add geometry functions to translate and rotate lists and define lines and cubic lines

add data function to fold a list and geometry_plot functions to plot lines and tests for the geometry functions

docs/build/html/geometry.html

@@ -37,20 +37,22 @@
 <p>2D geometry objects.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Date</dt>
-<dd class="field-odd"><p>2019-03-21</p>
+<dd class="field-odd"><p>2019-08-20</p>
 </dd>
 </dl>
 <span class="target" id="module-geometry"></span><dl class="function">
 <dt id="geometry.cubic">
-<code class="sig-name descname">cubic</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em>, <em class="sig-param">samples=50</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubic"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubic" title="Permalink to this definition">¶</a></dt>
-<dd><dl class="field-list simple">
+<code class="sig-name descname">cubic</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em>, <em class="sig-param">samples=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubic"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubic" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cubic line defined by two end points and the rotation in radians
+at the points.</p>
+<dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>point1</strong> (<em>tuple</em>) – one end point</p></li>
 <li><p><strong>angle1</strong> (<em>int</em><em> or </em><em>float</em>) – the slope at the one end point</p></li>
 <li><p><strong>point2</strong> (<em>tuple</em>) – other end point</p></li>
 <li><p><strong>angle2</strong> (<em>int</em><em> or </em><em>float</em>) – the slope at the other end point</p></li>
-<li><p><strong>samples</strong> (<em>int</em>) – number of sampling points</p></li>
+<li><p><strong>samples</strong> (<em>int</em>) – number of sampling points (default = 10)</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns</dt>
@@ -66,7 +68,9 @@
 <dl class="function">
 <dt id="geometry.cubic_deg">
 <code class="sig-name descname">cubic_deg</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubic_deg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubic_deg" title="Permalink to this definition">¶</a></dt>
-<dd><dl class="field-list simple">
+<dd><p>Cubic line defined by two end points and the roation in degree
+at the points.</p>
+<dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>point1</strong> (<em>tuple</em>) – one end point</p></li>
@@ -89,17 +93,91 @@
 </div>
 </dd></dl>
 
+<dl class="function">
+<dt id="geometry.cubics">
+<code class="sig-name descname">cubics</code><span class="sig-paren">(</span><em class="sig-param">pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubics"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubics" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cubic lines defined by a list of two end points. The deformation
+as displacement and rotation (radians) is defined element wise as
+keyword argument deformation or global node wise as
+global_deformation. The global coordinate system is xy. x in the
+right direction and y in the top direction.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>pts</strong> – list of points in absolute global coordinate system. If
+keyword inc is given than the inc decides what the left and the
+right end point of the line is, otherwise it is assumed that the
+points build a solid line, that is lines between the given points
+in given order.</p></li>
+<li><p><strong>**kwargs</strong> – <p>options:</p>
+<ul>
+<li><p>deformation – list of deformation element wise. Additional
+deformation (translation and rotation in radians) at element
+left and right node.</p></li>
+<li><p>rotation_plane – rotation plane of the element wise
+deformation defined by a string; either ‘xy’ or ‘xz’ (default
+= ‘xy’). x in the right direction and y in the top direction
+or z in the bottom direction.</p></li>
+<li><p>global_deformation – list of deformation global node wise.
+Additional deformation (horizontal translation, vertical
+translation and rotation in radians) at node.</p></li>
+<li><p>factor – factor of the derformation (default = 1).</p></li>
+<li><p>inc – the incidence table, a list of 2 element lists. The inc
+decides what the left and the right end point of the line is.</p></li>
+<li><p>index_offset – starting index of lists (default = 0).</p></li>
+</ul>
+</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p>list of endpoints for each line;
+[(((point1_x, point1_y) angle1), ((point2_x, point2_y), angle2),
+(p1, angle1, p2, angle2),
+…]</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>list</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="function">
+<dt id="geometry.interpolate_hermite">
+<code class="sig-name descname">interpolate_hermite</code><span class="sig-paren">(</span><em class="sig-param">lvd</em>, <em class="sig-param">lr</em>, <em class="sig-param">rvd</em>, <em class="sig-param">rr</em>, <em class="sig-param">lhd=0</em>, <em class="sig-param">rhd=0</em>, <em class="sig-param">scale_x=1</em>, <em class="sig-param">scale_y=1</em>, <em class="sig-param">samples=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#interpolate_hermite"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.interpolate_hermite" title="Permalink to this definition">¶</a></dt>
+<dd><p>Interpolate cubic line with hermite boundary conditions.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>lvd</strong> (<em>int</em><em> or </em><em>float</em>) – left vertcal deflection</p></li>
+<li><p><strong>lr</strong> (<em>int</em><em> or </em><em>float</em>) – left rotation</p></li>
+<li><p><strong>rvd</strong> (<em>int</em><em> or </em><em>float</em>) – right vertical deflection</p></li>
+<li><p><strong>rr</strong> (<em>int</em><em> or </em><em>float</em>) – right rotation</p></li>
+<li><p><strong>lhd</strong> (<em>int</em><em> or </em><em>float</em>) – left horizontal deformation (default = 0)</p></li>
+<li><p><strong>rhd</strong> (<em>int</em><em> or </em><em>float</em>) – right horizontal deformation (default = 0)</p></li>
+<li><p><strong>scale_x</strong> (<em>int</em><em> or </em><em>float</em>) – length of element (default = 1)</p></li>
+<li><p><strong>scale_y</strong> (<em>int</em><em> or </em><em>float</em>) – factor of the deformation (default = 1).
+This does not change the length.</p></li>
+<li><p><strong>samples</strong> (<em>int</em>) – number of sampling points (default = 10)</p></li>
+</ul>
+</dd>
+</dl>
+<div class="math notranslate nohighlight">
+\[\begin{split}s = \frac{x - x_1}{L} \\
+x = s\,L + x_1\end{split}\]</div>
+</dd></dl>
+
 <dl class="function">
 <dt id="geometry.line">
 <code class="sig-name descname">line</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2</em>, <em class="sig-param">samples=2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#line"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.line" title="Permalink to this definition">¶</a></dt>
-<dd><div class="math notranslate nohighlight">
+<dd><p>Line defined by two end points.</p>
+<div class="math notranslate nohighlight">
 \[y = \frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1\]</div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>point1</strong> (<em>tuple</em>) – one end point</p></li>
 <li><p><strong>point2</strong> (<em>tuple</em>) – other end point</p></li>
-<li><p><strong>samples</strong> (<em>int</em>) – number of sampling points</p></li>
+<li><p><strong>samples</strong> (<em>int</em>) – number of sampling points (default = 2)</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns</dt>
@@ -110,23 +188,55 @@
 <dt class="field-odd">Return type</dt>
 <dd class="field-odd"><p>tuple</p>
 </dd>
+<dt class="field-even">Example</dt>
+<dd class="field-even"><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">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">line</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">1</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">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+<span class="go">((0, 1), (0, 0))</span>
+</pre></div>
+</div>
 </dd></dl>
 
 <dl class="function">
-<dt id="geometry.points">
-<code class="sig-name descname">points</code><span class="sig-paren">(</span><em class="sig-param">*pts</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#points"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.points" title="Permalink to this definition">¶</a></dt>
-<dd><dl class="field-list simple">
+<dt id="geometry.lines">
+<code class="sig-name descname">lines</code><span class="sig-paren">(</span><em class="sig-param">pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.lines" title="Permalink to this definition">¶</a></dt>
+<dd><p>Lines defined by a list of end points.</p>
+<dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>*pts</strong> – points to rearrange</p>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>pts</strong> (<em>list</em>) – list of points in absolute global coordinate system. If
+keyword inc is given than the inc decides what the left and the
+right end point of the line is, otherwise it is assumed that the
+points build a solid line, that is lines between the given points
+in given order.</p></li>
+<li><p><strong>**kwargs</strong> – <p>options:</p>
+<ul>
+<li><p>deformation – list of points. Additional deformation
+(translation) at point.</p></li>
+<li><p>factor – factor of the deformation (default = 1).</p></li>
+<li><p>inc – the incidence table, a list of 2 element lists. The inc
+decides what the left and the right end point of the line is.</p></li>
+<li><p>index_offset – starting index of lists (default = 0).</p></li>
+</ul>
+</p></li>
+</ul>
 </dd>
 <dt class="field-even">Returns</dt>
-<dd class="field-even"><p>((point1_x, point2_x), (point1_y, point2_y), …)</p>
+<dd class="field-even"><p>list of endpoints for each line;
+[((point1_x, point1_y), (point2_x, point2_y)),
+(p1, p2),
+…]</p>
 </dd>
 <dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>tuple</p>
+<dd class="field-odd"><p>list</p>
 </dd>
 </dl>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="geometry_plot.html#geometry_plot.plot_lines" title="geometry_plot.plot_lines"><code class="xref py py-meth docutils literal notranslate"><span class="pre">plot_lines()</span></code></a> of the <a class="reference internal" href="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>
 
 <dl class="function">
@@ -151,8 +261,8 @@
 <dl class="function">
 <dt id="geometry.rotate">
 <code class="sig-name descname">rotate</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">*pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rotate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rotate" title="Permalink to this definition">¶</a></dt>
-<dd><p>Rotate a point or polygon counterclockwise by a given angle around a given
-origin. The angle should be given in radians.</p>
+<dd><p>Rotate a point or polygon counterclockwise by a given angle
+around a given origin. The angle should be given in radians.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
@@ -169,13 +279,17 @@ origin. The angle should be given in radians.</p>
 <dd class="field-odd"><p>tuple</p>
 </dd>
 </dl>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#geometry.rotate_xy" title="geometry.rotate_xy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate_xy()</span></code></a></p>
+</div>
 </dd></dl>
 
 <dl class="function">
 <dt id="geometry.rotate_deg">
 <code class="sig-name descname">rotate_deg</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">*pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rotate_deg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rotate_deg" title="Permalink to this definition">¶</a></dt>
-<dd><p>Rotate a point or polygon counterclockwise by a given angle around a given
-origin. The angle should be given in degrees.</p>
+<dd><p>Rotate a point or polygon counterclockwise by a given angle
+around a given origin. The angle should be given in degrees.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
@@ -198,6 +312,28 @@ origin. The angle should be given in degrees.</p>
 </div>
 </dd></dl>
 
+<dl class="function">
+<dt id="geometry.rotate_xy">
+<code class="sig-name descname">rotate_xy</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">x</em>, <em class="sig-param">y</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rotate_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rotate_xy" title="Permalink to this definition">¶</a></dt>
+<dd><p>Rotate x and y coordinates counterclockwise by a given angle
+around a given origin. The angle should be given in radians.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>origin</strong> (<em>tuple</em>) – the center of rotation</p></li>
+<li><p><strong>angle</strong> (<em>int</em><em> or </em><em>float</em>) – the rotation angle</p></li>
+<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em>) – x coordinates</p></li>
+<li><p><strong>y</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em>) – y coordinates</p></li>
+<li><p><strong>**kwargs</strong> – options</p></li>
+</ul>
+</dd>
+</dl>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#geometry.rotate" title="geometry.rotate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate()</span></code></a></p>
+</div>
+</dd></dl>
+
 <dl class="function">
 <dt id="geometry.square">
 <code class="sig-name descname">square</code><span class="sig-paren">(</span><em class="sig-param">width</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#square"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.square" title="Permalink to this definition">¶</a></dt>
@@ -236,6 +372,35 @@ origin. The angle should be given in degrees.</p>
 <dd class="field-odd"><p>tuple</p>
 </dd>
 </dl>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#geometry.translate_xy" title="geometry.translate_xy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">translate_xy()</span></code></a></p>
+</div>
+</dd></dl>
+
+<dl class="function">
+<dt id="geometry.translate_xy">
+<code class="sig-name descname">translate_xy</code><span class="sig-paren">(</span><em class="sig-param">vec</em>, <em class="sig-param">x</em>, <em class="sig-param">y</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#translate_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.translate_xy" title="Permalink to this definition">¶</a></dt>
+<dd><p>Translate a point or polygon by a given vector.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>vec</strong> (<em>tuple</em>) – translation vector</p></li>
+<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em>) – points to translate</p></li>
+<li><p><strong>y</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em>) – points to translate</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p>(x’, y’)</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>tuple</p>
+</dd>
+</dl>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#geometry.translate" title="geometry.translate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">translate()</span></code></a></p>
+</div>
 </dd></dl>
 
 </div>
@@ -291,7 +456,7 @@ origin. The angle should be given in degrees.</p>
       &copy;2019, Daniel Weschke.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 2.1.2</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 2.2.0</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
       
       |