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<h1>Source code for 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">:Date: 2019-08-28</span>
<span class="sd">.. module:: geometry</span>
<span class="sd"> :platform: *nix, Windows</span>
<span class="sd"> :synopsis: Geometry objects.</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="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<div class="viewcode-block" id="distance"><a class="viewcode-back" href="../geometry.html#geometry.distance">[docs]</a><span class="k">def</span> <span class="nf">distance</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="sd">&quot;&quot;&quot;Distance between two points (or length of a straight line).</span>
<span class="sd"> :param point1: first point (first end point of straight line)</span>
<span class="sd"> :type point1: tuple</span>
<span class="sd"> :param point2: second point (second end point of straight line)</span>
<span class="sd"> :type point2: tuple</span>
<span class="sd"> :returns: distance between the two points</span>
<span class="sd"> :rtype: float</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="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</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="o">+</span> <span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</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></div>
<div class="viewcode-block" id="angle"><a class="viewcode-back" href="../geometry.html#geometry.angle">[docs]</a><span class="k">def</span> <span class="nf">angle</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Angle of point or between two points.</span>
<span class="sd"> :param point1: (first) point</span>
<span class="sd"> :type point1: tuple</span>
<span class="sd"> :param point2: second point (default = None)</span>
<span class="sd"> :type point2: tuple</span>
<span class="sd"> :returns: angle of point or between two points</span>
<span class="sd"> :rtype: float</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">point2</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span></div>
<div class="viewcode-block" id="translate"><a class="viewcode-back" href="../geometry.html#geometry.translate">[docs]</a><span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Translate a point or polygon by a given vector.</span>
<span class="sd"> :param vec: translation vector</span>
<span class="sd"> :type vec: tuple</span>
<span class="sd"> :param `*pts`: points to translate</span>
<span class="sd"> :returns: (point_x, point_y) or (point1, point2, ...)</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`translate_xy`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">vx</span><span class="p">,</span> <span class="n">vy</span> <span class="o">=</span> <span class="n">vec</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">([(</span><span class="n">x</span><span class="o">+</span><span class="n">vx</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="n">vy</span><span class="p">)</span> <span class="k">for</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="ow">in</span> <span class="n">pts</span><span class="p">])</span></div>
<div class="viewcode-block" id="translate_xy"><a class="viewcode-back" href="../geometry.html#geometry.translate_xy">[docs]</a><span class="k">def</span> <span class="nf">translate_xy</span><span class="p">(</span><span class="n">vec</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="sd">&quot;&quot;&quot;Translate a point or polygon by a given vector.</span>
<span class="sd"> :param vec: translation vector</span>
<span class="sd"> :type vec: tuple</span>
<span class="sd"> :param x: points to translate</span>
<span class="sd"> :type x: int or float or list</span>
<span class="sd"> :param y: points to translate</span>
<span class="sd"> :type y: int or float or list</span>
<span class="sd"> :returns: (x&#39;, y&#39;)</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`translate`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">vx</span><span class="p">,</span> <span class="n">vy</span> <span class="o">=</span> <span class="n">vec</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s2">&quot;__len__&quot;</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="s2">&quot;__len__&quot;</span><span class="p">):</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">y</span><span class="p">]</span>
<span class="n">xp</span> <span class="o">=</span> <span class="p">[</span><span class="n">xi</span><span class="o">+</span><span class="n">vx</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">yp</span> <span class="o">=</span> <span class="p">[</span><span class="n">yi</span><span class="o">+</span><span class="n">vy</span> <span class="k">for</span> <span class="n">yi</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
<span class="c1"># no list if it is only one value</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">xp</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">xp</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">yp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">return</span> <span class="n">xp</span><span class="p">,</span> <span class="n">yp</span></div>
<div class="viewcode-block" id="rotate"><a class="viewcode-back" href="../geometry.html#geometry.rotate">[docs]</a><span class="k">def</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Rotate a point or polygon counterclockwise by a given angle</span>
<span class="sd"> around a given origin. The angle should be given in radians.</span>
<span class="sd"> :param origin: the center of rotation</span>
<span class="sd"> :type origin: tuple</span>
<span class="sd"> :param angle: the rotation angle</span>
<span class="sd"> :type angle: int or float</span>
<span class="sd"> :param `*pts`: points to rotate</span>
<span class="sd"> :param `**kwargs`: options</span>
<span class="sd"> :returns: (point_x, point_y) or (point1, point2, ...)</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`rotate_xy`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">ox</span><span class="p">,</span> <span class="n">oy</span> <span class="o">=</span> <span class="n">origin</span>
<span class="c1"># add first point to the end</span>
<span class="k">if</span> <span class="s2">&quot;closed&quot;</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="n">kwargs</span><span class="p">[</span><span class="s2">&quot;closed&quot;</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">pts</span> <span class="o">+=</span> <span class="p">(</span><span class="n">pts</span><span class="p">[</span><span class="mi">0</span><span class="p">],)</span>
<span class="n">result</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">([(</span><span class="n">ox</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">px</span> <span class="o">-</span> <span class="n">ox</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">py</span> <span class="o">-</span> <span class="n">oy</span><span class="p">),</span>
<span class="n">oy</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">px</span> <span class="o">-</span> <span class="n">ox</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">py</span> <span class="o">-</span> <span class="n">oy</span><span class="p">))</span>
<span class="k">for</span> <span class="p">(</span><span class="n">px</span><span class="p">,</span> <span class="n">py</span><span class="p">)</span> <span class="ow">in</span> <span class="n">pts</span><span class="p">])</span>
<span class="c1"># no tuple in tuple if it is only one point</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">pts</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">result</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">result</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">result</span></div>
<div class="viewcode-block" id="rotate_deg"><a class="viewcode-back" href="../geometry.html#geometry.rotate_deg">[docs]</a><span class="k">def</span> <span class="nf">rotate_deg</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Rotate a point or polygon counterclockwise by a given angle</span>
<span class="sd"> around a given origin. The angle should be given in degrees.</span>
<span class="sd"> :param origin: the center of rotation</span>
<span class="sd"> :type origin: tuple</span>
<span class="sd"> :param angle: the rotation angle</span>
<span class="sd"> :type angle: int or float</span>
<span class="sd"> :param `*pts`: points to rotate</span>
<span class="sd"> :param `**kwargs`: options</span>
<span class="sd"> :returns: (point_x, point_y) or (point1, point2, ...)</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`rotate`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</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="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
<div class="viewcode-block" id="rotate_xy"><a class="viewcode-back" href="../geometry.html#geometry.rotate_xy">[docs]</a><span class="k">def</span> <span class="nf">rotate_xy</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</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="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Rotate x and y coordinates counterclockwise by a given angle</span>
<span class="sd"> around a given origin. The angle should be given in radians.</span>
<span class="sd"> :param origin: the center of rotation</span>
<span class="sd"> :type origin: tuple</span>
<span class="sd"> :param angle: the rotation angle</span>
<span class="sd"> :type angle: int or float</span>
<span class="sd"> :param x: x coordinates</span>
<span class="sd"> :type x: int or float or list</span>
<span class="sd"> :param y: y coordinates</span>
<span class="sd"> :type y: int or float or list</span>
<span class="sd"> :param `**kwargs`: options</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`rotate`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">ox</span><span class="p">,</span> <span class="n">oy</span> <span class="o">=</span> <span class="n">origin</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s2">&quot;__len__&quot;</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="s2">&quot;__len__&quot;</span><span class="p">):</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">y</span><span class="p">]</span>
<span class="c1"># add first point to the end</span>
<span class="k">if</span> <span class="s2">&quot;closed&quot;</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="n">kwargs</span><span class="p">[</span><span class="s2">&quot;closed&quot;</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</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="n">append</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="n">x_result</span> <span class="o">=</span> <span class="p">[</span><span class="n">ox</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">xi</span> <span class="o">-</span> <span class="n">ox</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">yi</span> <span class="o">-</span> <span class="n">oy</span><span class="p">)</span>
<span class="k">for</span> <span class="n">xi</span><span class="p">,</span> <span class="n">yi</span> <span class="ow">in</span> <span class="nb">zip</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">y_result</span> <span class="o">=</span> <span class="p">[</span><span class="n">oy</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">xi</span> <span class="o">-</span> <span class="n">ox</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">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">yi</span> <span class="o">-</span> <span class="n">oy</span><span class="p">)</span>
<span class="k">for</span> <span class="n">xi</span><span class="p">,</span> <span class="n">yi</span> <span class="ow">in</span> <span class="nb">zip</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="c1"># no list if it is only one value</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x_result</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">x_result</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">y_result</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">return</span> <span class="n">x_result</span><span class="p">,</span> <span class="n">y_result</span></div>
<div class="viewcode-block" id="rectangle"><a class="viewcode-back" href="../geometry.html#geometry.rectangle">[docs]</a><span class="k">def</span> <span class="nf">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;\</span>
<span class="sd"> :param width: the width of the rectangle</span>
<span class="sd"> :type width: int or float</span>
<span class="sd"> :param height: the height of the rectangle</span>
<span class="sd"> :type height: int or float</span>
<span class="sd"> :returns: (point1, point2, point3, point4)</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">pt1</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pt2</span> <span class="o">=</span> <span class="p">(</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pt3</span> <span class="o">=</span> <span class="p">(</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pt4</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="n">pt1</span><span class="p">,</span> <span class="n">pt2</span><span class="p">,</span> <span class="n">pt3</span><span class="p">,</span> <span class="n">pt4</span><span class="p">,</span> <span class="n">pt1</span></div>
<div class="viewcode-block" id="square"><a class="viewcode-back" href="../geometry.html#geometry.square">[docs]</a><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">width</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;\</span>
<span class="sd"> :param width: the edge size of the square</span>
<span class="sd"> :type width: int or float</span>
<span class="sd"> :returns: (point1, point2, point3, point4)</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`rectangle`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span></div>
<div class="viewcode-block" id="lines"><a class="viewcode-back" href="../geometry.html#geometry.lines">[docs]</a><span class="k">def</span> <span class="nf">lines</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Lines defined by a list of end points.</span>
<span class="sd"> :param pts: list of points in absolute global coordinate system. If</span>
<span class="sd"> keyword inc is given than the inc decides what the left and the</span>
<span class="sd"> right end point of the line is, otherwise it is assumed that the</span>
<span class="sd"> points build a solid line, that is lines between the given points</span>
<span class="sd"> in given order.</span>
<span class="sd"> :type pts: list</span>
<span class="sd"> :param `**kwargs`: options:</span>
<span class="sd"> * deformation -- list of points. Additional deformation</span>
<span class="sd"> (translation) at point.</span>
<span class="sd"> * factor -- factor of the deformation (default = 1).</span>
<span class="sd"> * inc -- the incidence table, a list of 2 element lists. The inc</span>
<span class="sd"> decides what the left and the right end point of the line is.</span>
<span class="sd"> * index_offset -- starting index of lists (default = 0).</span>
<span class="sd"> :returns: list of endpoints for each line;</span>
<span class="sd"> [((point1_x, point1_y), (point2_x, point2_y)),</span>
<span class="sd"> (p1, p2),</span>
<span class="sd"> ...]</span>
<span class="sd"> :rtype: list</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`~geometry_plot.plot_lines` of the :mod:`geometry_plot`</span>
<span class="sd"> module to plot the lines</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="s1">&#39;index_offset&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">if</span> <span class="s1">&#39;deformation&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="k">if</span> <span class="s1">&#39;factor&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">pts</span> <span class="o">=</span> <span class="p">[(</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</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="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">d</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">])</span> <span class="k">for</span>
<span class="n">p</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">pts</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;deformation&#39;</span><span class="p">])]</span>
<span class="k">if</span> <span class="s1">&#39;inc&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="k">return</span> <span class="p">[(</span><span class="n">pts</span><span class="p">[</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]],</span>
<span class="n">pts</span><span class="p">[</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]])</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;inc&#39;</span><span class="p">]]</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="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
<div class="viewcode-block" id="cubics"><a class="viewcode-back" href="../geometry.html#geometry.cubics">[docs]</a><span class="k">def</span> <span class="nf">cubics</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Cubic lines defined by a list of two end points. The deformation</span>
<span class="sd"> as displacement and rotation (radians) is defined element wise as</span>
<span class="sd"> keyword argument deformation or global node wise as</span>
<span class="sd"> global_deformation. The global coordinate system is xy. x in the</span>
<span class="sd"> right direction and y in the top direction.</span>
<span class="sd"> :param pts: list of points in absolute global coordinate system. If</span>
<span class="sd"> keyword inc is given than the inc decides what the left and the</span>
<span class="sd"> right end point of the line is, otherwise it is assumed that the</span>
<span class="sd"> points build a solid line, that is lines between the given points</span>
<span class="sd"> in given order.</span>
<span class="sd"> :type pts_rot: list</span>
<span class="sd"> :param `**kwargs`: options:</span>
<span class="sd"> * deformation -- list of deformation element wise. Additional</span>
<span class="sd"> deformation (translation and rotation in radians) at element</span>
<span class="sd"> left and right node.</span>
<span class="sd"> * rotation_plane -- rotation plane of the element wise</span>
<span class="sd"> deformation defined by a string; either &#39;xy&#39; or &#39;xz&#39; (default</span>
<span class="sd"> = &#39;xy&#39;). x in the right direction and y in the top direction</span>
<span class="sd"> or z in the bottom direction.</span>
<span class="sd"> * global_deformation -- list of deformation global node wise.</span>
<span class="sd"> Additional deformation (horizontal translation, vertical</span>
<span class="sd"> translation and rotation in radians) at node.</span>
<span class="sd"> * factor -- factor of the derformation (default = 1).</span>
<span class="sd"> * inc -- the incidence table, a list of 2 element lists. The inc</span>
<span class="sd"> decides what the left and the right end point of the line is.</span>
<span class="sd"> * index_offset -- starting index of lists (default = 0).</span>
<span class="sd"> :returns: list of endpoints for each line;</span>
<span class="sd"> [(((point1_x, point1_y) angle1), ((point2_x, point2_y), angle2),</span>
<span class="sd"> (p1, angle1, p2, angle2),</span>
<span class="sd"> ...]</span>
<span class="sd"> :rtype: list</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="s1">&#39;index_offset&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">if</span> <span class="s1">&#39;deformation&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">or</span> <span class="s1">&#39;global_deformation&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="k">if</span> <span class="s1">&#39;factor&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="s1">&#39;inc&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="k">if</span> <span class="s1">&#39;global_deformation&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
<span class="n">lr</span> <span class="o">=</span> <span class="p">[(</span><span class="n">pts</span><span class="p">[</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]],</span>
<span class="n">pts</span><span class="p">[</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]])</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;inc&#39;</span><span class="p">]]</span>
<span class="n">ang</span> <span class="o">=</span> <span class="p">[</span><span class="n">angle</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">lr</span><span class="p">]</span>
<span class="c1"># system deformation</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;global_deformation&#39;</span><span class="p">]</span>
<span class="k">if</span> <span class="s1">&#39;rotation_plane&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="s1">&#39;xz&#39;</span> <span class="o">==</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;rotation_plane&#39;</span><span class="p">]:</span>
<span class="c1"># system deformation left X Z RY right X Z RY element wise</span>
<span class="c1"># Z downwards -&gt; convert to X Y RZ</span>
<span class="n">Ue</span> <span class="o">=</span> <span class="p">[[</span> <span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
<span class="o">-</span><span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">2</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
<span class="o">-</span><span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">2</span><span class="p">]]</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;inc&#39;</span><span class="p">]]</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># system deformation left X Y RZ right X Y RZ element wise</span>
<span class="n">Ue</span> <span class="o">=</span> <span class="p">[[</span><span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">2</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">])][</span><span class="mi">2</span><span class="p">]]</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;inc&#39;</span><span class="p">]]</span>
<span class="c1"># element deformation, X Y RZ to x r rz</span>
<span class="c1"># back transformation T^T = [[c, s, 0], [-s, c, 0], [0, 0, 1]]</span>
<span class="n">u</span> <span class="o">=</span> <span class="p">[[(</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">0</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">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</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">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">0</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">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="n">Uei</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="p">(</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">3</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">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</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">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">3</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">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="n">Uei</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span> <span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">]]</span>
<span class="k">for</span> <span class="n">Uei</span><span class="p">,</span> <span class="n">angi</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">Ue</span><span class="p">,</span> <span class="n">ang</span><span class="p">)]</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># deformation</span>
<span class="c1"># the deformation is in element coordinate system, therefore the angle is needed</span>
<span class="k">if</span> <span class="s1">&#39;rotation_plane&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="s1">&#39;xz&#39;</span> <span class="o">==</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;rotation_plane&#39;</span><span class="p">]:</span>
<span class="n">u</span> <span class="o">=</span> <span class="p">[[</span> <span class="n">ue</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="o">-</span><span class="n">ue</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="n">ue</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="n">ue</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="o">-</span><span class="n">ue</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">],</span>
<span class="n">ue</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">]]</span> <span class="k">for</span> <span class="n">ue</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;deformation&#39;</span><span class="p">]]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">u</span> <span class="o">=</span> <span class="p">[[</span><span class="n">ui</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;factor&#39;</span><span class="p">]</span> <span class="k">for</span> <span class="n">ui</span> <span class="ow">in</span> <span class="n">ue</span><span class="p">]</span> <span class="k">for</span> <span class="n">ue</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;deformation&#39;</span><span class="p">]]</span>
<span class="k">return</span> <span class="p">[(</span><span class="n">pts</span><span class="p">[</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]],</span>
<span class="n">pts</span><span class="p">[</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;index_offset&#39;</span><span class="p">]],</span>
<span class="n">d</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</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">kwargs</span><span class="p">[</span><span class="s1">&#39;inc&#39;</span><span class="p">],</span> <span class="n">u</span><span class="p">)]</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="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
<div class="viewcode-block" id="interpolate_hermite"><a class="viewcode-back" href="../geometry.html#geometry.interpolate_hermite">[docs]</a><span class="k">def</span> <span class="nf">interpolate_hermite</span><span class="p">(</span><span class="n">lvd</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">rvd</span><span class="p">,</span> <span class="n">rr</span><span class="p">,</span> <span class="n">lhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">rhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">scale_x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_y</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">&quot;&quot;&quot;Interpolate cubic line with hermite boundary conditions.</span>
<span class="sd"> :param lvd: left vertcal deflection</span>
<span class="sd"> :type lvd: int or float</span>
<span class="sd"> :param lr: left rotation</span>
<span class="sd"> :type lr: int or float</span>
<span class="sd"> :param rvd: right vertical deflection</span>
<span class="sd"> :type rvd: int or float</span>
<span class="sd"> :param rr: right rotation</span>
<span class="sd"> :type rr: int or float</span>
<span class="sd"> :param lhd: left horizontal deformation (default = 0)</span>
<span class="sd"> :type lhd: int or float</span>
<span class="sd"> :param rhd: right horizontal deformation (default = 0)</span>
<span class="sd"> :type rhd: int or float</span>
<span class="sd"> :param scale_x: length of element (default = 1)</span>
<span class="sd"> :type scale_x: int or float</span>
<span class="sd"> :param scale_y: factor of the deformation (default = 1).</span>
<span class="sd"> This does not change the length.</span>
<span class="sd"> :type scale_y: int or float</span>
<span class="sd"> :param samples: number of sampling points (default = 10)</span>
<span class="sd"> :type samples: int</span>
<span class="sd"> .. math::</span>
<span class="sd"> s = \frac{x - x_1}{L} \\</span>
<span class="sd"> x = s\,L + x_1</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">L</span> <span class="o">=</span> <span class="n">scale_x</span>
<span class="n">Lp</span> <span class="o">=</span> <span class="n">L</span> <span class="o">+</span> <span class="n">rhd</span> <span class="o">-</span> <span class="n">lhd</span>
<span class="c1"># x=[0,1] in non-dimensional coordinates</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">num</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
<span class="n">N1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span>
<span class="n">N2</span> <span class="o">=</span> <span class="p">(</span> <span class="n">x</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">*</span><span class="n">Lp</span>
<span class="n">N3</span> <span class="o">=</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span>
<span class="n">N4</span> <span class="o">=</span> <span class="p">(</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">*</span><span class="n">Lp</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">*</span><span class="n">Lp</span>
<span class="c1"># x=[0,L] in global coordinates</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">Lp</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
<span class="n">N1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">3</span>
<span class="n">N2</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span>
<span class="n">N3</span> <span class="o">=</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">3</span>
<span class="n">N4</span> <span class="o">=</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">N1</span><span class="o">*</span><span class="n">lvd</span> <span class="o">+</span> <span class="n">N2</span><span class="o">*</span><span class="n">lr</span> <span class="o">+</span> <span class="n">N3</span><span class="o">*</span><span class="n">rvd</span> <span class="o">+</span> <span class="n">N4</span><span class="o">*</span><span class="n">rr</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">lhd</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">v</span><span class="o">*</span><span class="n">scale_y</span>
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
<span class="c1">#</span>
<span class="c1"># matplotlib format, return lists for x and y</span>
<span class="c1">#</span>
<div class="viewcode-block" id="line"><a class="viewcode-back" href="../geometry.html#geometry.line">[docs]</a><span class="k">def</span> <span class="nf">line</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">samples</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Line defined by two end points.</span>
<span class="sd"> .. math::</span>
<span class="sd"> y = \\frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1</span>
<span class="sd"> :param point1: one end point</span>
<span class="sd"> :type point1: tuple</span>
<span class="sd"> :param point2: other end point</span>
<span class="sd"> :type point2: tuple</span>
<span class="sd"> :param samples: number of sampling points (default = 2)</span>
<span class="sd"> :type samples: int</span>
<span class="sd"> :returns: ((point1_x, point2_x), (points1_y, point2_y)) or</span>
<span class="sd"> ([sample_point1_x, sample_point2_x, ...],</span>
<span class="sd"> [sample_points1_y, sample_point2_y, ...])</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> :Example:</span>
<span class="sd"> &gt;&gt;&gt; x, y = line((0, 0), (1, 0))</span>
<span class="sd"> &gt;&gt;&gt; print(x, y)</span>
<span class="sd"> ((0, 1), (0, 0))</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">p1x</span><span class="p">,</span> <span class="n">p1y</span> <span class="o">=</span> <span class="n">point1</span>
<span class="n">p2x</span><span class="p">,</span> <span class="n">p2y</span> <span class="o">=</span> <span class="n">point2</span>
<span class="n">denominator</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span> <span class="o">-</span> <span class="n">p2x</span><span class="p">)</span>
<span class="k">if</span> <span class="n">samples</span> <span class="o">&gt;</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">denominator</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">,</span> <span class="n">samples</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1y</span> <span class="o">-</span> <span class="n">p2y</span><span class="p">)</span> <span class="o">/</span> <span class="n">denominator</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">*</span><span class="n">p1y</span><span class="p">)</span> <span class="o">/</span> <span class="n">denominator</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">b</span>
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
<span class="k">return</span> <span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">),</span> <span class="p">(</span><span class="n">p1y</span><span class="p">,</span> <span class="n">p2y</span><span class="p">)</span> <span class="c1"># matplotlib format</span></div>
<div class="viewcode-block" id="cubic"><a class="viewcode-back" href="../geometry.html#geometry.cubic">[docs]</a><span class="k">def</span> <span class="nf">cubic</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Cubic line defined by two end points and the rotation in radians</span>
<span class="sd"> at the points.</span>
<span class="sd"> :param point1: one end point</span>
<span class="sd"> :type point1: tuple</span>
<span class="sd"> :param angle1: the slope at the one end point</span>
<span class="sd"> :type angle1: int or float</span>
<span class="sd"> :param point2: other end point</span>
<span class="sd"> :type point2: tuple</span>
<span class="sd"> :param angle2: the slope at the other end point</span>
<span class="sd"> :type angle2: int or float</span>
<span class="sd"> :param samples: number of sampling points (default = 10)</span>
<span class="sd"> :type samples: int</span>
<span class="sd"> :returns: ([sample_point1_x, sample_point2_x, ...],</span>
<span class="sd"> [sample_points1_y, sample_point2_y, ...])</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">p1x</span><span class="p">,</span> <span class="n">p1y</span> <span class="o">=</span> <span class="n">point1</span>
<span class="n">p2x</span><span class="p">,</span> <span class="n">p2y</span> <span class="o">=</span> <span class="n">point2</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
<span class="n">p1ys</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">angle1</span><span class="p">)</span>
<span class="n">p2ys</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">angle2</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1y</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">p2y</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p1y</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1y</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2y</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="mi">6</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1y</span> <span class="o">+</span> <span class="mi">6</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p1ys</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p2y</span> <span class="o">-</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1y</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p1y</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span> <span class="o">+</span> <span class="n">b</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">c</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">d</span>
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
<div class="viewcode-block" id="cubic_deg"><a class="viewcode-back" href="../geometry.html#geometry.cubic_deg">[docs]</a><span class="k">def</span> <span class="nf">cubic_deg</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Cubic line defined by two end points and the roation in degree</span>
<span class="sd"> at the points.</span>
<span class="sd"> :param point1: one end point</span>
<span class="sd"> :type point1: tuple</span>
<span class="sd"> :param angle1: the slope at the one end point</span>
<span class="sd"> :type angle1: int or float</span>
<span class="sd"> :param point2: other end point</span>
<span class="sd"> :type point2: tuple</span>
<span class="sd"> :param angle2: the slope at the other end point</span>
<span class="sd"> :type angle2: int or float</span>
<span class="sd"> :returns: ([sample_point1_x, sample_point2_x, ...],</span>
<span class="sd"> [sample_points1_y, sample_point2_y, ...])</span>
<span class="sd"> :rtype: tuple</span>
<span class="sd"> .. seealso::</span>
<span class="sd"> :meth:`cubic`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">cubic</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</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="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</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="p">)</span></div>
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