the object when it’s located at the origin,
-perform a translation afterwards to move the object back to where
+or perform a translation afterwards to move the object back to
-it should be.</p>
+where it should be.</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}\begin{bmatrix}
   xx' &amp; xy' &amp; xz' &amp; t_x' \\
@@ -250,7 +366,7 @@ it should be.</p>
 <em class="property">static </em><code class="sig-name descname">t</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.t"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.t" title="Permalink to this definition">¶</a></dt>
 <dd><p>Translation matrix</p>
 <div class="math notranslate nohighlight">
-\[\begin{split}T =
+\[\begin{split}\mathbf{T} =
 \begin{bmatrix}
   1 &amp; 0 &amp; 0 &amp; t_x \\
   0 &amp; 1 &amp; 0 &amp; t_y \\
@@ -292,60 +408,385 @@ it should be.</p>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
 <p>Use/create vector like lists</p>
 <ul class="simple">
-<li><p>size  -&gt; len(a)</p></li>
+<li><p>size, length of a vector use len(a)</p></li>
-<li><p>abs   -&gt; abs(a)</p></li>
+<li><p>absolute, magntude, norm of a vector use abs(a), see
-<li><p>dot   -&gt; a * b</p></li>
+<a class="reference internal" href="#pylib.mathematics.vector.__abs__" title="pylib.mathematics.vector.__abs__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__abs__()</span></code></a></p></li>
-<li><p>outer -&gt; a &#64; b</p></li>
+<li><p>dot product use a * b, see <a class="reference internal" href="#pylib.mathematics.vector.__mul__" title="pylib.mathematics.vector.__mul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__mul__()</span></code></a> and  <a class="reference internal" href="#pylib.mathematics.vector.__rmul__" title="pylib.mathematics.vector.__rmul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__rmul__()</span></code></a></p></li>
+<li><p>outer product use a &#64; b, see <a class="reference internal" href="#pylib.mathematics.vector.__matmul__" title="pylib.mathematics.vector.__matmul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__matmul__()</span></code></a></p></li>
 </ul>
-<p>use super constructor</p>
+<dl class="field-list simple">
-<p>use super __iter__</p>
+<dt class="field-odd">__iter__</dt>
-<p>use super __setitem__</p>
+<dd class="field-odd"><p></p></dd>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
+</dl>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])]</span>
+<span class="go">[2, 4, 6]</span>
+</pre></div>
+</div>
+<dl class="field-list simple">
+<dt class="field-odd">__setitem__</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
 <span class="go">[1, 2, 3, 1, 2]</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">vector</span><span class="p">)</span>
 <span class="go">True</span>
 </pre></div>
 </div>
-<p>use super __lt__(a, b)</p>
+<dl class="field-list simple">
-<p>use super __le__(a, b)</p>
+<dt class="field-odd">__eq__(a, b)</dt>
-<p>use super __eq__(a, b)</p>
+<dd class="field-odd"><p></p></dd>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
+</dl>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">v2</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="o">==</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">==</span> <span class="n">v2</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="o">==</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
+<span class="go">False</span>
+</pre></div>
+</div>
+<dl class="field-list simple">
+<dt class="field-odd">__ne__(a, b)</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="o">!=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
+<span class="go">False</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span> <span class="o">!=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
 <span class="go">True</span>
 </pre></div>
 </div>
-<p>use super __ne__(a, b)</p>
+<dl class="field-list simple">
-<p>use super __ge__(a, b)</p>
+<dt class="field-odd">__contains__</dt>
-<p>use super __gt__(a, b)</p>
+<dd class="field-odd"><p></p></dd>
-<p>use super __contains__</p>
+</dl>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="mi">2</span> <span class="ow">in</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="mi">2</span> <span class="ow">in</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
 <span class="go">True</span>
 </pre></div>
 </div>
-<p>__isub__</p>
+<dl class="field-list simple">
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<dt class="field-odd">__isub__</dt>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">-=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">-=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
 <span class="go">[-2, -1, 0]</span>
 </pre></div>
 </div>
-<p>__imul__</p>
+<dl class="field-list simple">
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<dt class="field-odd">__imul__</dt>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">*=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">*=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
 <span class="go">18</span>
 </pre></div>
 </div>
-<p>__imatmul__</p>
+<dl class="field-list simple">
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<dt class="field-odd">__imatmul__</dt>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">*=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">*=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
 <span class="go">[[3, 3, 3], [6, 6, 6], [9, 9, 9]]</span>
 </pre></div>
 </div>
+<dl class="method">
+<dt id="pylib.mathematics.vector.__abs__">
+<code class="sig-name descname">__abs__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__abs__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__abs__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Magnitude / norm of a vector</p>
+<div class="math notranslate nohighlight">
+\[b = |\mathbf{a}| = \sqrt{\sum a_i^2} =
+\sqrt{\mathbf{a} \cdot \mathbf{a}}\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">abs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">5.0</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__add__">
+<code class="sig-name descname">__add__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__add__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__add__" title="Permalink to this definition">¶</a></dt>
+<dd><p>a + b (new object)</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{c} = \mathbf{a} + \mathbf{b}\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">+</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[2, 4, 6]</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__ge__">
+<code class="sig-name descname">__ge__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__ge__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__ge__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Test if this object is greater (larger) than or equal the
+other object.</p>
+<div class="math notranslate nohighlight">
+\[|\mathbf{a}| \ge |\mathbf{b}|\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">&gt;=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">&gt;=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
+<span class="go">False</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__getitem__">
+<code class="sig-name descname">__getitem__</code><span class="sig-paren">(</span><em class="sig-param">index</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__getitem__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__getitem__" title="Permalink to this definition">¶</a></dt>
+<dd><p>For index return value, for range return new vector object.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">]</span>
+<span class="go">[2, 3]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
+<span class="go">4</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__gt__">
+<code class="sig-name descname">__gt__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__gt__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__gt__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Test if this object is greater (larger) than the other
+object.</p>
+<div class="math notranslate nohighlight">
+\[|\mathbf{a}| \gt |\mathbf{b}|\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">&gt;</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
+<span class="go">False</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">&gt;</span> <span class="n">vector</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
+<span class="go">True</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__iadd__">
+<code class="sig-name descname">__iadd__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__iadd__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__iadd__" title="Permalink to this definition">¶</a></dt>
+<dd><p>a += b (new object)</p>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">+=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[4, 5, 6]</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__le__">
+<code class="sig-name descname">__le__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__le__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__le__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Test if this object is lower (smaller) than or equal the
+other object.</p>
+<div class="math notranslate nohighlight">
+\[|\mathbf{a}| \le |\mathbf{b}|\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span> <span class="o">&lt;=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="go">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span> <span class="o">&lt;=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
+<span class="go">False</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__lt__">
+<code class="sig-name descname">__lt__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__lt__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__lt__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Test if this object is lower (smaller) than the other object.</p>
+<div class="math notranslate nohighlight">
+\[|\mathbf{a}| \lt |\mathbf{b}|\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span> <span class="o">&lt;</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="go">False</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span> <span class="o">&lt;</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
+<span class="go">True</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__matmul__">
+<code class="sig-name descname">__matmul__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__matmul__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__matmul__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Outer product a &#64; b (new object)</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{c} = \mathbf{a} \otimes \mathbf{b}
+=
+\begin{pmatrix}
+  a_{1}\\
+  a_{2}\\
+  a_{3}
+\end{pmatrix}
+\otimes
+\begin{pmatrix}
+  b_{1}\\
+  b_{2}\\
+  b_{3}
+\end{pmatrix}
+=
+\begin{pmatrix}
+  a_{1}b_{1}&amp;a_{1}b_{2}&amp;a_{1}b_{3}\\
+  a_{2}b_{1}&amp;a_{2}b_{2}&amp;a_{2}b_{3}\\
+  a_{3}b_{1}&amp;a_{3}b_{2}&amp;a_{3}b_{3}
+\end{pmatrix}\end{split}\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">@</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+<span class="go">[[1, 2, 4], [2, 4, 8], [3, 6, 12]]</span>
+</pre></div>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__mul__">
+<code class="sig-name descname">__mul__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__mul__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__mul__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Scalar multiplication, dot product (inner product) or
+vector-matrix multiplication. (new object)</p>
+<dl class="field-list simple">
+</dl>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{c} &amp;= \mathbf{a} \cdot b \\
+\mathbf{c} &amp;= \mathbf{a} \cdot \mathbf{b} \\
+\mathbf{c} &amp;= \mathbf{a} \cdot \mathbf{B}\end{split}\]</div>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).</p>
+</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <span class="o">*</span> <span class="mi">3</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[3, 6, 9, 12, 15]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <span class="o">*</span> <span class="mf">3.</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[3.0, 6.0, 9.0, 12.0, 15.0]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">s</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">*</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+<span class="go">14</span>
+</pre></div>
+</div>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pylib.mathematics.vector.__rmul__" title="pylib.mathematics.vector.__rmul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__rmul__()</span></code></a></p>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__neg__">
+<code class="sig-name descname">__neg__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__neg__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__neg__" title="Permalink to this definition">¶</a></dt>
+<dd><p>- a (new object)</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{b} = -\mathbf{a}\]</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__pos__">
+<code class="sig-name descname">__pos__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__pos__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__pos__" title="Permalink to this definition">¶</a></dt>
+<dd><p>+ a (new object)</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{b} = +\mathbf{a}\]</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__repr__">
+<code class="sig-name descname">__repr__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__repr__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__repr__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return repr(self).</p>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__rmul__">
+<code class="sig-name descname">__rmul__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__rmul__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__rmul__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Scalar multiplication, dot product (inner product) or
+matrix-vector multiplication. (new object)</p>
+<dl class="field-list simple">
+</dl>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{c} &amp;= a \cdot \mathbf{b} \\
+\mathbf{c} &amp;= \mathbf{a} \cdot \mathbf{b} \\
+\mathbf{c} &amp;= \mathbf{A} \cdot \mathbf{b}\end{split}\]</div>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).</p>
+</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[3, 6, 9, 12, 15]</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="mf">3.</span> <span class="o">*</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[3.0, 6.0, 9.0, 12.0, 15.0]</span>
+</pre></div>
+</div>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pylib.mathematics.vector.__mul__" title="pylib.mathematics.vector.__mul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__mul__()</span></code></a> and <a class="reference internal" href="#pylib.mathematics.matrix.__mul__" title="pylib.mathematics.matrix.__mul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">matrix.__mul__()</span></code></a> for matrix * vector</p>
+</div>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__str__">
+<code class="sig-name descname">__str__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__str__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__str__" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return str(self).</p>
+</dd></dl>
+
+<dl class="method">
+<dt id="pylib.mathematics.vector.__sub__">
+<code class="sig-name descname">__sub__</code><span class="sig-paren">(</span><em class="sig-param">other</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.__sub__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.__sub__" title="Permalink to this definition">¶</a></dt>
+<dd><p>a - b (new object)</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{c} = \mathbf{a} - \mathbf{b}\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Example</dt>
+<dd class="field-odd"><p></p></dd>
+</dl>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">-</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+<span class="go">[0, 0, 0]</span>
+</pre></div>
+</div>
+</dd></dl>
+
 <dl class="method">
 <dt id="pylib.mathematics.vector.abs">
 <em class="property">static </em><code class="sig-name descname">abs</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.abs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.abs" title="Permalink to this definition">¶</a></dt>
@@ -370,9 +811,9 @@ it should be.</p>
 <dl class="method">
 <dt id="pylib.mathematics.vector.ch_cs">
 <code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.ch_cs" title="Permalink to this definition">¶</a></dt>
-<dd><p>Transform this vector from its defined coordinate system to a
+<dd><p>Transform this vector from its defined coordinate system to
-new coordinate system, defined by the given coordinate system (u,
+a new coordinate system, defined by the given coordinate system
-v and w direction vectors).</p>
+(u, v and w direction vectors).</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
 \begin{bmatrix}
@@ -401,7 +842,7 @@ v and w direction vectors).</p>
 <p>c is orthogonal to both a and b.
 The direction of c can be found with the right-hand rule.</p>
 <div class="math notranslate nohighlight">
-\[\vec{c} = \vec{a} \times \vec{b}\]</div>
+\[\mathbf{c} = \mathbf{a} \times \mathbf{b}\]</div>
 </dd></dl>
 
 <dl class="method">
@@ -444,10 +885,10 @@ columns filled with v.</p>
 <dl class="field-list simple">
 </dl>
 <div class="math notranslate nohighlight">
-\[\vec{e}_a = \frac{\vec{a}}{|\vec{a}|}\]</div>
+\[\mathbf{\hat{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}\]</div>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
-<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">norm()</span></code> for a norm (magnitude) of a vector</p>
+<p><a class="reference internal" href="#pylib.mathematics.vector.__abs__" title="pylib.mathematics.vector.__abs__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__abs__()</span></code></a> for a norm (magnitude) of a vector</p>
 </div>
 </dd></dl>
 
@@ -473,8 +914,8 @@ columns filled with ones.</p>
 <dl class="method">
 <dt id="pylib.mathematics.vector.random">
 <em class="property">static </em><code class="sig-name descname">random</code><span class="sig-paren">(</span><em class="sig-param">shape</em>, <em class="sig-param">lmin=0.0</em>, <em class="sig-param">lmax=1.0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.random"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.random" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns a random vector of length n or matrix of size m rows, n
+<dd><p>Returns a random vector of length n or matrix of size m rows,
-columns filled with random numbers.</p>
+n columns filled with random numbers.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Example</dt>
 <dd class="field-odd"><p></p></dd>
@@ -548,10 +989,10 @@ columns filled with random numbers.</p>
 <dd><p>Scaling</p>
 <p>uniform scaling if sx=sy=sz=s.
 Note that scaling happens around the origin, so objects not
-centered at the origin will have their centers move. To avoid this,
+centered at the origin will have their centers move. To avoid
-either scale the object when it’s located at the origin, or
+this, either scale the object when it’s located at the origin,
-perform a translation afterwards to move the object back to where
+or perform a translation afterwards to move the object back to
-it should be.</p>
+where it should be.</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
 \begin{bmatrix}
@@ -578,11 +1019,6 @@ it should be.</p>
 \begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
 </dd></dl>
 
-<dl class="method">
-<dt id="pylib.mathematics.vector.xyz">
-<code class="sig-name descname">xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.xyz" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
-
 <dl class="method">
 <dt id="pylib.mathematics.vector.zeros">
 <em class="property">static </em><code class="sig-name descname">zeros</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.zeros"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.zeros" title="Permalink to this definition">¶</a></dt>
@@ -637,7 +1073,7 @@ columns filled with zeros.</p>
   <li><a href="index.html">Documentation overview</a><ul>
   <li><a href="modules.html">pylib</a><ul>
   <li><a href="pylib.html">pylib package</a><ul>
-      <li>Previous: <a href="pylib.geometry2d_plot.html" title="previous chapter">pylib.geometry2d_plot module</a></li>
+      <li>Previous: <a href="pylib.geometry_plot_pylab.html" title="previous chapter">pylib.geometry_plot_pylab module</a></li>
       <li>Next: <a href="pylib.time_of_day.html" title="next chapter">pylib.time_of_day module</a></li>
   </ul></li>
   </ul></li>

docs/source/_static/custom.css

@@ -7,7 +7,7 @@ table.indextable tr.cap {
 }
 /* move doc link a bit up */
 .viewcode-back {
-    float: right;
+  float: right;
-    position: relative;
+  position: relative;
-    top: -1.5em;
+  top: -1.5em;
 }

docs/source/conf.py

@@ -82,4 +82,10 @@ html_theme_options = {
   'xref_border': 'transparent',
   'seealso_bg': '#25272c',
   'seealso_border': '#2C2C2C',
+  'note_bg': '#25272c',
+  'note_border': '#2C2C2C',
+}
+
+autodoc_default_options = {
+  'special-members': '__iter__, __contains__, __getitem__, __setitem__, __pos__, __neg__, __add__, __iadd__, __sub__, __isub__, __mul__, __rmul__, __imul__, __matmul__, __imatmul__, __abs__, __lt__, __le__, __gt__, __ge__, __eq__, __ne__, __str__, __repr__'
 }

docs/source/pylib.geometry_plot.rst

@@ -0,0 +1,7 @@
+pylib.geometry\_plot module
+===========================
+
+.. automodule:: pylib.geometry_plot
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/pylib.geometry_plot_pylab.rst

@@ -0,0 +1,7 @@
+pylib.geometry\_plot\_pylab module
+==================================
+
+.. automodule:: pylib.geometry_plot_pylab
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/pylib.rst

@@ -25,5 +25,7 @@ Submodules
    pylib.geometry
    pylib.geometry2d
    pylib.geometry2d_plot
+   pylib.geometry_plot
+   pylib.geometry_plot_pylab
    pylib.mathematics
    pylib.time_of_day

examples/geometry_hexahedra.py

@@ -0,0 +1,30 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Example geometry of hexahedra.
+
+:Date: 2019-12-24
+
+.. module:: geometry_hexahedra
+  :platform: *nix, Windows
+  :synopsis: Example geometry of hexahedra.
+
+.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+"""
+from pylib.geometry import World, Hexahedron
+from pylib.geometry_plot_pylab import cad_wireframe
+
+def geometry():
+  w = World()
+  for i in range(3):
+    for j in range(3):
+      for k in range(3):
+        w.add(Hexahedron().scale(0.8).translate(-2+2*i, -2+2*j, -2+2*k))
+  return w
+
+
+if __name__ == "__main__":
+  w = geometry()
+  #print(w.bounding_box())
+  #print(*w)
+  #print(w.wireframes_xyz())
+  cad_wireframe(w)

examples/geometry_lines_circles.py

@@ -0,0 +1,41 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Example geometry of lines and circles.
+
+:Date: 2019-12-23
+
+.. module:: geometry_pyramidal_frustum
+  :platform: *nix, Windows
+  :synopsis: Example geometry of lines and circles.
+
+.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+"""
+import math
+from pylib.geometry import World, Point, Line, Circle
+from pylib.geometry_plot_pylab import cad_wireframe, wireframe3d
+
+def geometry():
+  w = World()
+
+  p0 = Point(0, 0, 0)
+  p = Point(1, 1, 1)
+
+  # add Lines to the Word
+  theta = math.pi/4
+  w.add(*[Line(p0, p.rotate_x(theta/5)) for i in range(30)])
+  w.add(*[Line(p0, p.rotate_x(theta/5)).translate(.1*i, 0, 0) for i in range(30)])
+
+  # add Circles to the Word
+  c1 = Circle()
+  c2 = Circle(2)
+  c3 = Circle(n=18).scale(3).rotate_x(math.pi/4)
+  w.add(c1, c2, c3)
+
+  return w
+
+
+if __name__ == "__main__":
+  w = geometry()
+  print(*w)
+  wireframe3d(w)
+  cad_wireframe(w, False)

examples/geometry_pyramidal_frustum.py

@@ -0,0 +1,40 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Example geometry of a pyramidal frustum.
+
+:Date: 2019-12-23
+
+.. module:: geometry_pyramidal_frustum
+  :platform: *nix, Windows
+  :synopsis: Example geometry of a pyramidal frustum.
+
+.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+"""
+from pylib.geometry import World, Point, Polygon, Hexahedron
+from pylib.geometry_plot_pylab import cad_wireframe
+
+def geometry():
+  w = World()
+  p0 = Point()
+  p1 = Point(1.00, 0, 0)
+  p2 = Point(1.00, 1, 0)
+  p3 = Point(0.00, 1, 0)
+  p4 = Point(0.25, 0.25, 1)
+  p5 = Point(0.75, 0.25, 1)
+  p6 = Point(0.75, 0.75, 1)
+  p7 = Point(0.25, 0.75, 1)
+  pg0 = Polygon(p0, p1, p2, p3)
+  pg1 = Polygon(p4, p5, p6, p7)
+  pg2 = Polygon(p0, p1, p5, p4)
+  pg3 = Polygon(p2, p3, p7, p6)
+  w.add(pg0, pg1, pg2, pg3)
+  h = Hexahedron()
+  w.add(h)
+  return w
+
+
+if __name__ == "__main__":
+  w = geometry()
+  print(*w)
+  print(w.wireframes_xyz())
+  cad_wireframe(w)

pylib/data.py

@@ -12,6 +12,36 @@
 """
 import math
 import pickle
+import collections
+
+def issequence(obj):
+  """
+  True for tuple, list, str
+  False for int, dict, set
+
+  :Example:
+
+  >>> issequence(())
+  True
+  >>> issequence((3, ))
+  True
+  >>> issequence([])
+  True
+  >>> issequence([1])
+  True
+  >>> issequence([1, 2])
+  True
+  >>> issequence('')
+  True
+
+  >>> issequence((3))
+  False
+  >>> issequence({})
+  False
+  >>> issequence(set())
+  False
+  """
+  return isinstance(obj, collections.abc.Sequence)
 
 def read(file_name, x_column, y_column, default=None, verbose=False):
   """Read ascii data file.

pylib/function.py

@@ -200,7 +200,7 @@ def hypotrochoid(R, r, d):
   >>> x, y, theta_end = hyotrochoid(20, 6, 6)
 
   .. seealso::
-    :meth:`mathematics.lcm`
+    :meth:`pylib.mathematics.lcm`
   """
   x = lambda theta: (R-r)*math.cos(theta) + d*math.cos((R-r)/r * theta)
   y = lambda theta: (R-r)*math.sin(theta) - d*math.sin((R-r)/r * theta)
@@ -377,7 +377,7 @@ def to_str(f, x=None, x_0=0, x_1=1, t=None, h=10, w=80, density=1, char_set="lin
 
 
   .. seealso::
-    :meth:`pylib.function.transformation`
+    :meth:`transformation`
   """
   # scale function to used chars and dots/pixel in y direction (4 for braille characters): from [0, 1] to [0, chars*4-1]
   # negate the function because the y axis is pointing downwards: from [0, 1] to [-1, 0] or from [0, chars*4-1] to [-(chars*4-1), 0]
@@ -402,7 +402,7 @@ def to_str(f, x=None, x_0=0, x_1=1, t=None, h=10, w=80, density=1, char_set="lin
     #frame = canvas.frame(min_x=a*pixel_per_char, min_y=1, max_x=b*pixel_per_char, max_y=21)
     frame = canvas.frame()
   elif char_set in ["histogram", "block"]:
-    import drawblock
+    from .drawblock import histogram
 
     pixels_horizontal = 1
     pixels_vertical = 8
@@ -412,6 +412,6 @@ def to_str(f, x=None, x_0=0, x_1=1, t=None, h=10, w=80, density=1, char_set="lin
     density = min(density, 1)  # density max 1!
     x = seq(x_0*window_factor, x_1*window_factor, 1/pixels_horizontal/density)
     f = [f(xi, t) for xi in x]
-    frame = drawblock.histogram(f, x)
+    frame = histogram(f, x)
 
   return frame

pylib/geometry.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python
 # -*- coding: utf-8 -*-
-"""2D geometry objects.
+"""Geometry objects.
 
 :Date: 2019-12-21
 
@@ -9,26 +9,37 @@
   :synopsis: Geometry objects.
 
 .. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+
+Affine transforms
+-----------------
+
+Functions in augmented space, in homogenous coordinates.
+Points are augment to 4 dimensions, by adding a dummy coordinate.
+For points the dummy coordinate is always normalized to 1.
+With homogenous coordinates translation of points is repesentable
+as a linear transformation.
 """
 import math
 import copy
-from pylib.mathematics import vector, matrix
+from .mathematics import vector, matrix
 
 class Direction(vector):
   """Direction in local coordinate system"""
   def __init__(self, x=1, y=0, z=0):
     super().__init__([x, y, z, 0])
 
-  def __str__(self):
-    return str(self.xyz())
-
 class Point(vector):
   """Point in local coordinate system"""
   def __init__(self, x=0, y=0, z=0):
     super().__init__([x, y, z, 1])
 
-  def __str__(self):
+  # TODO
-    return str(self.xyz())
+  def projection(self):
+    """Orthographic projection to the xy-plane
+    """
+    # P = matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
+    #return (P*self)[:2]
+    return self[:2]
 
 class CS(matrix):
   """Coordinate system
@@ -36,9 +47,6 @@ class CS(matrix):
   def __init__(self, x=[1, 0, 0], y=[0, 1, 0], z=[0, 0, 1]):
     super().__init__([[*x, 0], [*y, 0], [*z, 0], [0, 0, 0, 1]])
 
-  def __str__(self):
-    return '[' + ', '.join([str(i) for i in self.get_coordinates()]) + ']'
-
   @staticmethod
   def x90():
     return CS((1, 0, 0), (0, 0, -1), (0, 1, 0))
@@ -59,7 +67,133 @@ class CS(matrix):
     """Get coordinates in 3d space"""
     return self[:3,:3]
 
-class World():
+# TODO: Wireframe(list) or Wireframe(matrix) ?
+# list of Points
+class Wireframe:
+  """Open and closed wireframe object in local coordinate system
+
+  This class create its own points (copy).
+  """
+  def __init__(self, *points, closed=False):
+    self._points = [copy.copy(i) for i in points]
+    self.closed = closed
+
+  def __str__(self):
+    return '[' + ', '.join([str(point) for point in self._points]) + ']'
+
+  def __iter__(self):
+    """Returns the Iterator object"""
+    return iter(self.points())
+
+  def points(self):
+    """Get coordinates in 3d space"""
+    result = [i for i in self._points]
+    return result if not self.closed else result + [result[0]]
+
+  def xy(self):
+    """Get coordinates in 3d space"""
+    return list(zip(*[i[:2] for i in self.points()]))
+
+  def xyz(self):
+    """Get coordinates in 3d space"""
+    return list(zip(*[i[:3] for i in self.points()]))
+
+  def rotate_x(self, theta):
+    self._points = [point.rotate_x(theta) for point in self._points]
+    return self
+
+  def rotate_y(self, theta):
+    self._points = [point.rotate_y(theta) for point in self._points]
+    return self
+
+  def rotate_z(self, theta):
+    self._points = [point.rotate_z(theta) for point in self._points]
+    return self
+
+  def translate(self, tx, ty, tz):
+    self._points = [point.translate(tx, ty, tz) for
+                    point in self._points]
+    return self
+
+  def scale(self, sx, sy=None, sz=None):
+    # if not sy is not suitable because 0 is also false
+    if sy is None:
+      sy = sx
+      sz = sx
+    self._points = [point.scale(sx, sy, sz) for
+                    point in self._points]
+    return self
+
+  def ch_cs(self, cs):
+    self._points = [point.ch_cs(cs) for point in self._points]
+    return self
+
+class Line(Wireframe):
+  """Line a open wireframe object in local coordinate system"""
+  def __init__(self, point1=Point(-1, 0, 0), point2=Point(1, 0, 0)):
+    super().__init__(point1, point2)
+
+class Polygon(Wireframe):
+  """Polygon as closed wireframe object in local coordinate system"""
+  def __init__(self, *points):
+    super().__init__(*points, closed=True)
+
+class Circle(Polygon):
+  """Circle a closed wireframe object in local coordinate system"""
+  def __init__(self, radius=1, n=10):
+    points = []
+    for i in range(n):
+      x = radius * math.cos(i*2*math.pi/n)
+      y = radius * math.sin(i*2*math.pi/n)
+      points.append(Point(x, y, 0))
+    super().__init__(*points)
+
+class Solid:
+  """Solid object in local coordinate system
+
+  This class lists Wireframe objects.
+  The Wireframe class create its own points (copy).
+  """
+  def __init__(self, *wireframes):
+    self._wireframes = wireframes
+
+  def wireframes(self):
+    return self._wireframes
+
+  def translate(self, tx, ty, tz):
+    self._wireframes = [wireframe.translate(tx, ty, tz) for
+                        wireframe in self._wireframes]
+    return self
+
+  def scale(self, sx, sy=None, sz=None):
+    # if not sy is not suitable because 0 is also false
+    if sy is None:
+      sy = sx
+      sz = sx
+    self._wireframes = [wireframe.scale(sx, sy, sz) for
+                        wireframe in self._wireframes]
+    return self
+
+  def ch_cs(self, cs):
+    self._wireframes = [wireframe.ch_cs(cs) for
+                        wireframe in self._wireframes]
+    return self
+
+class Hexahedron(Solid):
+  """Line a open wireframe object in local coordinate system"""
+  def __init__(self,
+               point1=Point(-1, -1, -1), point2=Point(1, -1, -1),
+               point3=Point(1, 1, -1), point4=Point(-1, 1, -1),
+               point5=Point(-1, -1, 1), point6=Point(1, -1, 1),
+               point7=Point(1, 1, 1), point8=Point(-1, 1, 1)):
+    super().__init__(
+      Polygon(point1, point2, point3, point4),
+      Polygon(point5, point6, point7, point8),
+      Polygon(point1, point2, point6, point5),
+      Polygon(point3, point4, point8, point7)
+      )
+
+class World:
   """World-space with world-space coordinates
   """
   def __init__(self):
@@ -72,7 +206,8 @@ class World():
     return iter(self.objects())
 
   def _store_init(self):
-    """Initialize or reset calculated values, because a new object was added.
+    """Initialize or reset calculated values, because a new object
+    was added.
     """
     self._bb = None
     self._sd = None
@@ -106,6 +241,33 @@ class World():
     self._cs.scale(sx, sy, sz)
     return self
 
+  def wireframes(self):
+    result = []
+    for i in self.objects():
+      if isinstance(i, Wireframe):
+        result.append(i.points())
+      elif isinstance(i, Solid):
+        [result.append(j.points()) for j in i.wireframes()]
+    return result
+
+  def wireframes_xy(self):
+    result = []
+    for i in self.objects():
+      if isinstance(i, Wireframe):
+        result.append(i.xy())
+      elif isinstance(i, Solid):
+        [result.append(j.xy()) for j in i.wireframes()]
+    return result
+
+  def wireframes_xyz(self):
+    result = []
+    for i in self.objects():
+      if isinstance(i, Wireframe):
+        result.append(i.xyz())
+      elif isinstance(i, Solid):
+        [result.append(j.xyz()) for j in i.wireframes()]
+    return result
+
   def objects(self):
     return [copy.deepcopy(i).ch_cs(self._cs) for i in self._objects]
 
@@ -124,10 +286,9 @@ class World():
     xmax = -math.inf
     ymax = -math.inf
     zmax = -math.inf
-    for i in self._objects:
+    for i in self.wireframes_xyz():
-      xi, yi, zi = map(min, i.xyz())
+      xi, yi, zi = map(min, i)
-      xs, ys, zs = map(max, i.xyz())
+      xs, ys, zs = map(max, i)
-      #xmax = x if x > xmax: xmax = x
       xmin = xi if xi < xmin else xmin
       ymin = yi if yi < ymin else ymin
       zmin = zi if zi < zmin else zmin
@@ -148,78 +309,8 @@ class World():
 
   def center(self):
     bb = self.bounding_box()
-    self.ch_cs([[1,0,0,-(bb[1]-bb[0])/2],[0,1,0,-(bb[3]-bb[2])/2],[0,0,1,-(bb[5]-bb[4])/2],[0,0,0,1]])
+    self.ch_cs([[1, 0, 0, -(bb[0]+bb[1])/2],
+                [0, 1, 0, -(bb[2]+bb[3])/2],
+                [0, 0, 1, -(bb[4]+bb[5])/2],
+                [0, 0, 0, 1]])
     return self
-
-# TODO: Wireframe(list) or Wireframe(matrix) ?
-# list of Points
-class Wireframe():
-  """Open and closed wireframe object in local coordinate system
-
-  This class create its own points (copy).
-  """
-  def __init__(self, *points, closed=False):
-    self._points = [copy.copy(i) for i in points]
-    self.closed = closed
-
-  def __str__(self):
-    return '[' + ', '.join([str(point) for point in self._points]) + ']'
-
-  def __iter__(self):
-    """Returns the Iterator object"""
-    return iter(self.points())
-
-  def points(self):
-    """Get coordinates in 3d space"""
-    result = [i for i in self._points]
-    return result if not self.closed else result + [result[0]]
-
-  def xyz(self):
-    return zip(*[i.xyz() for i in self.points()])
-
-  def rotate_x(self, theta):
-    self._points = [point.rotate_x(theta) for point in self._points]
-    return self
-
-  def rotate_y(self, theta):
-    self._points = [point.rotate_y(theta) for point in self._points]
-    return self
-
-  def rotate_z(self, theta):
-    self._points = [point.rotate_z(theta) for point in self._points]
-    return self
-
-  def translate(self, tx, ty, tz):
-    self._points = [point.translate(tx, ty, tz) for point in self._points]
-    return self
-
-  def scale(self, sx, sy=None, sz=None):
-    if not sy:
-      sy = sx
-      sz = sx
-    self._points = [point.scale(sx, sy, sz) for point in self._points]
-    return self
-
-  def ch_cs(self, cs):
-    self._points = [point.ch_cs(cs) for point in self._points]
-    return self
-
-class Line(Wireframe):
-  """Line a open wireframe object in local coordinate system"""
-  def __init__(self, point1=Point(-1, 0, 0), point2=Point(1, 0, 0)):
-    super().__init__(point1, point2)
-
-class Polygon(Wireframe):
-  """Polygon as closed wireframe object in local coordinate system"""
-  def __init__(self, *points):
-    super().__init__(*points, closed=True)
-
-class Circle(Polygon):
-  """Circle a closed wireframe object in local coordinate system"""
-  def __init__(self, radius=1, n=10):
-    points = []
-    for i in range(n):
-      x = radius * math.sin(i*2*math.pi/n)
-      y = radius * math.cos(i*2*math.pi/n)
-      points.append(Point(x, y, 0))
-    super().__init__(*points)

pylib/geometry2d_plot.py

@@ -11,7 +11,7 @@
 .. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
 """
 import pylab
-from geometry2d import (
+from .geometry2d import (
   distance, angle, line, interpolate_hermite, rotate_xy, translate_xy
 )
 

pylib/geometry_plot.py

@@ -0,0 +1,17 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Geometry plotter using  matplotlib (pylab).
+
+:Date: 2019-12-23
+
+.. module:: geometry_plot
+  :platform: *nix, Windows
+  :synopsis: Geometry plotting.
+
+.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+"""
+
+backend = 'pylab'
+
+if backend == 'pylab':
+  from .geometry_plot_pylab import cad_wireframe, wireframe3d

pylib/geometry_plot_pylab.py

@@ -0,0 +1,243 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Geometry plotter using pylab (matplotlib).
+
+:Date: 2019-12-23
+
+.. module:: geometry_plot_pylab
+  :platform: *nix, Windows
+  :synopsis: Geometry plotting (pylab).
+
+.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+"""
+import math
+# This import registers the 3D projection, but is otherwise unused.
+from mpl_toolkits.mplot3d import Axes3D
+assert Axes3D  # silence pyflakes
+import pylab
+pylab.style.use('dark_background')
+pylab.rcParams['text.color'] = 'grey'      # lightgrey
+pylab.rcParams['axes.edgecolor'] = 'grey'  # lightgrey
+pylab.rcParams['grid.color'] = 'grey'      # lightgrey
+pylab.rcParams['xtick.color'] = 'grey'     # lightgrey
+pylab.rcParams['ytick.color'] = 'grey'     # lightgrey
+pylab.rcParams['axes3d.grid'] = False
+# default for dark_background cycler(
+# 'color', ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',
+#           '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf'])
+pylab.rcParams['axes.prop_cycle'] = pylab.cycler(
+  "color", ['#3498DB', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',
+            '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf'])
+
+# remove f for fullscreen toggle, default ['f', 'ctrl+f']
+pylab.rcParams['keymap.fullscreen'] = ['ctrl+f']
+# remove L for log/lin toggle, default ['k', 'L']
+pylab.rcParams['keymap.xscale'] = ['k']
+# remove l for log/lin toggle, default ['l']
+pylab.rcParams['keymap.yscale'] = []
+
+from pylab import mean
+from .geometry import CS
+
+# type of ax
+# - matplotlib.axes._subplots.Axes3DSubplot)
+# - matplotlib.axes.Axes
+# - pylab.Axes
+
+def set_aspect_equal(ax):
+  '''Make axes of 3D plot have equal scale so that spheres appear as
+  spheres, cubes as cubes, etc..  This is one possible solution to
+  Matplotlib's ax.set_aspect('equal') and ax.axis('equal') not
+  working for 3D.
+
+  :param ax: a pylab axis
+  :type ax: pylab.Axes
+
+  Source: https://stackoverflow.com/a/35126679
+  '''
+  if ax.name == '3d':
+
+    xlim = ax.get_xlim3d()
+    ylim = ax.get_ylim3d()
+    zlim = ax.get_zlim3d()
+
+    xmean = mean(xlim)
+    ymean = mean(ylim)
+    zmean = mean(zlim)
+
+    plot_radius = max([abs(lim - mean_)
+                       for lims, mean_ in ((xlim, xmean),
+                                           (ylim, ymean),
+                                           (zlim, zmean))
+                       for lim in lims])
+
+    ax.set_xlim3d([xmean - plot_radius, xmean + plot_radius])
+    ax.set_ylim3d([ymean - plot_radius, ymean + plot_radius])
+    ax.set_zlim3d([zmean - plot_radius, zmean + plot_radius])
+  else:
+    ax.axis('equal')
+
+def plot_post(ax):
+  if isinstance(ax, pylab.Axes):
+    ax = [ax]
+  for axi in ax:
+    if axi.name == '3d':
+      #axi.w_xaxis.set_pane_color((0, 0, 0, 0))
+      #axi.w_yaxis.set_pane_color((0, 0, 0, 0))
+      #axi.w_zaxis.set_pane_color((0, 0, 0, 0))
+      axi.w_xaxis.pane.fill = False
+      axi.w_yaxis.pane.fill = False
+      axi.w_zaxis.pane.fill = False
+    set_aspect_equal(axi)
+
+def wireframe3d(world):
+  fig = pylab.figure()
+  ax = fig.add_subplot(111, projection='3d')
+  [ax.plot(*i, 'C0') for i in world.wireframes_xyz()]
+  plot_post(ax)
+
+def cad_wireframe(world, centering=True):
+  """
+  Graphical projections
+
+  * Parallel projections
+
+    * Orthographic
+
+      * Multiview
+
+        * \* First-angle
+        * Third-angle
+        * Plan Elevation
+
+      * Axonometric
+
+        * \* Isometric
+        * Dimetric
+        * Trimetri
+
+    * Oblique
+
+      * Carbinet
+      * Cavalier
+      * Military
+      * Top-down
+
+  * Perspective projections
+
+    * 1-point
+    * 2-point
+    * 3-point
+    * Curvilinear
+
+  """
+  if centering:
+    world.center()
+
+  fig = pylab.figure('geometry-cad')
+  fig.clf()
+  ax = fig.add_subplot(111)
+
+  pylab.axis('off')
+  pylab.subplots_adjust(left=0, right=1, top=1, bottom=0)
+
+  lps = [ax.plot(*i, 'C0')[0] for i in world.wireframes_xy()]
+
+  plot_post(ax)
+
+  def press(event, world, lps):
+    #print('key pressed:', event.key)
+    #sys.stdout.flush()
+    if event.key in [
+        'left', 'right', 'up', 'down',
+        'f', 't', 'b', 'l', 'r', 'i', 'd',
+        'shift+left', 'shift+right', 'shift+up', 'shift+down',
+        'ctrl+up', 'ctrl+down', 'ctrl+left', 'ctrl+right']:
+      d = world.space_diagonal()
+      if event.key == 'left':
+        world.rotate_y(-math.pi/180*10)
+      elif event.key == 'right':
+        world.rotate_y(+math.pi/180*10)
+      elif event.key == 'up':
+        world.rotate_x(-math.pi/180*10)
+      elif event.key == 'down':
+        world.rotate_x(+math.pi/180*10)
+      elif event.key == 'f':
+        world.cs(CS())
+        if centering:
+          world.center()
+      elif event.key == 't':
+        world.cs(CS.x90())
+        if centering:
+          world.center()
+      elif event.key == 'b':
+        world.cs(CS.xm90())
+        if centering:
+          world.center()
+      elif event.key == 'l':
+        world.cs(CS.y90())
+        if centering:
+          world.center()
+      elif event.key == 'r':
+        world.cs(CS.ym90())
+        if centering:
+          world.center()
+      elif event.key == 'i':
+        #theta_y = -math.pi/2/3
+        #theta_x = math.pi/2/3
+        theta_y = -math.pi/2/2
+        theta_x = math.asin(math.tan(math.pi/2/3))
+        world.cs(CS().rotate_y(theta_y).rotate_x(theta_x))
+        if centering:
+          world.center()
+      elif event.key == 'd':
+        #theta_x = math.asin(math.tan(math.pi/2/3/2))
+        theta_y = -math.pi/2/2
+        theta_x = math.atan(1/2)
+        world.cs(CS().rotate_y(theta_y).rotate_x(theta_x))
+        if centering:
+          world.center()
+      elif event.key == 'shift+left':
+        world.translate(-0.1*d, 0, 0)
+      elif event.key == 'shift+right':
+        world.translate(0.1*d, 0, 0)
+      elif event.key == 'shift+up':
+        world.translate(0, 0.1*d, 0)
+      elif event.key == 'shift+down':
+        world.translate(0, -0.1*d, 0)
+      elif event.key == 'ctrl+left':
+        world.rotate_z(+math.pi/180*10)
+      elif event.key == 'ctrl+right':
+        world.rotate_z(-math.pi/180*10)
+      elif event.key == 'ctrl+up':
+        world.scale(1.1)
+      elif event.key == 'ctrl+down':
+        world.scale(0.9)
+      for i, j in zip(lps, world.wireframes_xy()):
+        i.set_data(j)
+    fig.canvas.draw()
+
+  def onresize(event, w):
+    r = 2 * w.space_diagonal()/2
+    pylab.xlim((-r, r))
+    pylab.ylim((-r, r))
+
+  fig.canvas.mpl_connect('key_press_event',
+                         lambda event: press(event, world, lps))
+  fig.canvas.mpl_connect('resize_event',
+                         lambda event: onresize(event, world))
+
+  pylab.text(
+    0+.01, 1-.015,
+    'rotate: left, right, up, down, ctrl+left, ctrl+right\n' +
+    'pan: shift+left, shift+right, shift+up, shift+down\n' +
+    'zoom: ctrl+up, ctrl+down\n' +
+    'view: f (front), l (left), r (right), t (top), b (bottom)\n' +
+    '      i (isometric), d (dimetric)',
+    horizontalalignment='left',
+    verticalalignment='top',
+    transform=fig.transFigure,
+    bbox=dict(facecolor='black', alpha=0.5),
+    family='monospace'
+    )
+  pylab.show()

pylib/mathematics.py

@@ -21,64 +21,63 @@ def lcm(a, b):
 class vector(list):
   """Use/create vector like lists
 
-  * size  -> len(a)
+  * size, length of a vector use len(a)
-  * abs   -> abs(a)
+  * absolute, magntude, norm of a vector use abs(a), see
-  * dot   -> a * b
+    :meth:`__abs__`
-  * outer -> a @ b
+  * dot product use a * b, see :meth:`__mul__` and  :meth:`__rmul__`
+  * outer product use a @ b, see :meth:`__matmul__`
 
-  use super constructor
+  :__iter__:
 
-  use super __iter__
+  >>> [i*2 for i in vector([1, 2, 3])]
+  [2, 4, 6]
 
-  use super __setitem__
+  :__setitem__:
 
-  >>> v = vector([1,2,3,4,5])
+  >>> v = vector([1, 2, 3, 4, 5])
-  >>> v[3:5] = [1,2]
+  >>> v[3:5] = [1, 2]
   >>> print(v)
   [1, 2, 3, 1, 2]
   >>> isinstance(v, vector)
   True
 
-  use super __lt__(a, b)
+  :__eq__(a, b):
 
-  use super __le__(a, b)
+  >>> vector([1, 2, 3, 1, 2]) == vector([1, 2, 3, 1, 2])
+  True
+  >>> vector([1, 2, 3, 1, 2]) == vector([1, 2, 3, 2, 1])
+  False
 
-  use super __eq__(a, b)
+  :__ne__(a, b):
 
-  >>> v = vector([1,2,3,1,2])
+  >>> vector([1, 2, 3, 1, 2]) != vector([1, 2, 3, 1, 2])
-  >>> v2 = vector([1,2,3,1,2])
+  False
-  >>> v == v2
+  >>> vector([1, 2, 3, 1, 2]) != vector([1, 2, 3, 2, 1])
   True
 
-  use super __ne__(a, b)
+  :__contains__:
 
-  use super __ge__(a, b)
+  >>> 2 in vector([1, 2, 3])
-
-  use super __gt__(a, b)
-
-  use super __contains__
-
-  >>> 2 in vector([1,2,3])
   True
 
-  __isub__
+  :__isub__:
 
-  >>> v = vector([1,2,3])
+  >>> v = vector([1, 2, 3])
-  >>> v -= vector([3,3,3])
+  >>> v -= vector([3, 3, 3])
   >>> print(v)
   [-2, -1, 0]
 
-  __imul__
+  :__imul__:
 
-  >>> v = vector([1,2,3])
+  >>> v = vector([1, 2, 3])
-  >>> v *= vector([3,3,3])
+  >>> v *= vector([3, 3, 3])
   >>> print(v)
   18
 
-  __imatmul__
+  :__imatmul__:
 
-  >>> m = vector([1,2,3])
+  >>> m = vector([1, 2, 3])
-  >>> m *= vector([3,3,3])
+  >>> m *= vector([3, 3, 3])
   >>> print(v)
   [[3, 3, 3], [6, 6, 6], [9, 9, 9]]
   """
@@ -101,33 +100,43 @@ class vector(list):
     return vector(item) if isinstance(item, list) else item
 
   def __pos__(self):
-    """+ a (new object)
+    """\+ a (new object)
+
+    .. math::
+      \mathbf{b} = +\mathbf{a}
     """
     return vector([*self])
 
   def __neg__(self):
-    """- a (new object)
+    """\- a (new object)
+
+    .. math::
+      \mathbf{b} = -\mathbf{a}
     """
     return vector([-i for i in self])
 
   def __add__(self, other):
     """a + b (new object)
 
+    .. math::
+      \mathbf{c} = \mathbf{a} + \mathbf{b}
+
     :Example:
 
-    >>> v = vector([1,2,3]) + vector([1,2,3])
+    >>> v = vector([1, 2, 3]) + vector([1, 2, 3])
     >>> print(v)
     [2, 4, 6]
     """
     return vector([i+j for i, j in zip(self, other)])
 
+  # overwrite because [1, 2] + [5, 8] = [1, 2, 5, 8]
   def __iadd__(self, other):
     """a += b (new object)
 
     :Example:
 
-    >>> v = vector([1,2,3])
+    >>> v = vector([1, 2, 3])
-    >>> v += vector([3,3,3])
+    >>> v += vector([3, 3, 3])
     >>> print(v)
     [4, 5, 6]
     """
@@ -136,9 +145,12 @@ class vector(list):
   def __sub__(self, other):
     """a - b (new object)
 
+    .. math::
+      \mathbf{c} = \mathbf{a} - \mathbf{b}
+
     :Example:
 
-    >>> v = vector([1,2,3]) - vector([1,2,3])
+    >>> v = vector([1, 2, 3]) - vector([1, 2, 3])
     >>> print(v)
     [0, 0, 0]
     """
@@ -146,9 +158,7 @@ class vector(list):
 
   def __mul__(self, other):
     r"""Scalar multiplication, dot product (inner product) or
-    vector-matrix multiplication.
+    vector-matrix multiplication. (new object)
-
-    a * b (new object)
 
     :type other: scalar, vector (or 1d list), matrix (or 2d list)
 
@@ -158,18 +168,18 @@ class vector(list):
       \mathbf{c} &= \mathbf{a} \cdot \mathbf{B}
 
     .. note::
-      No size checking will be conducted, therefore no exceptions for
+      No size checking will be conducted, therefore no exceptions
-      wrong usage (result will be nonsense).
+      for wrong usage (result will be nonsense).
 
     :Example:
 
-    >>> v = vector([1,2,3,4,5])*3
+    >>> v = vector([1, 2, 3, 4, 5]) * 3
     >>> print(v)
     [3, 6, 9, 12, 15]
-    >>> v = vector([1,2,3,4,5])*3.
+    >>> v = vector([1, 2, 3, 4, 5]) * 3.
     >>> print(v)
     [3.0, 6.0, 9.0, 12.0, 15.0]
-    >>> s = vector([1,2,3])*vector([1,2,3])
+    >>> s = vector([1, 2, 3]) * vector([1, 2, 3])
     >>> print(s)
     14
 
@@ -180,15 +190,14 @@ class vector(list):
       return sum([i*j for i, j in zip(self, other)])
     except:
       try:     # vector * matrix
-        return vector([sum(c*d for c, d in zip(self, b_col)) for b_col in zip(*other)])
+        return vector([sum(c*d for c, d in zip(self, b_col)) for
+                       b_col in zip(*other)])
       except:  # vector * scalar
         return vector([i*other for i in self])
 
   def __rmul__(self, other):
     r"""Scalar multiplication, dot product (inner product) or
-    matrix-vector multiplication.
+    matrix-vector multiplication. (new object)
-
-    a * b (new object)
 
     :type other: scalar (or 1d list and 2d list)
 
@@ -198,24 +207,24 @@ class vector(list):
       \mathbf{c} &= \mathbf{A} \cdot \mathbf{b}
 
     .. note::
-      No size checking will be conducted, therefore no exceptions for
+      No size checking will be conducted, therefore no exceptions
-      wrong usage (result will be nonsense).
+      for wrong usage (result will be nonsense).
 
     :Example:
 
-    >>> v = 3*vector([1,2,3,4,5])
+    >>> v = 3 * vector([1, 2, 3, 4, 5])
     >>> print(v)
     [3, 6, 9, 12, 15]
-    >>> v = 3.*vector([1,2,3,4,5])
+    >>> v = 3. * vector([1, 2, 3, 4, 5])
     >>> print(v)
     [3.0, 6.0, 9.0, 12.0, 15.0]
 
     .. seealso::
-      :meth:`__mul__`
+      :meth:`__mul__` and :meth:`matrix.__mul__` for matrix * vector
-      :meth:`matrix.__mul__` for matrix * vector
     """
     try:     # 2d list * vector (matrix * vector see matrix.__mul__)
-      return vector([sum(c*d for c, d in zip(a_row, self)) for a_row in other])
+      return vector([sum(c*d for c, d in zip(a_row, self)) for
+                     a_row in other])
     except:  # scalar * vector
       return self*other
 
@@ -223,7 +232,7 @@ class vector(list):
     r"""Outer product a @ b (new object)
 
     .. math::
-      \vec{a} \otimes \vec{b}
+      \mathbf{c} = \mathbf{a} \otimes \mathbf{b}
       =
       \begin{pmatrix}
         a_{1}\\
@@ -246,7 +255,7 @@ class vector(list):
 
     :Example:
 
-    >>> m = vector([1,2,3]) @ vector([1,2,4])
+    >>> m = vector([1, 2, 3]) @ vector([1, 2, 4])
     >>> print(m)
     [[1, 2, 4], [2, 4, 8], [3, 6, 12]]
     """
@@ -259,17 +268,80 @@ class vector(list):
     r"""Magnitude / norm of a vector
 
     .. math::
-      b = \sqrt{\sum a_i^2}
+      b = |\mathbf{a}| = \sqrt{\sum a_i^2} =
+      \sqrt{\mathbf{a} \cdot \mathbf{a}}
 
     :Example:
 
-    >>> norm([3, 4])
+    >>> v = vector([3, 4])
-    5
+    >>> abs(v)
-    >>> norm(vector([3, 4]))
+    5.0
-    5
     """
     return math.sqrt(self * self)
 
+  def __lt__(self, other):
+    """Test if this object is lower (smaller) than the other object.
+
+    .. math::
+      |\mathbf{a}| \lt |\mathbf{b}|
+
+    :Example:
+
+    >>> vector([3, 2, 1]) < vector([1, 2, 3])
+    False
+    >>> vector([3, 2, 1]) < vector([1, 2, 4])
+    True
+    """
+    return abs(self) < abs(other)
+
+  def __le__(self, other):
+    """Test if this object is lower (smaller) than or equal the
+    other object.
+
+    .. math::
+      |\mathbf{a}| \le |\mathbf{b}|
+
+    :Example:
+
+    >>> vector([3, 2, 1]) <= vector([1, 2, 3])
+    True
+    >>> vector([3, 2, 1]) <= vector([1, 2, 2])
+    False
+    """
+    return abs(self) <= abs(other)
+
+  def __gt__(self, other):
+    """Test if this object is greater (larger) than the other
+    object.
+
+    .. math::
+      |\mathbf{a}| \gt |\mathbf{b}|
+
+    :Example:
+
+    >>> vector([1, 2, 3]) > vector([3, 2, 1])
+    False
+    >>> vector([1, 2, 3]) > vector([2, 2, 1])
+    True
+    """
+    return abs(self) > abs(other)
+
+  def __ge__(self, other):
+    """Test if this object is greater (larger) than or equal the
+    other object.
+
+    .. math::
+      |\mathbf{a}| \ge |\mathbf{b}|
+
+    :Example:
+
+    >>> vector([1, 2, 3]) >= vector([3, 2, 1])
+    True
+    >>> vector([1, 2, 3]) >= vector([4, 2, 1])
+    False
+    """
+    return abs(self) >= abs(other)
+
   def __str__(self):
     return str([*self])
 
@@ -328,8 +400,8 @@ class vector(list):
 
   @staticmethod
   def random(shape, lmin=0.0, lmax=1.0):
-    """Returns a random vector of length n or matrix of size m rows, n
+    """Returns a random vector of length n or matrix of size m rows,
-    columns filled with random numbers.
+    n columns filled with random numbers.
 
     :Example:
 
@@ -351,10 +423,10 @@ class vector(list):
     :type a: vector
 
     .. math::
-      \vec{e}_a = \frac{\vec{a}}{|\vec{a}|}
+      \mathbf{\hat{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}
 
     .. seealso::
-      :meth:`norm` for a norm (magnitude) of a vector
+      :meth:`__abs__` for a norm (magnitude) of a vector
     """
     a_mag = abs(a)
     return vector([i/a_mag for i in a])
@@ -415,15 +487,12 @@ class vector(list):
     The direction of c can be found with the right-hand rule.
 
     .. math::
-      \vec{c} = \vec{a} \times \vec{b}
+      \mathbf{c} = \mathbf{a} \times \mathbf{b}
     """
     return [a[1]*b[2] - a[2]*b[1],
             a[2]*b[0] - a[0]*b[2],
             a[0]*b[1] - a[1]*b[0]]
 
-  def xyz(self):
-    return self[:3]
-
   def rotate_x(self, theta):
     r"""Rotation about the x dirction.
 
@@ -493,10 +562,10 @@ class vector(list):
 
     uniform scaling if sx=sy=sz=s.
     Note that scaling happens around the origin, so objects not
-    centered at the origin will have their centers move. To avoid this,
+    centered at the origin will have their centers move. To avoid
-    either scale the object when it's located at the origin, or
+    this, either scale the object when it's located at the origin,
-    perform a translation afterwards to move the object back to where
+    or perform a translation afterwards to move the object back to
-    it should be.
+    where it should be.
 
     .. math::
       \begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
@@ -508,16 +577,17 @@ class vector(list):
       \end{bmatrix}
       \begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}
     """
-    if not sy:
+    # if not sy is not suitable because 0 is also false
+    if sy is None:
       sy = sx
       sz = sx
     self[:] = matrix.s(sx, sy, sz) * self
     return self
 
   def ch_cs(self, cs):
-    r"""Transform this vector from its defined coordinate system to a
+    r"""Transform this vector from its defined coordinate system to
-    new coordinate system, defined by the given coordinate system (u,
+    a new coordinate system, defined by the given coordinate system
-    v and w direction vectors).
+    (u, v and w direction vectors).
 
     .. math::
       \begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
@@ -542,21 +612,23 @@ class matrix(list):
 
     :Example:
 
-    >>> m = matrix([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], [0, 0, 0, 0]])
+    >>> m = matrix([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], \
+                    [0, 0, 0, 0]])
     >>> print(m[2])
     [7, 8, 9, 0]
-    >>> print(m[:,1:3])
+    >>> print(m[:, 1:3])
     [[2, 3], [5, 6], [8, 9], [0, 0]]
-    >>> print(m[0:2,1:3])
+    >>> print(m[0:2, 1:3])
     [[2, 3], [5, 6]]
-    >>> print(m[::2,::2])
+    >>> print(m[::2, ::2])
     [[1, 3], [7, 9]]
     """
     # index: slice(stop), slice(start, stop[, step])
-    # for e. g. m[(1,3),:] -> index = ((1, 3), slice(None, None, None))
+    # for m[(1,3),:] -> index = ((1, 3), slice(None, None, None))
     # use the list.__getslice__ method and convert result to vector
     try:    # 2d slicing (tuple of sclices)
-      item = [row.__getitem__(index[1]) for row in super().__getitem__(index[0])]
+      item = [row.__getitem__(index[1]) for
+              row in super().__getitem__(index[0])]
     except: # 1d slicing
       item = super().__getitem__(index)
     return matrix(item) if isinstance(item, list) else item
@@ -568,7 +640,7 @@ class matrix(list):
     Rotates the coordinate system of vectors
 
     .. math::
-      R_{x}(\theta) =
+      \mathbf{R}_{x}(\theta) =
       \begin{bmatrix}
         1 & 0 & 0 & 0 \\
         0 & \cos \theta & -\sin \theta & 0 \\
@@ -591,7 +663,7 @@ class matrix(list):
     Rotates the coordinate system of vectors
 
     .. math::
-      R_{y}(\theta) =
+      \mathbf{R}_{y}(\theta) =
       \begin{bmatrix}
         \cos \theta & 0 & \sin \theta & 0 \\
         0 & 1 & 0 & 0 \\
@@ -614,7 +686,7 @@ class matrix(list):
     Rotates the coordinate system of vectors
 
     .. math::
-      R_{z}(\theta) =
+      \mathbf{R}_{z}(\theta) =
       \begin{bmatrix}
         \cos \theta & -\sin \theta & 0 & 0 \\
         \sin \theta & \cos \theta & 0 & 0 \\
@@ -625,14 +697,17 @@ class matrix(list):
     :Example:
 
     .. math::
-      R_{z}(\theta) \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+      \mathbf{R}_{z}(\theta)
+      \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix}
+      &=
       \begin{bmatrix}
         \cos 90° & -\sin 90° & 0 & 0 \\
         \sin 90° & \cos 90° & 0 & 0 \\
         0 & 0 & 1 & 0 \\
         0 & 0 & 0 & 1
       \end{bmatrix}
-      \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+      \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} \\
+      &=
       \begin{bmatrix}
         0 & -1 & 0 & 0 \\
         1 & 0 & 0 & 0 \\
@@ -655,7 +730,7 @@ class matrix(list):
     r"""Translation matrix
 
     .. math::
-      T =
+      \mathbf{T} =
       \begin{bmatrix}
         1 & 0 & 0 & t_x \\
         0 & 1 & 0 & t_y \\
@@ -675,13 +750,13 @@ class matrix(list):
 
     uniform scaling if sx=sy=sz=s.
     Note that scaling happens around the origin, so objects not
-    centered at the origin will have their centers move. To avoid this,
+    centered at the origin will have their centers move. To avoid
-    either scale the object when it's located at the origin, or
+    this, either scale the object when it's located at the origin,
-    perform a translation afterwards to move the object back to where
+    or perform a translation afterwards to move the object back to
-    it should be.
+    where it should be.
 
     .. math::
-      S =
+      \mathbf{S} =
       \begin{bmatrix}
         s_x & 0 & 0 & 0 \\
         0 & s_y & 0 & 0 \\
@@ -689,7 +764,8 @@ class matrix(list):
         0 & 0 & 0 & 1
       \end{bmatrix}
     """
-    if not sy:
+    # if not sy is not suitable because 0 is also false
+    if sy is None:
       sy = sx
       sz = sx
     T = matrix([[sx, 0, 0, 0],
@@ -700,9 +776,7 @@ class matrix(list):
 
   def __mul__(self, other):
     r"""Scalar multiplication, dot product (inner product) or
-    matrix-vector multiplication.
+    matrix-vector multiplication. (new object)
-
-    a * b (new object)
 
     :type other: scalar, vector (or 1d list), matrix (or 2d list)
 
@@ -712,21 +786,25 @@ class matrix(list):
       \mathbf{C} &= \mathbf{A} \cdot \mathbf{B}
 
     .. note::
-      No size checking will be conducted, therefore no exceptions for
+      No size checking will be conducted, therefore no exceptions
-      wrong usage (result will be nonsense).
+      for wrong usage (result will be nonsense).
 
     :Example:
 
-    >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5
+    >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], \
+                    [0, 0, 0, 1]]) * 5
     >>> print(m)
     [[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]
-    >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5.
+    >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], \
+                    [0, 0, 0, 1]]) * 5.
     >>> print(m)
     [[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]
-    >>> v = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * vector([12, 12, 13])
+    >>> v = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * \
+        vector([12, 12, 13])
     >>> print(v)
     [75, 186, 297]
-    >>> m = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])
+    >>> m = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * \
+        matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])
     >>> print(m)
     [[91, 96, 102], [220, 231, 246], [349, 366, 390]]
 
@@ -734,18 +812,18 @@ class matrix(list):
       :meth:`__rmul__`
     """
     try:       # matrix * matrix
-      return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for b_col in zip(*other)] for a_row in self])
+      return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for
+                      b_col in zip(*other)] for a_row in self])
     except:
       try:     # matrix * vector
-        return vector([sum(c*d for c, d in zip(a_row, other)) for a_row in self])
+        return vector([sum(c*d for c, d in zip(a_row, other)) for
+                       a_row in self])
       except:  # matrix * scalar
         return matrix([[a*other for a in a_row] for a_row in self])
 
   def __rmul__(self, other):
     r"""Scalar multiplication, dot product (inner product) or
-    vector-matrix multiplication.
+    vector-matrix multiplication. (new object)
-
-    a * b (new object)
 
     :type other: scalar (or 1d list and 2d list)
 
@@ -755,27 +833,30 @@ class matrix(list):
       \mathbf{C} &= \mathbf{A} \cdot \mathbf{B}
 
     .. note::
-      No size checking will be conducted, therefore no exceptions for
+      No size checking will be conducted, therefore no exceptions
-      wrong usage (result will be nonsense).
+      for wrong usage (result will be nonsense).
 
     :Example:
 
-    >>> m = 5 * matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5
+    >>> m = 5 * matrix([[1, 2, 3, 4], [5, 6, 7, 8], \
+                        [9, 10, 11, 12], [0, 0, 0, 1]])
     >>> print(m)
     [[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]
-    >>> m = 5. * matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]])
+    >>> m = 5. * matrix([[1, 2, 3, 4], [5, 6, 7, 8], \
+                         [9, 10, 11, 12], [0, 0, 0, 1]])
     >>> print(m)
     [[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]
 
     .. seealso::
-      :meth:`__mul__`
+      :meth:`__mul__` and :meth:`vector.__mul__` for vector * matrix
-      :meth:`vector.__mul__` for vector * matrix
     """
     try:       # 2d list * matrix (matrix * matrix see matrix.__mul__)
-      return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for b_col in zip(*self)] for a_row in other])
+      return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for
+                      b_col in zip(*self)] for a_row in other])
     except:
       try:     # 1d list * matrix (vector * matrix see vector.__mul__)
-        return vector([sum(c*d for c, d in zip(other, b_col)) for b_col in zip(*self)])
+        return vector([sum(c*d for c, d in zip(other, b_col)) for
+                       b_col in zip(*self)])
       except:  # scalar * vector
         return self*other
 
@@ -894,10 +975,10 @@ class matrix(list):
 
     uniform scaling if sx=sy=sz=s.
     Note that scaling happens around the origin, so objects not
-    centered at the origin will have their centers move. To avoid this,
+    centered at the origin will have their centers move. To avoid
-    either scale the object when it's located at the origin, or
+    this, either scale the object when it's located at the origin,
-    perform a translation afterwards to move the object back to where
+    or perform a translation afterwards to move the object back to
-    it should be.
+    where it should be.
 
     .. math::
       \begin{bmatrix}
@@ -919,7 +1000,8 @@ class matrix(list):
         0 & 0 & 0 & h
       \end{bmatrix}
     """
-    if not sy:
+    # if not sy is not suitable because 0 is also false
+    if sy is None:
       sy = sx
       sz = sx
     self[:] = matrix.s(sx, sy, sz) * self

tests/test_data.py

@@ -12,8 +12,8 @@ import unittest
 
 import os
 import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
-from data import read, unique_ending, get_id, seq
+from pylib.data import read, unique_ending, get_id, seq
 
 
 class TestData(unittest.TestCase):

tests/test_fit.py

@@ -13,9 +13,9 @@ import unittest
 import os
 import sys
 from pylab import array, argmax, subplot, plot, title, xlim, show, gradient, linspace
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
-from data import data_read
+from pylib.data import read
-from numerical.fit import gauss_fit
+from pylib.numerical.fit import gauss_fit
 
 
 class TestFit(unittest.TestCase):
@@ -23,7 +23,7 @@ class TestFit(unittest.TestCase):
   def test_gauss(self):
     """test function"""
     file_name = "test_fit.dat"
-    x, y = data_read(file_name, 3, 2)
+    x, y = read(file_name, 3, 2)
 
     subplot(2, 2, 1)
     plot(x, y, '.-')

tests/test_geometry.py

@@ -13,69 +13,85 @@ import unittest
 import os
 import sys
 import math
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
-from mathematics import vector
+from pylib.geometry import Direction, Point, CS, Wireframe, Line, Polygon, Circle
-from geometry import Direction, Point, CS, Wireframe, Polygon
 
 class TestGeometry(unittest.TestCase):
 
   def test_Direction(self):
     p = Direction()
     self.assertIsInstance(
-        p, list)
+        p,
+        list)
     self.assertEqual(
-        p, [1, 0, 0, 0])
+        p,
+        [1, 0, 0, 0])
     self.assertEqual(
-        Direction(2, 3, 4), [2, 3, 4, 0])
+        Direction(2, 3, 4),
+        [2, 3, 4, 0])
 
-    self.assertIsInstance(
+  def test_Direction_getitem(self):
-        p, vector)
     self.assertEqual(
-        p, vector([1, 0, 0, 0]))
+        Direction()[:3],
+        [1, 0, 0])
     self.assertEqual(
-        Direction(2, 3, 4), vector([2, 3, 4, 0]))
+        Direction(1, -1, 1)[:3],
-
+        [1, -1, 1])
-  def test_Direction_xyz(self):
-    self.assertEqual(
-        Direction().xyz(), [1, 0, 0])
-    self.assertEqual(
-        Direction(1, -1, 1).xyz(), [1, -1, 1])
 
   def test_Point(self):
     p = Point()
     self.assertIsInstance(
-        p, list)
+        p,
+        list)
     self.assertEqual(
-        p, [0, 0, 0, 1])
+        p,
+        [0, 0, 0, 1])
     self.assertEqual(
-        Point(2, 3, 4), [2, 3, 4, 1])
+        Point(2, 3, 4),
+        [2, 3, 4, 1])
 
-    self.assertIsInstance(
+  def test_Point_getitem(self):
-        p, vector)
     self.assertEqual(
-        p, vector([0, 0, 0, 1]))
+        Point()[:3],
+        [0, 0, 0])
     self.assertEqual(
-        Point(2, 3, 4), vector([2, 3, 4, 1]))
+        Point(1, -1, 1)[:3],
+        [1, -1, 1])
 
-  def test_Point_xyz(self):
+  def test_Point_rotate(self):
+    [self.assertAlmostEqual(i, j) for i, j in
+     zip(Point(1, 1, 1).rotate_x(math.pi/4), [1, 0, 1.414213562373095, 1])]
+
+  def test_CS(self):
     self.assertEqual(
-        Point().xyz(), [0, 0, 0])
+        CS(),
-    self.assertEqual(
+        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
-        Point(1, -1, 1).xyz(), [1, -1, 1])
+
+  def test_CS_rotate(self):
+    [self.assertAlmostEqual(k, l) for i, j in
+     zip(CS().rotate_y(-math.pi/2),
+         [[0, 0.0, -1.0, 0.0], [0, 1, 0, 0], [1.0, 0.0, 0, 0.0], [0, 0, 0, 1]])
+     for k, l in zip(i, j)]
 
   def test_Wireframe(self):
     self.assertEqual(
-        Wireframe().points(), [])
+        Wireframe().points(),
+        [])
 
     # it is possible to assign other objects then Points but/and the
     # class will not test if Points are used, this is just assumed
     self.assertEqual(
-        Wireframe([]).points(), [[]])
+        Wireframe([]).points(),
+        [[]])
 
     self.assertEqual(
-        Wireframe(Point()).points(), [[0, 0, 0, 1]])
+        Wireframe(Point()).points(),
+        [[0, 0, 0, 1]])
+
+  def test_Line(self):
     self.assertEqual(
-        Wireframe(Point()).points(), [vector([0, 0, 0, 1])])
+        Line().points(),
+        [[-1, 0, 0, 1], [1, 0, 0, 1]])
 
   def test_Polygon(self):
     p0 = Point()
@@ -87,6 +103,14 @@ class TestGeometry(unittest.TestCase):
         pg.points(),
         [[0, 0, 0, 1], [1, 0 , 0, 1], [1, 1, 1, 1], [0, 1, 1, 1], [0, 0, 0, 1]])
 
+  def test_Polygon_rotate(self):
+    pg = Polygon(Point(1, 1, 1)).rotate_x(math.pi/4)
+    [self.assertAlmostEqual(i, j) for i, j in
+     zip(pg.points()[0], [1, 0, 1.414213562373095, 1])]
+    [self.assertAlmostEqual(k, l) for i, j in
+     zip(pg.xyz(), ((1, 1), (0, 0), (1.414213562373095, 1.414213562373095)))
+     for k, l in zip(i, j)]
+
   def test_Polygon_ch_cs(self):
     # example object to rotate
     p0 = Point()
@@ -103,5 +127,23 @@ class TestGeometry(unittest.TestCase):
     pg.ch_cs(cs)
     [self.assertAlmostEqual(i, j) for i, j in zip(pg.points(), test)]
 
+  def test_Circle(self):
+    cs = Circle(n=4).points()
+    test = [[1, 0, 0, 1], [0, 1, 0, 1], [-1, 0, 0, 1], [0, -1, 0 ,1], [1, 0, 0, 1]]
+    [self.assertAlmostEqual(i, j) for i, j in zip(cs, test)]
+
+    cs = Circle().points()
+    test = [[1.0, 0.0, 0, 1],
+            [0.8090169943749475, 0.5877852522924731, 0, 1],
+            [0.30901699437494745, 0.9510565162951535, 0, 1],
+            [-0.30901699437494734, 0.9510565162951536, 0, 1],
+            [-0.8090169943749473, 0.5877852522924732, 0, 1],
+            [-1.0, 1.2246467991473532e-16, 0, 1],
+            [-0.8090169943749476, -0.587785252292473, 0, 1],
+            [-0.30901699437494756, -0.9510565162951535, 0, 1],
+            [0.30901699437494723, -0.9510565162951536, 0, 1],
+            [0.8090169943749473, -0.5877852522924734, 0, 1]]
+    [self.assertAlmostEqual(k, l) for i, j in zip(cs, test) for k, l in zip(i, j) ]
+
 if __name__ == '__main__':
   unittest.main(verbosity=2)

tests/test_geometry2d.py

@@ -14,10 +14,10 @@ import os
 import sys
 import math
 from numpy import allclose
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
-from data import fold_list
+from pylib.data import fold_list
-from geometry2d import translate_xy, rotate_xy, interpolate_hermite, lines, cubics
+from pylib.geometry2d import translate_xy, rotate_xy, interpolate_hermite, lines, cubics
-from geometry2d_plot import plot_lines, plot_cubic_lines
+from pylib.geometry2d_plot import plot_lines, plot_cubic_lines
 
 
 class TestGeometry2d(unittest.TestCase):

tests/test_mathematics.py

@@ -12,10 +12,10 @@ import unittest
 
 import os
 import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
 
 import math
-from mathematics import vector, matrix
+from pylib.mathematics import vector, matrix
 
 class TestGeometry(unittest.TestCase):
 

tests/test_ode.py

@@ -19,10 +19,10 @@ from matplotlib.pyplot import figure, subplots, plot, show
 
 import os
 import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
-from numerical.ode import (e1, e2, e4, i1, newmark_newtonraphson,
+from pylib.numerical.ode import (e1, e2, e4, i1,
-  newmark_newtonraphson_rdk)
+  newmark_newtonraphson, newmark_newtonraphson_rdk)
-from numerical.ode_model import disk, disk_nm, disk_nmmdk
+from pylib.numerical.ode_model import disk, disk_nm, disk_nmmdk
 
 def plotx1rphi(x, t, title):
   """Plot plane rotation (x, y, phi)

tests/test_time_of_day.py

@@ -14,8 +14,8 @@ from time import mktime
 
 import os
 import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
-from time_of_day import (in_seconds, seconds, seconds_norm,
+from pylib.time_of_day import (in_seconds, seconds, seconds_norm,
   minutes, minutes_norm, hours, hours_norm, days, days_norm,
   transform)