add parametric equations for hypotrochoid
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@@ -35,17 +35,18 @@
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<h1>Source code for function</h1><div class="highlight"><pre>
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<span></span><span class="ch">#!/usr/bin/env python</span>
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<span class="c1"># -*- coding: utf-8 -*-</span>
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<span class="sd">"""Mathematical functions.</span>
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<span class="sd">"""Mathematical equations.</span>
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<span class="sd">:Date: 2019-10-27</span>
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<span class="sd">:Date: 2019-11-01</span>
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<span class="sd">.. module:: function</span>
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<span class="sd"> :platform: *nix, Windows</span>
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<span class="sd"> :synopsis: Mathematical functions.</span>
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<span class="sd"> :synopsis: Mathematical equations.</span>
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<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
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<span class="sd">"""</span>
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<span class="kn">import</span> <span class="nn">math</span>
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<span class="kn">from</span> <span class="nn">pylib.mathematics</span> <span class="k">import</span> <span class="n">lcm</span>
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<div class="viewcode-block" id="sine_wave"><a class="viewcode-back" href="../function.html#function.sine_wave">[docs]</a><span class="k">def</span> <span class="nf">sine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
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<span class="sa">r</span><span class="sd">"""A sine wave or sinusoid is a mathematical curve that describes a</span>
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@@ -64,6 +65,10 @@
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<span class="sd"> :param degree: boolean to switch between radians and degree. If</span>
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<span class="sd"> False phi is interpreted in radians and if True then phi is</span>
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<span class="sd"> interpreted in degrees.</span>
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<span class="sd"> :type degree: bool</span>
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<span class="sd"> :results: sine wave function of spatial variable x and optional</span>
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<span class="sd"> time t</span>
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<span class="sd"> In general, the function is:</span>
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@@ -124,6 +129,10 @@
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<span class="sd"> :param degree: boolean to switch between radians and degree. If</span>
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<span class="sd"> False phi is interpreted in radians and if True then phi is</span>
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<span class="sd"> interpreted in degrees.</span>
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<span class="sd"> :type degree: bool</span>
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<span class="sd"> :results: sine wave function of spatial variable x and optional</span>
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<span class="sd"> time t</span>
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<span class="sd"> .. seealso::</span>
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<span class="sd"> :meth:`function_sine_wave_degree`</span>
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@@ -133,6 +142,59 @@
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<span class="k">else</span><span class="p">:</span>
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<span class="n">phi</span> <span class="o">=</span> <span class="n">phi</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span>
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<span class="k">return</span> <span class="n">sine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="n">phi</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="n">D</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="n">degree</span><span class="p">)</span></div>
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<span class="c1">#</span>
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<span class="c1"># Parametric equations</span>
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<span class="c1">#</span>
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<div class="viewcode-block" id="hypotrochoid"><a class="viewcode-back" href="../function.html#function.hypotrochoid">[docs]</a><span class="k">def</span> <span class="nf">hypotrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
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<span class="sa">r</span><span class="sd">"""Hypotrochoid</span>
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<span class="sd"> A point is attached with a distance d from the center of a circle</span>
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<span class="sd"> of radius r. The circle is rolling around the inside of a fixed</span>
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<span class="sd"> circle of radius R.</span>
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<span class="sd"> :param R: radius of the fixed exterior circle</span>
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<span class="sd"> :type R: float</span>
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<span class="sd"> :param r: radius of the rolling circle inside of the fixed circle</span>
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<span class="sd"> :typre r: float</span>
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<span class="sd"> :param d: distance from the center of the interior circle</span>
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<span class="sd"> :type d: float</span>
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<span class="sd"> :results: functions for x of theta and y of theta</span>
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<span class="sd"> :rtype: tuple</span>
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<span class="sd"> .. math::</span>
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<span class="sd"> x(\theta) = (R - r)\cos\theta + d\cos\left(\frac{R-r}{r}\theta\right) \\</span>
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<span class="sd"> y(\theta) = (R - r)\sin\theta - d\sin\left(\frac{R-r}{r}\theta\right) \\</span>
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<span class="sd"> \theta = \left[0, 2\pi\frac{\mathrm{lcm}(r, R)}{R}\right]</span>
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<span class="sd"> ::</span>
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<span class="sd"> * * *</span>
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<span class="sd"> * R *</span>
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<span class="sd"> * *</span>
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<span class="sd"> * * * *</span>
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<span class="sd"> * * r **</span>
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<span class="sd"> * * .... *</span>
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<span class="sd"> * * d *</span>
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<span class="sd"> * * **</span>
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<span class="sd"> * * * *</span>
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<span class="sd"> * *</span>
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<span class="sd"> * *</span>
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<span class="sd"> * * *</span>
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<span class="sd"> >>> x, y = hyotrochoid(20, 6, 6)[:1]</span>
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<span class="sd"> >>> x, y, theta_end = hyotrochoid(20, 6, 6)</span>
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<span class="sd"> .. seealso::</span>
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<span class="sd"> :meth:`mathematics.lcm`</span>
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<span class="sd"> """</span>
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<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">((</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
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<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">((</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
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<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">lcm</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">R</span><span class="p">)</span><span class="o">/</span><span class="n">R</span>
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<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
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</pre></div>
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</div>
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