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pylib/docs/build/html/geometry.html
Daniel Weschke f47fa19cd2 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
2019-08-28 11:39:50 +02:00

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<div class="section" id="module-geometry">
<span id="geometry-module"></span><h1>geometry module<a class="headerlink" href="#module-geometry" title="Permalink to this headline"></a></h1>
<p>2D geometry objects.</p>
<dl class="field-list simple">
<dt class="field-odd">Date</dt>
<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=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 (default = 10)</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>([sample_point1_x, sample_point2_x, …],
[sample_points1_y, sample_point2_y, …])</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
<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><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>
<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>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>([sample_point1_x, sample_point2_x, …],
[sample_points1_y, sample_point2_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.cubic" title="geometry.cubic"><code class="xref py py-meth docutils literal notranslate"><span class="pre">cubic()</span></code></a></p>
</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><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 (default = 2)</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>((point1_x, point2_x), (points1_y, point2_y)) or
([sample_point1_x, sample_point2_x, …],
[sample_points1_y, sample_point2_y, …])</p>
</dd>
<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.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"><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>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>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">
<dt id="geometry.rectangle">
<code class="sig-name descname">rectangle</code><span class="sig-paren">(</span><em class="sig-param">width</em>, <em class="sig-param">height</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rectangle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rectangle" title="Permalink to this definition"></a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>width</strong> (<em>int</em><em> or </em><em>float</em>) the width of the rectangle</p></li>
<li><p><strong>height</strong> (<em>int</em><em> or </em><em>float</em>) the height of the rectangle</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point1, point2, point3, point4)</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
<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>
<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>*pts</strong> points to rotate</p></li>
<li><p><strong>**kwargs</strong> options</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point_x, point_y) or (point1, point2, …)</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.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>
<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>*pts</strong> points to rotate</p></li>
<li><p><strong>**kwargs</strong> options</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point_x, point_y) or (point1, point2, …)</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.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.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>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>width</strong> (<em>int</em><em> or </em><em>float</em>) the edge size of the square</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point1, point2, point3, point4)</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.rectangle" title="geometry.rectangle"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rectangle()</span></code></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="geometry.translate">
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">vec</em>, <em class="sig-param">*pts</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.translate" 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>*pts</strong> points to translate</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point_x, point_y) or (point1, point2, …)</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_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>
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