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<a href="VisionEgg-module.html">Package VisionEgg</a> ::
Module ThreeDeeMath
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<h1 class="epydoc">Source Code for <a href="VisionEgg.ThreeDeeMath-module.html">Module VisionEgg.ThreeDeeMath</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno"> 1</tt> <tt class="py-line"><tt class="py-comment"># The Vision Egg: ThreeDeeMath</tt> </tt>
<a name="L2"></a><tt class="py-lineno"> 2</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment">#</tt> </tt>
<a name="L3"></a><tt class="py-lineno"> 3</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment"># Copyright (C) 2001-2003 Andrew Straw.</tt> </tt>
<a name="L4"></a><tt class="py-lineno"> 4</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment"># Copyright (C) 2008 California Institute of Technology</tt> </tt>
<a name="L5"></a><tt class="py-lineno"> 5</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment">#</tt> </tt>
<a name="L6"></a><tt class="py-lineno"> 6</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment"># URL: <http://www.visionegg.org/></tt> </tt>
<a name="L7"></a><tt class="py-lineno"> 7</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment">#</tt> </tt>
<a name="L8"></a><tt class="py-lineno"> 8</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment"># Distributed under the terms of the GNU Lesser General Public License</tt> </tt>
<a name="L9"></a><tt class="py-lineno"> 9</tt> <tt class="py-line"><tt class="py-comment"></tt><tt class="py-comment"># (LGPL). See LICENSE.TXT that came with this file.</tt> </tt>
<a name="L10"></a><tt class="py-lineno">10</tt> <tt class="py-line"><tt class="py-comment"></tt> </tt>
<a name="L11"></a><tt class="py-lineno">11</tt> <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L12"></a><tt class="py-lineno">12</tt> <tt class="py-line"><tt class="py-docstring">Vertex and matrix operations - simulate OpenGL transforms.</tt> </tt>
<a name="L13"></a><tt class="py-lineno">13</tt> <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L14"></a><tt class="py-lineno">14</tt> <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L15"></a><tt class="py-lineno">15</tt> <tt class="py-line"> </tt>
<a name="L16"></a><tt class="py-lineno">16</tt> <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">math</tt> </tt>
<a name="L17"></a><tt class="py-lineno">17</tt> <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt> </tt>
<a name="L18"></a><tt class="py-lineno">18</tt> <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">oldnumeric</tt> <tt class="py-keyword">as</tt> <tt class="py-name">Numeric</tt><tt class="py-op">,</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">oldnumeric</tt><tt class="py-op">.</tt><tt class="py-name">mlab</tt> <tt class="py-keyword">as</tt> <tt class="py-name">MLab</tt> </tt>
<a name="L19"></a><tt class="py-lineno">19</tt> <tt class="py-line"> </tt>
<a name="make_homogeneous_coord_rows"></a><div id="make_homogeneous_coord_rows-def"><a name="L20"></a><tt class="py-lineno">20</tt> <a class="py-toggle" href="#" id="make_homogeneous_coord_rows-toggle" onclick="return toggle('make_homogeneous_coord_rows');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath-module.html#make_homogeneous_coord_rows">make_homogeneous_coord_rows</a><tt class="py-op">(</tt><tt class="py-param">v</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="make_homogeneous_coord_rows-collapsed" style="display:none;" pad="++" indent="++++"></div><div id="make_homogeneous_coord_rows-expanded"><a name="L21"></a><tt class="py-lineno">21</tt> <tt class="py-line"> <tt class="py-docstring">"""Convert vertex (or row-wise vertices) into homogeneous coordinates."""</tt> </tt>
<a name="L22"></a><tt class="py-lineno">22</tt> <tt class="py-line"> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">array</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt><tt class="py-name">typecode</tt><tt class="py-op">=</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt> <tt class="py-comment"># copy</tt> </tt>
<a name="L23"></a><tt class="py-lineno">23</tt> <tt class="py-line"> <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L24"></a><tt class="py-lineno">24</tt> <tt class="py-line"> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">v</tt><tt class="py-op">[</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">NewAxis</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-comment"># make a rank-2 array</tt> </tt>
<a name="L25"></a><tt class="py-lineno">25</tt> <tt class="py-line"> <tt class="py-keyword">if</tt> <tt class="py-name">v</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-number">3</tt><tt class="py-op">:</tt> </tt>
<a name="L26"></a><tt class="py-lineno">26</tt> <tt class="py-line"> <tt class="py-name">ws</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">ones</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt><tt class="py-name">typecode</tt><tt class="py-op">=</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt> </tt>
<a name="L27"></a><tt class="py-lineno">27</tt> <tt class="py-line"> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">concatenate</tt><tt class="py-op">(</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt><tt class="py-name">ws</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">1</tt> <tt class="py-op">)</tt> </tt>
<a name="L28"></a><tt class="py-lineno">28</tt> <tt class="py-line"> <tt class="py-keyword">return</tt> <tt class="py-name">v</tt> </tt>
</div><a name="L29"></a><tt class="py-lineno">29</tt> <tt class="py-line"> </tt>
<a name="normalize_homogeneous_rows"></a><div id="normalize_homogeneous_rows-def"><a name="L30"></a><tt class="py-lineno">30</tt> <a class="py-toggle" href="#" id="normalize_homogeneous_rows-toggle" onclick="return toggle('normalize_homogeneous_rows');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath-module.html#normalize_homogeneous_rows">normalize_homogeneous_rows</a><tt class="py-op">(</tt><tt class="py-param">v</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="normalize_homogeneous_rows-collapsed" style="display:none;" pad="++" indent="++++"></div><div id="normalize_homogeneous_rows-expanded"><a name="L31"></a><tt class="py-lineno">31</tt> <tt class="py-line"> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt> </tt>
<a name="L32"></a><tt class="py-lineno">32</tt> <tt class="py-line"> <tt class="py-name">homog</tt> <tt class="py-op">=</tt> <tt id="link-0" class="py-name" targets="Function VisionEgg.ThreeDeeMath.make_homogeneous_coord_rows()=VisionEgg.ThreeDeeMath-module.html#make_homogeneous_coord_rows"><a title="VisionEgg.ThreeDeeMath.make_homogeneous_coord_rows" class="py-name" href="#" onclick="return doclink('link-0', 'make_homogeneous_coord_rows', 'link-0');">make_homogeneous_coord_rows</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt> </tt>
<a name="L33"></a><tt class="py-lineno">33</tt> <tt class="py-line"> <tt class="py-name">r</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">homog</tt><tt class="py-op">/</tt><tt class="py-name">homog</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">NewAxis</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-number">3</tt><tt class="py-op">]</tt> </tt>
<a name="L34"></a><tt class="py-lineno">34</tt> <tt class="py-line"> <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">homog</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-op">></tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L35"></a><tt class="py-lineno">35</tt> <tt class="py-line"> <tt class="py-name">r</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">reshape</tt><tt class="py-op">(</tt><tt class="py-name">r</tt><tt class="py-op">,</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L36"></a><tt class="py-lineno">36</tt> <tt class="py-line"> <tt class="py-keyword">return</tt> <tt class="py-name">r</tt> </tt>
</div><a name="L37"></a><tt class="py-lineno">37</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix"></a><div id="TransformMatrix-def"><a name="L38"></a><tt class="py-lineno">38</tt> <a class="py-toggle" href="#" id="TransformMatrix-toggle" onclick="return toggle('TransformMatrix');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html">TransformMatrix</a><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix-collapsed" style="display:none;" pad="++" indent="++++"></div><div id="TransformMatrix-expanded"><a name="TransformMatrix.__init__"></a><div id="TransformMatrix.__init__-def"><a name="L39"></a><tt class="py-lineno">39</tt> <a class="py-toggle" href="#" id="TransformMatrix.__init__-toggle" onclick="return toggle('TransformMatrix.__init__');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt><tt class="py-param">matrix</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.__init__-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.__init__-expanded"><a name="L40"></a><tt class="py-lineno">40</tt> <tt class="py-line"> <tt class="py-keyword">if</tt> <tt class="py-name">matrix</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L41"></a><tt class="py-lineno">41</tt> <tt class="py-line"> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> <tt class="py-op">=</tt> <tt class="py-name">MLab</tt><tt class="py-op">.</tt><tt class="py-name">eye</tt><tt class="py-op">(</tt><tt class="py-number">4</tt><tt class="py-op">,</tt><tt class="py-name">typecode</tt><tt class="py-op">=</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt> </tt>
<a name="L42"></a><tt class="py-lineno">42</tt> <tt class="py-line"> <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L43"></a><tt class="py-lineno">43</tt> <tt class="py-line"> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> <tt class="py-op">=</tt> <tt class="py-name">matrix</tt> </tt>
</div><a name="L44"></a><tt class="py-lineno">44</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix.__make_normalized_vert3"></a><div id="TransformMatrix.__make_normalized_vert3-def"><a name="L45"></a><tt class="py-lineno">45</tt> <a class="py-toggle" href="#" id="TransformMatrix.__make_normalized_vert3-toggle" onclick="return toggle('TransformMatrix.__make_normalized_vert3');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#__make_normalized_vert3">__make_normalized_vert3</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">z</tt> <tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.__make_normalized_vert3-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.__make_normalized_vert3-expanded"><a name="L46"></a><tt class="py-lineno">46</tt> <tt class="py-line"> <tt id="link-1" class="py-name" targets="Function VisionEgg.PyroApps.MouseTargetServer.mag()=VisionEgg.PyroApps.MouseTargetServer-module.html#mag"><a title="VisionEgg.PyroApps.MouseTargetServer.mag" class="py-name" href="#" onclick="return doclink('link-1', 'mag', 'link-1');">mag</a></tt> <tt class="py-op">=</tt> <tt class="py-name">math</tt><tt class="py-op">.</tt><tt class="py-name">sqrt</tt><tt class="py-op">(</tt> <tt class="py-name">x</tt><tt class="py-op">**</tt><tt class="py-number">2</tt> <tt class="py-op">+</tt> <tt class="py-name">y</tt><tt class="py-op">**</tt><tt class="py-number">2</tt> <tt class="py-op">+</tt> <tt class="py-name">z</tt><tt class="py-op">**</tt><tt class="py-number">2</tt> <tt class="py-op">)</tt> </tt>
<a name="L47"></a><tt class="py-lineno">47</tt> <tt class="py-line"> <tt class="py-keyword">return</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">array</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">,</tt><tt class="py-name">y</tt><tt class="py-op">,</tt><tt class="py-name">z</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt id="link-2" class="py-name"><a title="VisionEgg.PyroApps.MouseTargetServer.mag" class="py-name" href="#" onclick="return doclink('link-2', 'mag', 'link-1');">mag</a></tt> </tt>
</div><a name="L48"></a><tt class="py-lineno">48</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix.rotate"></a><div id="TransformMatrix.rotate-def"><a name="L49"></a><tt class="py-lineno">49</tt> <a class="py-toggle" href="#" id="TransformMatrix.rotate-toggle" onclick="return toggle('TransformMatrix.rotate');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#rotate">rotate</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">angle_degrees</tt><tt class="py-op">,</tt> <tt class="py-param">axis_x</tt><tt class="py-op">,</tt> <tt class="py-param">axis_y</tt><tt class="py-op">,</tt> <tt class="py-param">axis_z</tt> <tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.rotate-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.rotate-expanded"><a name="L50"></a><tt class="py-lineno">50</tt> <tt class="py-line"> <tt class="py-docstring">"""Follows the right hand rule.</tt> </tt>
<a name="L51"></a><tt class="py-lineno">51</tt> <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L52"></a><tt class="py-lineno">52</tt> <tt class="py-line"><tt class="py-docstring"> I visualize the right hand rule most easily as follows:</tt> </tt>
<a name="L53"></a><tt class="py-lineno">53</tt> <tt class="py-line"><tt class="py-docstring"> Naturally, using your right hand, wrap it around the axis of</tt> </tt>
<a name="L54"></a><tt class="py-lineno">54</tt> <tt class="py-line"><tt class="py-docstring"> rotation. Your fingers now point in the direction of rotation.</tt> </tt>
<a name="L55"></a><tt class="py-lineno">55</tt> <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L56"></a><tt class="py-lineno">56</tt> <tt class="py-line"><tt class="py-docstring"> """</tt> </tt>
<a name="L57"></a><tt class="py-lineno">57</tt> <tt class="py-line"> <tt class="py-name">angleRadians</tt> <tt class="py-op">=</tt> <tt class="py-name">angle_degrees</tt> <tt class="py-op">/</tt> <tt class="py-number">180.0</tt> <tt class="py-op">*</tt> <tt class="py-name">math</tt><tt class="py-op">.</tt><tt class="py-name">pi</tt> </tt>
<a name="L58"></a><tt class="py-lineno">58</tt> <tt class="py-line"> <tt class="py-name">u</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__make_normalized_vert3</tt><tt class="py-op">(</tt><tt class="py-name">axis_x</tt><tt class="py-op">,</tt> <tt class="py-name">axis_y</tt><tt class="py-op">,</tt> <tt class="py-name">axis_z</tt> <tt class="py-op">)</tt> </tt>
<a name="L59"></a><tt class="py-lineno">59</tt> <tt class="py-line"> <tt class="py-name">u</tt><tt class="py-op">=</tt><tt class="py-op">-</tt><tt class="py-name">u</tt> <tt class="py-comment">#follow right hand rule</tt> </tt>
<a name="L60"></a><tt class="py-lineno">60</tt> <tt class="py-line"> <tt class="py-name">S</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt> <tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt> <tt class="py-op">)</tt> </tt>
<a name="L61"></a><tt class="py-lineno">61</tt> <tt class="py-line"> <tt class="py-name">S</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">u</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> </tt>
<a name="L62"></a><tt class="py-lineno">62</tt> <tt class="py-line"> <tt class="py-name">S</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">u</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L63"></a><tt class="py-lineno">63</tt> <tt class="py-line"> <tt class="py-name">S</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">u</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> </tt>
<a name="L64"></a><tt class="py-lineno">64</tt> <tt class="py-line"> <tt class="py-name">S</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">u</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L65"></a><tt class="py-lineno">65</tt> <tt class="py-line"> <tt class="py-name">S</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-name">u</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L66"></a><tt class="py-lineno">66</tt> <tt class="py-line"> <tt class="py-name">S</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">u</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L67"></a><tt class="py-lineno">67</tt> <tt class="py-line"> <tt class="py-name">U</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">outerproduct</tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt><tt class="py-name">u</tt><tt class="py-op">)</tt> </tt>
<a name="L68"></a><tt class="py-lineno">68</tt> <tt class="py-line"> <tt class="py-name">R</tt> <tt class="py-op">=</tt> <tt class="py-name">U</tt> <tt class="py-op">+</tt> <tt class="py-name">math</tt><tt class="py-op">.</tt><tt class="py-name">cos</tt><tt class="py-op">(</tt><tt class="py-name">angleRadians</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-name">MLab</tt><tt class="py-op">.</tt><tt class="py-name">eye</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">-</tt><tt class="py-name">U</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">math</tt><tt class="py-op">.</tt><tt class="py-name">sin</tt><tt class="py-op">(</tt><tt class="py-name">angleRadians</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-name">S</tt> </tt>
<a name="L69"></a><tt class="py-lineno">69</tt> <tt class="py-line"> <tt class="py-name">R</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">concatenate</tt><tt class="py-op">(</tt> <tt class="py-op">(</tt><tt class="py-name">R</tt><tt class="py-op">,</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt> <tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt> </tt>
<a name="L70"></a><tt class="py-lineno">70</tt> <tt class="py-line"> <tt class="py-name">R</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">concatenate</tt><tt class="py-op">(</tt> <tt class="py-op">(</tt><tt class="py-name">R</tt><tt class="py-op">,</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">4</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">)</tt> </tt>
<a name="L71"></a><tt class="py-lineno">71</tt> <tt class="py-line"> <tt class="py-name">R</tt><tt class="py-op">[</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-number">3</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-number">1.0</tt> </tt>
<a name="L72"></a><tt class="py-lineno">72</tt> <tt class="py-line"> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">dot</tt><tt class="py-op">(</tt><tt class="py-name">R</tt><tt class="py-op">,</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">)</tt> </tt>
</div><a name="L73"></a><tt class="py-lineno">73</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix.translate"></a><div id="TransformMatrix.translate-def"><a name="L74"></a><tt class="py-lineno">74</tt> <a class="py-toggle" href="#" id="TransformMatrix.translate-toggle" onclick="return toggle('TransformMatrix.translate');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#translate">translate</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">z</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.translate-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.translate-expanded"><a name="L75"></a><tt class="py-lineno">75</tt> <tt class="py-line"> <tt class="py-name">T</tt> <tt class="py-op">=</tt> <tt class="py-name">MLab</tt><tt class="py-op">.</tt><tt class="py-name">eye</tt><tt class="py-op">(</tt><tt class="py-number">4</tt><tt class="py-op">,</tt><tt class="py-name">typecode</tt><tt class="py-op">=</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt> </tt>
<a name="L76"></a><tt class="py-lineno">76</tt> <tt class="py-line"> <tt class="py-name">T</tt><tt class="py-op">[</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">x</tt> </tt>
<a name="L77"></a><tt class="py-lineno">77</tt> <tt class="py-line"> <tt class="py-name">T</tt><tt class="py-op">[</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">y</tt> </tt>
<a name="L78"></a><tt class="py-lineno">78</tt> <tt class="py-line"> <tt class="py-name">T</tt><tt class="py-op">[</tt><tt class="py-number">3</tt><tt class="py-op">,</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">z</tt> </tt>
<a name="L79"></a><tt class="py-lineno">79</tt> <tt class="py-line"> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">dot</tt><tt class="py-op">(</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">)</tt> </tt>
</div><a name="L80"></a><tt class="py-lineno">80</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix.scale"></a><div id="TransformMatrix.scale-def"><a name="L81"></a><tt class="py-lineno">81</tt> <a class="py-toggle" href="#" id="TransformMatrix.scale-toggle" onclick="return toggle('TransformMatrix.scale');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#scale">scale</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">z</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.scale-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.scale-expanded"><a name="L82"></a><tt class="py-lineno">82</tt> <tt class="py-line"> <tt class="py-name">T</tt> <tt class="py-op">=</tt> <tt class="py-name">MLab</tt><tt class="py-op">.</tt><tt class="py-name">eye</tt><tt class="py-op">(</tt><tt class="py-number">4</tt><tt class="py-op">,</tt><tt class="py-name">typecode</tt><tt class="py-op">=</tt><tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">Float</tt><tt class="py-op">)</tt> </tt>
<a name="L83"></a><tt class="py-lineno">83</tt> <tt class="py-line"> <tt class="py-name">T</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">x</tt> </tt>
<a name="L84"></a><tt class="py-lineno">84</tt> <tt class="py-line"> <tt class="py-name">T</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">y</tt> </tt>
<a name="L85"></a><tt class="py-lineno">85</tt> <tt class="py-line"> <tt class="py-name">T</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">,</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">z</tt> </tt>
<a name="L86"></a><tt class="py-lineno">86</tt> <tt class="py-line"> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">dot</tt><tt class="py-op">(</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">)</tt> </tt>
</div><a name="L87"></a><tt class="py-lineno">87</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix.get_matrix"></a><div id="TransformMatrix.get_matrix-def"><a name="L88"></a><tt class="py-lineno">88</tt> <a class="py-toggle" href="#" id="TransformMatrix.get_matrix-toggle" onclick="return toggle('TransformMatrix.get_matrix');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#get_matrix">get_matrix</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.get_matrix-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.get_matrix-expanded"><a name="L89"></a><tt class="py-lineno">89</tt> <tt class="py-line"> <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt> </tt>
</div><a name="L90"></a><tt class="py-lineno">90</tt> <tt class="py-line"> </tt>
<a name="TransformMatrix.transform_vertices"></a><div id="TransformMatrix.transform_vertices-def"><a name="L91"></a><tt class="py-lineno">91</tt> <a class="py-toggle" href="#" id="TransformMatrix.transform_vertices-toggle" onclick="return toggle('TransformMatrix.transform_vertices');">-</a><tt class="py-line"> <tt class="py-keyword">def</tt> <a class="py-def-name" href="VisionEgg.ThreeDeeMath.TransformMatrix-class.html#transform_vertices">transform_vertices</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt><tt class="py-param">verts</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="TransformMatrix.transform_vertices-collapsed" style="display:none;" pad="++" indent="++++++++"></div><div id="TransformMatrix.transform_vertices-expanded"><a name="L92"></a><tt class="py-lineno">92</tt> <tt class="py-line"> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">verts</tt><tt class="py-op">)</tt> </tt>
<a name="L93"></a><tt class="py-lineno">93</tt> <tt class="py-line"> <tt class="py-name">homog</tt> <tt class="py-op">=</tt> <tt id="link-3" class="py-name"><a title="VisionEgg.ThreeDeeMath.make_homogeneous_coord_rows" class="py-name" href="#" onclick="return doclink('link-3', 'make_homogeneous_coord_rows', 'link-0');">make_homogeneous_coord_rows</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt> </tt>
<a name="L94"></a><tt class="py-lineno">94</tt> <tt class="py-line"> <tt class="py-name">r</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">dot</tt><tt class="py-op">(</tt><tt class="py-name">homog</tt><tt class="py-op">,</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">matrix</tt><tt class="py-op">)</tt> </tt>
<a name="L95"></a><tt class="py-lineno">95</tt> <tt class="py-line"> <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">homog</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-op">></tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L96"></a><tt class="py-lineno">96</tt> <tt class="py-line"> <tt class="py-name">r</tt> <tt class="py-op">=</tt> <tt class="py-name">Numeric</tt><tt class="py-op">.</tt><tt class="py-name">reshape</tt><tt class="py-op">(</tt><tt class="py-name">r</tt><tt class="py-op">,</tt><tt class="py-op">(</tt><tt class="py-number">4</tt><tt class="py-op">,</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L97"></a><tt class="py-lineno">97</tt> <tt class="py-line"> <tt class="py-keyword">return</tt> <tt class="py-name">r</tt> </tt>
</div></div><a name="L98"></a><tt class="py-lineno">98</tt> <tt class="py-line"> </tt><script type="text/javascript">
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