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  <h1>Source code for animation3d</h1><div class="highlight"><pre>
<span></span><span class="ch">#!/usr/bin/python2.7</span>
<span class="c1"># -*- coding: utf-8 -*-</span>

<span class="sd">&quot;&quot;&quot; </span>
<span class="sd">**Project Name:**      MakeHuman</span>

<span class="sd">**Product Home Page:** http://www.makehuman.org/</span>

<span class="sd">**Code Home Page:**    https://bitbucket.org/MakeHuman/makehuman/</span>

<span class="sd">**Authors:**           Marc Flerackers</span>

<span class="sd">**Copyright(c):**      MakeHuman Team 2001-2017</span>

<span class="sd">**Licensing:**         AGPL3</span>

<span class="sd">    This file is part of MakeHuman (www.makehuman.org).</span>

<span class="sd">    This program is free software: you can redistribute it and/or modify</span>
<span class="sd">    it under the terms of the GNU Affero General Public License as</span>
<span class="sd">    published by the Free Software Foundation, either version 3 of the</span>
<span class="sd">    License, or (at your option) any later version.</span>

<span class="sd">    This program is distributed in the hope that it will be useful,</span>
<span class="sd">    but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<span class="sd">    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
<span class="sd">    GNU Affero General Public License for more details.</span>

<span class="sd">    You should have received a copy of the GNU Affero General Public License</span>
<span class="sd">    along with this program.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span>


<span class="sd">Abstract</span>
<span class="sd">--------</span>

<span class="sd">This module contains functions and classes to animate a wide range of objects and attributes.</span>

<span class="sd">To know more about the interpolation methods used, see the following references:</span>

<span class="sd">* http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/interpolation/</span>
<span class="sd">* http://en.wikipedia.org/wiki/Cubic_Hermite_spline</span>
<span class="sd">* http://en.wikipedia.org/wiki/Kochanek-Bartels_spline</span>
<span class="sd">* http://www.geometrictools.com/Documentation/KBSplines.pdf</span>
<span class="sd">* http://www.tinaja.com/glib/cubemath.pdf</span>
<span class="sd">&quot;&quot;&quot;</span>

<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">math</span>

<div class="viewcode-block" id="linearInterpolate"><a class="viewcode-back" href="../module_animation3d.html#animation3d.linearInterpolate">[docs]</a><span class="k">def</span> <span class="nf">linearInterpolate</span><span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Good interpolator when you have two values to interpolate between, but doesn&#39;t give fluid animation</span>
<span class="sd">    when more points are involved since it follows straight lines between the points.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">alpha</span> <span class="o">*</span> <span class="p">(</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span></div>

<div class="viewcode-block" id="cosineInterpolate"><a class="viewcode-back" href="../module_animation3d.html#animation3d.cosineInterpolate">[docs]</a><span class="k">def</span> <span class="nf">cosineInterpolate</span><span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    When you have more than 2 points two interpolate (for example following a path), this is a better</span>
<span class="sd">    choice than a linear interpolator.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</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">alpha</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> <span class="o">/</span> <span class="mi">2</span>
    <span class="k">return</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="p">(</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span></div>

<div class="viewcode-block" id="cubicInterpolate"><a class="viewcode-back" href="../module_animation3d.html#animation3d.cubicInterpolate">[docs]</a><span class="k">def</span> <span class="nf">cubicInterpolate</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Cubic interpolator. Gives better continuity along the spline than the cosine interpolator,</span>
<span class="sd">    however needs 4 points to interpolate.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">a0</span> <span class="o">=</span> <span class="p">(</span><span class="n">v3</span> <span class="o">-</span> <span class="n">v2</span><span class="p">)</span> <span class="o">-</span> <span class="n">v0</span> <span class="o">+</span> <span class="n">v1</span>
    <span class="n">a1</span> <span class="o">=</span> <span class="p">(</span><span class="n">v0</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span> <span class="o">-</span> <span class="n">a0</span>
    <span class="n">a2</span> <span class="o">=</span> <span class="n">v2</span> <span class="o">-</span> <span class="n">v0</span>
    <span class="n">a3</span> <span class="o">=</span> <span class="n">v1</span>

    <span class="k">return</span> <span class="p">(</span><span class="n">a0</span> <span class="o">*</span> <span class="n">alpha</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="n">a1</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="n">a2</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">a3</span></div>
    
<div class="viewcode-block" id="hermiteInterpolate"><a class="viewcode-back" href="../module_animation3d.html#animation3d.hermiteInterpolate">[docs]</a><span class="k">def</span> <span class="nf">hermiteInterpolate</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">tension</span><span class="p">,</span> <span class="n">bias</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Hermite interpolator. Allows better control of the bends in the spline by providing two</span>
<span class="sd">    parameters to adjust them:</span>
<span class="sd">    </span>
<span class="sd">    * tension: 1 for high tension, 0 for normal tension and -1 for low tension.</span>
<span class="sd">    * bias: 1 for bias towards the next segment, 0 for even bias, -1 for bias towards the previous segment.</span>
<span class="sd">    </span>
<span class="sd">    Using 0 bias gives a cardinal spline with just tension, using both 0 tension and 0 bias gives a Catmul-Rom spline.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">alpha3</span> <span class="o">=</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">m0</span> <span class="o">=</span> <span class="p">(((</span><span class="n">v1</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">m0</span> <span class="o">+=</span> <span class="p">(((</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">m1</span> <span class="o">=</span> <span class="p">(((</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">m1</span> <span class="o">+=</span> <span class="p">(((</span><span class="n">v3</span> <span class="o">-</span> <span class="n">v2</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">a0</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="mi">1</span>
    <span class="n">a1</span> <span class="o">=</span> <span class="n">alpha3</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="n">alpha</span>
    <span class="n">a2</span> <span class="o">=</span> <span class="n">alpha3</span> <span class="o">-</span> <span class="n">alpha2</span>
    <span class="n">a3</span> <span class="o">=</span> <span class="o">-</span><span class="mi">2</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">alpha2</span>

    <span class="k">return</span> <span class="n">a0</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">a1</span> <span class="o">*</span> <span class="n">m0</span> <span class="o">+</span> <span class="n">a2</span> <span class="o">*</span> <span class="n">m1</span> <span class="o">+</span> <span class="n">a3</span> <span class="o">*</span> <span class="n">v2</span></div>

<div class="viewcode-block" id="kochanekBartelsInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.kochanekBartelsInterpolator">[docs]</a><span class="k">def</span> <span class="nf">kochanekBartelsInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">tension</span><span class="p">,</span> <span class="n">continuity</span><span class="p">,</span> <span class="n">bias</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Kochanek-Bartels interpolator. Allows even better control of the bends in the spline by providing three</span>
<span class="sd">    parameters to adjust them:</span>
<span class="sd">    </span>
<span class="sd">    * tension: 1 for high tension, 0 for normal tension and -1 for low tension.</span>
<span class="sd">    * continuity: 1 for inverted corners, 0 for normal corners, -1 for box corners.</span>
<span class="sd">    * bias: 1 for bias towards the next segment, 0 for even bias, -1 for bias towards the previous segment.</span>
<span class="sd">    </span>
<span class="sd">    Using 0 continuity gives a hermite spline.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">alpha3</span> <span class="o">=</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">m0</span> <span class="o">=</span> <span class="p">((((</span><span class="n">v1</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">continuity</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">m0</span> <span class="o">+=</span> <span class="p">((((</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">continuity</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">m1</span> <span class="o">=</span> <span class="p">((((</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">continuity</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">m1</span> <span class="o">+=</span> <span class="p">((((</span><span class="n">v3</span> <span class="o">-</span> <span class="n">v2</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tension</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">continuity</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">bias</span><span class="p">))</span> <span class="o">/</span> <span class="mf">2.0</span>
    <span class="n">a0</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="mi">1</span>
    <span class="n">a1</span> <span class="o">=</span> <span class="n">alpha3</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="n">alpha</span>
    <span class="n">a2</span> <span class="o">=</span> <span class="n">alpha3</span> <span class="o">-</span> <span class="n">alpha2</span>
    <span class="n">a3</span> <span class="o">=</span> <span class="o">-</span><span class="mi">2</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">alpha2</span>

    <span class="k">return</span> <span class="n">a0</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">a1</span> <span class="o">*</span> <span class="n">m0</span> <span class="o">+</span> <span class="n">a2</span> <span class="o">*</span> <span class="n">m1</span> <span class="o">+</span> <span class="n">a3</span> <span class="o">*</span> <span class="n">v2</span></div>

<div class="viewcode-block" id="quadraticBezierInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.quadraticBezierInterpolator">[docs]</a><span class="k">def</span> <span class="nf">quadraticBezierInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Quadratic Bezier interpolator. v0 and v2 are begin and end point respectively, v1 is a control point.</span>
<span class="sd">    </span>
<span class="sd">    .. math::</span>
<span class="sd">        \begin{bmatrix} 1 &amp; -2 &amp; 1 \\ -2 &amp; 2 &amp; 0 \\ 1 &amp; 1 &amp; 0 \end{bmatrix}</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>

    <span class="k">return</span> <span class="p">(</span><span class="n">v2</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="p">((</span><span class="n">v1</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">v0</span></div>


<div class="viewcode-block" id="cubicBezierInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.cubicBezierInterpolator">[docs]</a><span class="k">def</span> <span class="nf">cubicBezierInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Cubic Bezier interpolator. v0 and v3 are begin and end point respectively, v1 and v2 are control points.</span>

<span class="sd">    .. math::</span>
<span class="sd">        \begin{bmatrix} -1 &amp; 3 &amp; -3 &amp; 1 \\ 3 &amp; -6 &amp; 3 &amp; 0 \\ -3 &amp; 3 &amp; 0 &amp; 0 \\ 1 &amp; 0 &amp; 0 &amp; 0 \end{bmatrix}</span>
<span class="sd">    &quot;&quot;&quot;</span>

    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">alpha3</span> <span class="o">=</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="n">alpha</span>

    <span class="k">return</span> <span class="p">((</span><span class="n">v3</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v1</span><span class="p">)</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">+</span> <span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">-</span> <span class="mi">6</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">v0</span></div>

<div class="viewcode-block" id="quadraticBSplineInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.quadraticBSplineInterpolator">[docs]</a><span class="k">def</span> <span class="nf">quadraticBSplineInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Quadratic b-spline interpolator. v0 and v2 are begin and end point respectively, v1 is a control point.</span>

<span class="sd">    .. math::</span>
<span class="sd">        \frac{1}{2} \begin{bmatrix} 1 &amp; -2 &amp; 1 \\ -2 &amp; 2 &amp; 0 \\ 1 &amp; 1 &amp; 0 \end{bmatrix}</span>
<span class="sd">    &quot;&quot;&quot;</span>

    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>

    <span class="k">return</span> <span class="p">((</span><span class="n">v2</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="p">((</span><span class="n">v1</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">v0</span> <span class="o">+</span> <span class="n">v1</span><span class="p">)</span> <span class="o">/</span> <span class="mf">2.0</span></div>

<div class="viewcode-block" id="cubicBSplineInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.cubicBSplineInterpolator">[docs]</a><span class="k">def</span> <span class="nf">cubicBSplineInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&#39;&#39;&#39;</span>
<span class="sd">    Cubic b-spline interpolator. v0 and v3 are begin and end point respectively, v1 and v2 are control points.</span>

<span class="sd">    .. math::</span>
<span class="sd">        \frac{1}{6} \begin{bmatrix} -1 &amp; 3 &amp; -3 &amp; 1 \\ 3 &amp; -6 &amp; 3 &amp; 0 \\ -3 &amp; 0 &amp; 3 &amp; 0 \\ 1 &amp; 4 &amp; 1 &amp; 0 \end{bmatrix}</span>
<span class="sd">    &#39;&#39;&#39;</span>

    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">alpha3</span> <span class="o">=</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="n">alpha</span>

    <span class="k">return</span> <span class="p">(((</span><span class="n">v3</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v1</span><span class="p">)</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">+</span> <span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">-</span> <span class="mi">6</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">v0</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">v2</span><span class="p">)</span> <span class="o">/</span> <span class="mf">6.0</span></div>

<div class="viewcode-block" id="cubicCatmullRomInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.cubicCatmullRomInterpolator">[docs]</a><span class="k">def</span> <span class="nf">cubicCatmullRomInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Cubic Catmull Rom interpolator. v0 and v3 are begin and end point respectively, v1 and v2 are control points.</span>
<span class="sd">    </span>
<span class="sd">    .. math::</span>
<span class="sd">        \frac{1}{2} \begin{bmatrix} -1 &amp; 3 &amp; -3 &amp; 1 \\ 2 &amp; -5 &amp; 4 &amp; -1 \\ -1 &amp; 0 &amp; 1 &amp; 0 \\ 1 &amp; 2 &amp; 0 &amp; 0 \end{bmatrix}</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">alpha3</span> <span class="o">=</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="n">alpha</span>

    <span class="k">return</span> <span class="p">(((</span><span class="n">v3</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v1</span><span class="p">)</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">+</span> <span class="p">((</span><span class="o">-</span><span class="n">v3</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">v2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="p">(</span><span class="n">v2</span> <span class="o">-</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">v0</span><span class="p">)</span> <span class="o">/</span> <span class="mf">2.0</span></div>

<div class="viewcode-block" id="cubicHermiteInterpolator"><a class="viewcode-back" href="../module_animation3d.html#animation3d.cubicHermiteInterpolator">[docs]</a><span class="k">def</span> <span class="nf">cubicHermiteInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">v3</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Cubic hermite interpolator. v0 and v3 are begin and end point respectively, v1 and v2 are control points.</span>
<span class="sd">    </span>
<span class="sd">    .. math::</span>
<span class="sd">        \frac{1}{6} \begin{bmatrix} 2 &amp; 1 &amp; -2 &amp; 1 \\ -3 &amp; -2 &amp; 3 &amp; -1 \\ 0 &amp; 1 &amp; 0 &amp; 0 \\ 1 &amp; 0 &amp; 0 &amp; 0 \end{bmatrix}</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">alpha2</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">alpha</span>
    <span class="n">alpha3</span> <span class="o">=</span> <span class="n">alpha2</span> <span class="o">*</span> <span class="n">alpha</span>

    <span class="k">return</span> <span class="p">(</span><span class="n">v3</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v2</span> <span class="o">+</span> <span class="n">v1</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha3</span> <span class="o">+</span> <span class="p">(((</span><span class="o">-</span><span class="n">v3</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v1</span><span class="p">)</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">v0</span><span class="p">)</span> <span class="o">*</span> <span class="n">alpha2</span> <span class="o">+</span> <span class="n">v1</span> <span class="o">*</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">v0</span></div>


<span class="k">def</span> <span class="nf">ThreeDQBspline</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
    <span class="k">return</span> <span class="p">[</span><span class="n">quadraticBSplineInterpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">v1</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">v2</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">alpha</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">v1</span><span class="p">))]</span>

<div class="viewcode-block" id="lerpVector"><a class="viewcode-back" href="../module_animation3d.html#animation3d.lerpVector">[docs]</a><span class="k">def</span> <span class="nf">lerpVector</span><span class="p">(</span><span class="n">v0</span><span class="p">,</span> <span class="n">v1</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">interpolator</span><span class="o">=</span><span class="n">linearInterpolate</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Interpolates a whole vector at once.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="p">[</span><span class="n">interpolator</span><span class="p">(</span><span class="n">v0</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">v1</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">alpha</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">v1</span><span class="p">))]</span></div>

<div class="viewcode-block" id="Action"><a class="viewcode-back" href="../module_animation3d.html#animation3d.Action">[docs]</a><span class="k">class</span> <span class="nc">Action</span><span class="p">:</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Base action class, does nothing</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">pass</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="k">pass</span></div>


<div class="viewcode-block" id="PathAction"><a class="viewcode-back" href="../module_animation3d.html#animation3d.PathAction">[docs]</a><span class="k">class</span> <span class="nc">PathAction</span><span class="p">(</span><span class="n">Action</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Path action class. Moves an object along a path</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">,</span> <span class="n">positions</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span> <span class="o">=</span> <span class="n">obj</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">positions</span> <span class="o">=</span> <span class="n">positions</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="n">keys</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
        <span class="n">key</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">alpha</span> <span class="o">*</span> <span class="n">keys</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">key</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>

            <span class="c1"># Use last value</span>

            <span class="n">value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
        <span class="k">else</span><span class="p">:</span>

            <span class="c1"># Offset alpha to it&#39;s own slice, and expand the slice to 0-1</span>

            <span class="n">sliceLength</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">keys</span>
            <span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">key</span> <span class="o">*</span> <span class="n">sliceLength</span><span class="p">)</span> <span class="o">*</span> <span class="n">keys</span>

            <span class="c1"># Interpolate between current and next using the new alpha</span>

            <span class="n">value</span> <span class="o">=</span> <span class="n">lerpVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="n">key</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="n">a</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span><span class="o">.</span><span class="n">setPosition</span><span class="p">(</span><span class="n">value</span><span class="p">)</span></div>

<div class="viewcode-block" id="ZoomAction"><a class="viewcode-back" href="../module_animation3d.html#animation3d.ZoomAction">[docs]</a><span class="k">class</span> <span class="nc">ZoomAction</span><span class="p">(</span><span class="n">Action</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    A zoom transition for a camera</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">,</span> <span class="n">startZoom</span><span class="p">,</span> <span class="n">endZoom</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span> <span class="o">=</span> <span class="n">obj</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">startZoom</span> <span class="o">=</span> <span class="n">startZoom</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">endZoom</span> <span class="o">=</span> <span class="n">endZoom</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="n">value</span> <span class="o">=</span> <span class="n">lerpVector</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">startZoom</span><span class="p">],</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">endZoom</span><span class="p">],</span> <span class="n">alpha</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span><span class="o">.</span><span class="n">setZoomFactor</span><span class="p">(</span><span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span></div>

<div class="viewcode-block" id="RotateAction"><a class="viewcode-back" href="../module_animation3d.html#animation3d.RotateAction">[docs]</a><span class="k">class</span> <span class="nc">RotateAction</span><span class="p">(</span><span class="n">Action</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Rotate action class. Rotates an object from a start orientation to an end orientation.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">,</span> <span class="n">startAngles</span><span class="p">,</span> <span class="n">endAngles</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span> <span class="o">=</span> <span class="n">obj</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">startAngle</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">clipRotation</span><span class="p">(</span><span class="n">startAngles</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">endAngle</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">clipRotation</span><span class="p">(</span><span class="n">endAngles</span><span class="p">)</span>

        <span class="bp">self</span><span class="o">.</span><span class="n">endAngle</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">closestRotation</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">startAngle</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">endAngle</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="n">value</span> <span class="o">=</span> <span class="n">lerpVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">startAngle</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">endAngle</span><span class="p">,</span> <span class="n">alpha</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span><span class="o">.</span><span class="n">setRotation</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>

    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">clipRotation</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">rotation</span><span class="p">):</span>
        <span class="n">rotation</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">rotation</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">%</span> <span class="mi">360</span>
        <span class="n">rotation</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">rotation</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">%</span> <span class="mi">360</span>
        <span class="n">rotation</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">rotation</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">%</span> <span class="mi">360</span>
        <span class="k">return</span> <span class="n">rotation</span>

    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">closestRotation</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">beginRot</span><span class="p">,</span> <span class="n">endRot</span><span class="p">):</span>
        <span class="n">rotation</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]</span>
        <span class="n">rotation</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">cls</span><span class="o">.</span><span class="n">closestAngle</span><span class="p">(</span><span class="n">beginRot</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">endRot</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
        <span class="n">rotation</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">cls</span><span class="o">.</span><span class="n">closestAngle</span><span class="p">(</span><span class="n">beginRot</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">endRot</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
        <span class="n">rotation</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">cls</span><span class="o">.</span><span class="n">closestAngle</span><span class="p">(</span><span class="n">beginRot</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">endRot</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
        <span class="k">return</span> <span class="n">rotation</span>

    <span class="nd">@classmethod</span>
<div class="viewcode-block" id="RotateAction.closestAngle"><a class="viewcode-back" href="../module_animation3d.html#animation3d.RotateAction.closestAngle">[docs]</a>    <span class="k">def</span> <span class="nf">closestAngle</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">beginAngle</span><span class="p">,</span> <span class="n">endAngle</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        Assumes that beginAngle and endAngle are clipped between [0, 360[</span>
<span class="sd">        Calculates end angle so that linear interpolation between beginAngle</span>
<span class="sd">        and the returned end angle results in a minimal rotation.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="k">if</span> <span class="n">endAngle</span> <span class="o">&lt;</span> <span class="n">beginAngle</span><span class="p">:</span>
            <span class="n">endAngle</span> <span class="o">=</span> <span class="mf">360.0</span> <span class="o">+</span> <span class="n">endAngle</span>
        <span class="n">angleDiff</span> <span class="o">=</span> <span class="n">endAngle</span> <span class="o">-</span> <span class="n">beginAngle</span>
        <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">angleDiff</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">180</span><span class="p">:</span>
            <span class="k">return</span> <span class="o">-</span><span class="p">(</span><span class="mf">360.0</span> <span class="o">-</span> <span class="n">endAngle</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">endAngle</span></div></div>

<div class="viewcode-block" id="ScaleAction"><a class="viewcode-back" href="../module_animation3d.html#animation3d.ScaleAction">[docs]</a><span class="k">class</span> <span class="nc">ScaleAction</span><span class="p">(</span><span class="n">Action</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Scale action class. Scales an object from a start scale to an end scale.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">,</span> <span class="n">startScale</span><span class="p">,</span> <span class="n">endScale</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span> <span class="o">=</span> <span class="n">obj</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">startScale</span> <span class="o">=</span> <span class="n">startScale</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">endScale</span> <span class="o">=</span> <span class="n">endScale</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="n">value</span> <span class="o">=</span> <span class="n">lerpVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">startScale</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">endScale</span><span class="p">,</span> <span class="n">alpha</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">obj</span><span class="o">.</span><span class="n">setScale</span><span class="p">(</span><span class="n">value</span><span class="p">)</span></div>
        

<div class="viewcode-block" id="CameraAction"><a class="viewcode-back" href="../module_animation3d.html#animation3d.CameraAction">[docs]</a><span class="k">class</span> <span class="nc">CameraAction</span><span class="p">(</span><span class="n">Action</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    CameraAction action class. Animates all camera attributes.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="c1"># TODO remove?</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cam</span><span class="p">,</span> <span class="n">startParams</span><span class="p">,</span> <span class="n">endParams</span><span class="p">):</span>
        
        <span class="bp">self</span><span class="o">.</span><span class="n">cam</span> <span class="o">=</span> <span class="n">cam</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">startParams</span> <span class="o">=</span> <span class="n">startParams</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeZ</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusZ</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upZ</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">endParams</span> <span class="o">=</span> <span class="n">endParams</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeZ</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusZ</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upZ</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="n">value</span> <span class="o">=</span> <span class="n">lerpVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">startParams</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">endParams</span><span class="p">,</span> <span class="n">alpha</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">eyeZ</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">focusZ</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upX</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upY</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cam</span><span class="o">.</span><span class="n">upZ</span> <span class="o">=</span> <span class="n">value</span></div>

<div class="viewcode-block" id="UpdateAction"><a class="viewcode-back" href="../module_animation3d.html#animation3d.UpdateAction">[docs]</a><span class="k">class</span> <span class="nc">UpdateAction</span><span class="p">(</span><span class="n">Action</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Updates the scene. Without this acton and animation is not visible.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">app</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">app</span> <span class="o">=</span> <span class="n">app</span>

    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">app</span><span class="o">.</span><span class="n">redraw</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">app</span><span class="o">.</span><span class="n">processEvents</span><span class="p">()</span></div>


<div class="viewcode-block" id="Timeline"><a class="viewcode-back" href="../module_animation3d.html#animation3d.Timeline">[docs]</a><span class="k">class</span> <span class="nc">Timeline</span><span class="p">:</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    A timeline combines several animation3d.Action objects to an animation.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">seconds</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">seconds</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">actions</span> <span class="o">=</span> <span class="p">[]</span>

    <span class="k">def</span> <span class="nf">append</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">action</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">actions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">action</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">start</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">reference</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
        <span class="n">t</span> <span class="o">=</span> <span class="mi">0</span>
        <span class="k">while</span> <span class="n">t</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">:</span>
            <span class="n">a</span> <span class="o">=</span> <span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
            <span class="k">for</span> <span class="n">action</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">actions</span><span class="p">:</span>
                <span class="n">action</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
            <span class="n">t</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">reference</span>
        <span class="k">for</span> <span class="n">action</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">actions</span><span class="p">:</span>
            <span class="n">action</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span></div>

<div class="viewcode-block" id="animate"><a class="viewcode-back" href="../module_animation3d.html#animation3d.animate">[docs]</a><span class="k">def</span> <span class="nf">animate</span><span class="p">(</span><span class="n">app</span><span class="p">,</span> <span class="n">seconds</span><span class="p">,</span> <span class="n">actions</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Animates the given actions by creating a animation3d.Timeline, adding an animation3d.UpdateAction and calling start.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">tl</span> <span class="o">=</span> <span class="n">Timeline</span><span class="p">(</span><span class="n">seconds</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">action</span> <span class="ow">in</span> <span class="n">actions</span><span class="p">:</span>
        <span class="n">tl</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">action</span><span class="p">)</span>
    <span class="n">tl</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">UpdateAction</span><span class="p">(</span><span class="n">app</span><span class="p">))</span>
    <span class="n">tl</span><span class="o">.</span><span class="n">start</span><span class="p">()</span></div>
</pre></div>

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