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<div class="title">al_Matrix4.hpp</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef INCLUDE_AL_MATRIX4_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define INCLUDE_AL_MATRIX4_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>  </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/* Allocore --</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Multimedia / virtual environment application class library</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"></span> </div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Copyright (C) 2012. The Regents of the University of California.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> All rights reserved.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"></span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> modification, are permitted provided that the following conditions are met:</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"></span> </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> Redistributions of source code must retain the above copyright notice,</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> this list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"></span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> Redistributions in binary form must reproduce the above copyright</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> notice, this list of conditions and the following disclaimer in the</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> documentation and/or other materials provided with the distribution.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"></span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> Neither the name of the University of California nor the names of its</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> contributors may be used to endorse or promote products derived from</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> this software without specific prior written permission.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"></span> </div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"> SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment"> INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"> CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"></span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"></span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> File description:</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> This is a more specialized 4x4 matrix including transformations commonly</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> used in computer graphics.</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"></span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> File author(s):</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"> Graham Wakefield, 2010, [email protected]</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include "al/math/al_Constants.hpp"</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#include "al/math/al_Mat.hpp"</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#include "al/math/al_Quat.hpp"</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#include "al/math/al_Vec.hpp"</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">namespace </span><a class="code" href="namespaceal.html">al</a> {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">class </span>Matrix4;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
<div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="namespaceal.html#ad2d48f8ee7cfa29f2c8be8c0fb118b28"> 56</a></span> <span class="keyword">typedef</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4<double></a> <a class="code" href="namespaceal.html#ad2d48f8ee7cfa29f2c8be8c0fb118b28">Matrix4d</a>; </div>
<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="namespaceal.html#a4b47c3c871060f3a288d5066b452586a"> 57</a></span> <span class="keyword">typedef</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4<float></a> <a class="code" href="namespaceal.html#a4b47c3c871060f3a288d5066b452586a">Matrix4f</a>; </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T = <span class="keywordtype">double</span>></div>
<div class="line"><a name="l00063"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html"> 63</a></span> <span class="keyword">class </span><a class="code" href="classal_1_1_matrix4.html">Matrix4</a> : <span class="keyword">public</span> <a class="code" href="classal_1_1_mat.html">Mat</a><4, T> {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">typedef</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a> <a class="code" href="classal_1_1_mat.html">Base</a>;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  </div>
<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513"> 68</a></span>  <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>() : <a class="code" href="classal_1_1_mat.html">Base</a>(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1) {}</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">/*</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> The constructor will map into memory locations as follows:</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"></span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> Matrix4(arg1, arg2, arg3, ...)</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"></span> </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"> arg1 ->m[0] arg2 ->m[4] arg3 ->m[8] arg4 ->m[12]</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> arg5 ->m[1] arg6 ->m[5] arg7 ->m[9] arg8 ->m[13]</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> arg9 ->m[2] arg10->m[6] arg11->m[10] arg12->m[14]</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> arg13->m[3] arg14->m[7] arg15->m[11] arg16->m[15]</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"></span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> Matrix4(r1c1, r1c2, r1c3, r1c4,</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> r2c1, r2c2, r2c3, r2c4,</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> r3c1, r3c2, r3c3, r3c4,</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> r4c1, r4c2, r4c3, r4c4)</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(<span class="keyword">const</span> T& r1c1, <span class="keyword">const</span> T& r1c2, <span class="keyword">const</span> T& r1c3, <span class="keyword">const</span> T& r1c4,</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">const</span> T& r2c1, <span class="keyword">const</span> T& r2c2, <span class="keyword">const</span> T& r2c3, <span class="keyword">const</span> T& r2c4,</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">const</span> T& r3c1, <span class="keyword">const</span> T& r3c2, <span class="keyword">const</span> T& r3c3, <span class="keyword">const</span> T& r3c4,</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">const</span> T& r4c1, <span class="keyword">const</span> T& r4c2, <span class="keyword">const</span> T& r4c3, <span class="keyword">const</span> T& r4c4)</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  : Base(r1c1, r1c2, r1c3, r1c4, r2c1, r2c2, r2c3, r2c4, r3c1, r3c2, r3c3,</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  r3c4, r4c1, r4c2, r4c3, r4c4) {}</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(<span class="keyword">const</span> Vec<3, T>& xaxis, <span class="keyword">const</span> Vec<3, T>& yaxis,</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keyword">const</span> Vec<3, T>& zaxis, <span class="keyword">const</span> Vec<3, T>& position)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  : Base(xaxis[0], yaxis[0], zaxis[0], position[0], xaxis[1], yaxis[1],</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  zaxis[1], position[1], xaxis[2], yaxis[2], zaxis[2], position[2],</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  0, 0, 0, 1) {}</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#acdb19ebd1f752bc3a7d8cd7c3ef099be"> 99</a></span>  <a class="code" href="classal_1_1_matrix4.html#acdb19ebd1f752bc3a7d8cd7c3ef099be">Matrix4</a>(<span class="keyword">const</span> T* src) : <a class="code" href="classal_1_1_mat.html">Base</a>(src) {}</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a7a02e36e11cd247d6b8dba65fd58fcb6"> 102</a></span>  <a class="code" href="classal_1_1_matrix4.html#a7a02e36e11cd247d6b8dba65fd58fcb6">Matrix4</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a>& src) : <a class="code" href="classal_1_1_mat.html">Base</a>(src) {}</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#adce4e41e81e94612748487e9b7a50206"> 105</a></span>  <a class="code" href="classal_1_1_quat.html">Quat<T></a> <a class="code" href="classal_1_1_matrix4.html#adce4e41e81e94612748487e9b7a50206">toQuat</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_quat.html">Quat<T></a>().<a class="code" href="classal_1_1_quat.html#a49e8ad00ebd60347af2d671260e39cbd">fromMatrix</a>(<a class="code" href="classal_1_1_mat.html#a289ba4b7f55059fab225e368551c2004">Base::elems</a>()); }</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  </div>
<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a0ec875fcd68db0642906059e9c7a1ea6"> 108</a></span>  <a class="code" href="classal_1_1_matrix4.html">Matrix4</a>& <a class="code" href="classal_1_1_matrix4.html#a0ec875fcd68db0642906059e9c7a1ea6">fromQuat</a>(<a class="code" href="classal_1_1_quat.html">Quat<T></a>& q) {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  q.<a class="code" href="classal_1_1_quat.html#a63cc4051e9aa05de6356bb1b547f8c81">toMatrix</a>(<a class="code" href="classal_1_1_mat.html#a289ba4b7f55059fab225e368551c2004">Base::elems</a>());</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="classal_1_1_matrix4.html">Matrix4</a>& fromQuatTransposed(<a class="code" href="classal_1_1_quat.html">Quat<T></a>& q) {</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  q.<a class="code" href="classal_1_1_quat.html#a8688ba3bf4737c8541a9e73c42852514">toMatrixTransposed</a>(<a class="code" href="classal_1_1_mat.html#a289ba4b7f55059fab225e368551c2004">Base::elems</a>());</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  }</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> rotate(<span class="keywordtype">float</span> <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>, <span class="keywordtype">float</span> x, <span class="keywordtype">float</span> y, <span class="keywordtype">float</span> z) {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">return</span> Matrix4::rotate(<a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>, <a class="code" href="namespaceal.html#a2c986862410061adeaba684e7fffb06b">Vec3d</a>(x, y, z));</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  }</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  </div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> rotate(<span class="keywordtype">float</span> <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>, <span class="keyword">const</span> Vec<3, T>& v) {</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  Vec<3, T> axis(v);</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  axis.normalize();</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordtype">float</span> c = cos(<a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordtype">float</span> s = sin(<a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> m(axis[0] * axis[0] * (1 - c) + c,</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  axis[1] * axis[0] * (1 - c) + axis[2] * s,</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  axis[0] * axis[2] * (1 - c) - axis[1] * s, 0,</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  axis[0] * axis[1] * (1 - c) - axis[2] * s,</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  axis[1] * axis[1] * (1 - c) + c,</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  axis[1] * axis[2] * (1 - c) + axis[0] * s, 0,</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  axis[0] * axis[2] * (1 - c) + axis[1] * s,</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  axis[1] * axis[2] * (1 - c) - axis[0] * s,</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  axis[2] * axis[2] * (1 - c) + c, 0,</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  0, 0, 0, 1);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">return</span> m;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div>
<div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#ab733d545f97a2db7c36a227fd5db3930"> 146</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#ab733d545f97a2db7c36a227fd5db3930">shearXY</a>(T x, T y) {</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(1, 0, x, 0, 0, 1, y, 0, 0, 0, 1, 0, 0, 0, 0, 1);</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  }</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  </div>
<div class="line"><a name="l00151"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a3762d032592d19af4958ad45c20033e0"> 151</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a3762d032592d19af4958ad45c20033e0">shearYZ</a>(T y, T z) {</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(1, 0, 0, 0, y, 1, 0, 0, z, 0, 1, 0, 0, 0, 0, 1);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  </div>
<div class="line"><a name="l00156"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a6a0d3df8f114343d2c83023b7c062c90"> 156</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a6a0d3df8f114343d2c83023b7c062c90">shearZX</a>(T z, T x) {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(1, x, 0, 0, 0, 1, 0, 0, 0, z, 1, 0, 0, 0, 0, 1);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  }</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a904c343eabcd544fa11b9f659594faf6"> 168</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a904c343eabcd544fa11b9f659594faf6">perspective</a>(T l, T r, T b, T t, T n, T f) {</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  T W = r - l;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  T W2 = r + l;</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  T H = t - b;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  T H2 = t + b;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  T D = f - n;</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  T D2 = f + n;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  T n2 = n * 2;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  T fn2 = f * n2;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(n2 / W, 0, W2 / W, 0, 0, n2 / H, H2 / H, 0, 0, 0, -D2 / D,</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  -fn2 / D, 0, 0, -1, 0);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  }</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  </div>
<div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a2d22a3042933340e391d8a25df8a5bc8"> 187</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a2d22a3042933340e391d8a25df8a5bc8">perspective</a>(T fovy, T aspect, T near, T far) {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordtype">double</span> f = 1. / tan(fovy * M_DEG2RAD / 2.);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  T D = far - near;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  T D2 = far + near;</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  T fn2 = far * near * 2;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(f / aspect, 0, 0, 0, 0, f, 0, 0, 0, 0, -D2 / D, -fn2 / D, 0,</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  0, -1, 0);</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  }</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  </div>
<div class="line"><a name="l00208"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a013398f378bdaca67c911fa21c796427"> 208</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a013398f378bdaca67c911fa21c796427">perspective</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& nearBL, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& nearBR,</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& nearTL, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& eye,</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  T near, T far) {</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <a class="code" href="classal_1_1_vec.html">Vec<3, T></a> va, vb, vc;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <a class="code" href="classal_1_1_vec.html">Vec<3, T></a> vr, vu, vn;</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  T l, r, b, t, d;</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">// compute orthonormal basis for the screen</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  vr = (nearBR - nearBL).normalize(); <span class="comment">// right vector</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  vu = (nearTL - nearBL).normalize(); <span class="comment">// up vector</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <a class="code" href="namespaceal.html#ad14a4f234c06e599950cccc84adaab80">cross</a>(vn, vr, vu); <span class="comment">// normal(forward) vector (out from screen)</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  vn.<a class="code" href="classal_1_1_vec.html#a2737e88df374bcf0874ecf24bd72ed64">normalize</a>();</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  </div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// compute vectors from eye to screen corners:</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  va = nearBL - eye;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  vb = nearBR - eye;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  vc = nearTL - eye;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// distance from eye to screen-plane</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="comment">// = component of va along vector vn (normal to screen)</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  d = -va.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(vn);</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  </div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">// find extent of perpendicular projection</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  T nbyd = near / d;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  l = vr.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(va) * nbyd;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  r = vr.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(vb) * nbyd;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  b = vu.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(va) * nbyd; <span class="comment">// not vd?</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  t = vu.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(vc) * nbyd;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a904c343eabcd544fa11b9f659594faf6">perspective</a>(l, r, b, t, near, far);</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  }</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  </div>
<div class="line"><a name="l00241"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a35e08a87da86bda23ea3fd0a47426250"> 241</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a35e08a87da86bda23ea3fd0a47426250">perspectiveLeft</a>(T fovy, T aspect, T near, T far, T eyeSep,</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  T focal) {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a2a5a266029011521b1d0ebe455720851">perspectiveOffAxis</a>(fovy, aspect, near, far, -0.5 * eyeSep, focal);</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  }</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  </div>
<div class="line"><a name="l00247"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a4ac074812fdb8e439443e16c80416da5"> 247</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a4ac074812fdb8e439443e16c80416da5">perspectiveRight</a>(T fovy, T aspect, T near, T far, T eyeSep,</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  T focal) {</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a2a5a266029011521b1d0ebe455720851">perspectiveOffAxis</a>(fovy, aspect, near, far, 0.5 * eyeSep, focal);</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  }</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  </div>
<div class="line"><a name="l00253"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a2a5a266029011521b1d0ebe455720851"> 253</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a2a5a266029011521b1d0ebe455720851">perspectiveOffAxis</a>(T fovy, T aspect, T near, T far, T xShift,</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  T focal) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  T top = near *</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  tan(fovy * M_DEG2RAD * 0.5); <span class="comment">// height of view at distance = near</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  T bottom = -top;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  T shift = -xShift * near / focal;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  T left = -aspect * top + shift;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  T right = aspect * top + shift;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a904c343eabcd544fa11b9f659594faf6">perspective</a>(left, right, bottom, top, near, far);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  }</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  </div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  </div>
<div class="line"><a name="l00273"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a1b9f9f5cc7b578b62e0244cc1884de72"> 273</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a1b9f9f5cc7b578b62e0244cc1884de72">perspectiveOffAxis</a>(T fovy, T aspect, T near, T far, T xShift,</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  T yShift, T focal) {</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keywordtype">double</span> tanfovy = tan(fovy * M_DEG2RAD / 2.);</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  T t = near * tanfovy; <span class="comment">// height of view at distance = near</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  T b = -t;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  T l = -aspect * t;</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  T r = aspect * t;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  </div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  T shift = -xShift * near / focal;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  l += shift;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  r += shift;</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  shift = -yShift * near / focal;</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  t += shift;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  b += shift;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  </div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a904c343eabcd544fa11b9f659594faf6">perspective</a>(l, r, b, t, near, far);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  }</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> unPerspective(T l, T r, T b, T t, T n, T f) {</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  T W = r - l;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  T W2 = r + l;</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  T H = t - b;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  T H2 = t + b;</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  T D = f - n;</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  T D2 = f + n;</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  T n2 = n * 2;</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  T fn2 = f * n2;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(W / n2, 0, 0, W2 / n2, 0, H / n2, 0, H2 / n2, 0, 0, 0, -1, 0,</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  0, -D / fn2, D2 / fn2);</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  }</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  </div>
<div class="line"><a name="l00312"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a4b648d23d4b8f60f9eb72c1e460b870a"> 312</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a4b648d23d4b8f60f9eb72c1e460b870a">ortho</a>(T l, T r, T b, T t, T n, T f) {</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  T W = r - l;</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  T W2 = r + l;</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  T H = t - b;</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  T H2 = t + b;</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  T D = f - n;</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  T D2 = f + n;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(2 / W, 0, 0, -W2 / W, 0, 2 / H, 0, -H2 / H, 0, 0, -2 / D,</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  -D2 / D, 0, 0, 0, 1);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  }</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  </div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> unOrtho(T l, T r, T b, T t, T n, T f) {</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  T W = r - l;</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  T W2 = r + l;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  T H = t - b;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  T H2 = t + b;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  T D = f - n;</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  T D2 = f + n;</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(W / 2, 0, 0, W2 / 2, 0, H / 2, 0, H2 / 2, 0, 0, D / -2,</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  D2 / 2, 0, 0, 0, 1);</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  }</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  </div>
<div class="line"><a name="l00341"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a18c4e3451b2dfcf15a9cbcde214e7b3f"> 341</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a18c4e3451b2dfcf15a9cbcde214e7b3f">ortho2D</a>(T l, T r, T b, T t) {</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  T W = r - l;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  T W2 = r + l;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  T H = t - b;</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  T H2 = t + b;</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(2 / W, 0, 0, -W2 / W, 0, 2 / H, 0, -H2 / H, 0, 0, -1, 0, 0,</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  0, 0, 1);</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  }</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  </div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  </div>
<div class="line"><a name="l00356"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#af33c8412c17906013a6e2cf2c9d682fe"> 356</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#af33c8412c17906013a6e2cf2c9d682fe">lookAt</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& ur, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uu,</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uf, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& eyePos) {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a>(ur[0], ur[1], ur[2], -(ur.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(eyePos)), uu[0], uu[1], uu[2],</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  -(uu.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(eyePos)), uf[0], uf[1], uf[2], -(uf.<a class="code" href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">dot</a>(eyePos)), 0,</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  0, 0, 1);</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  }</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  </div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  </div>
<div class="line"><a name="l00368"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a75fbce67ec6620b64347b76d13322814"> 368</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a75fbce67ec6620b64347b76d13322814">lookAt</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& eyePos, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& at,</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& up) {</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <a class="code" href="classal_1_1_vec.html">Vec<3, T></a> z = (at - eyePos).normalize();</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <a class="code" href="classal_1_1_vec.html">Vec<3, T></a> y = up;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  y.<a class="code" href="classal_1_1_vec.html#a2737e88df374bcf0874ecf24bd72ed64">normalize</a>();</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <a class="code" href="classal_1_1_vec.html">Vec<3, T></a> x = <a class="code" href="namespaceal.html#ad14a4f234c06e599950cccc84adaab80">cross</a>(z, up).normalize();</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#af33c8412c17906013a6e2cf2c9d682fe">lookAt</a>(x, y, -z, eyePos);</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  }</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="comment">// static Matrix4 lookAtRH(const Vec<3,T>& ux, const Vec<3,T>& uy, const</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="comment">// Vec<3,T>& uz, const Vec<3,T>& pos) {</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="comment">// return Matrix4(</span></div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="comment">// ux[0], ux[1], ux[2], -(ux.dot(pos)),</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="comment">// uy[0], uy[1], uy[2], -(uy.dot(pos)),</span></div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="comment">// uz[0],uz[1],uz[2], -(uz.dot(pos)),</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="comment">// 0, 0, 0, 1</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="comment">// );</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="comment">// }</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="comment">// static Matrix4 lookAtRH(const Vec<3,T>& eye, const Vec<3,T>& at, const</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="comment">// Vec<3,T>& up) {</span></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="comment">// Vec<3,T> z = (at - eye).normalize();</span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="comment">// Vec<3,T> x = cross(up, z);</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="comment">// Vec<3,T> y = cross(z, x);</span></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="comment">// return lookAt(x, y, z, eye);</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="comment">// }</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  </div>
<div class="line"><a name="l00396"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a03cf4259bb47590eed26b183d836d0f9"> 396</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a03cf4259bb47590eed26b183d836d0f9">lookAtLeft</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& ux, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uy,</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uz, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& pos,</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keywordtype">double</span> eyeSep) {</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a43fee81f5d41e0652c0b2c3d14abc30d">lookAtOffAxis</a>(ux, uy, uz, pos, -0.5 * eyeSep);</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  }</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  </div>
<div class="line"><a name="l00403"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a9d5e8c7cbd2e6b3720f394ca3fe439bb"> 403</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a9d5e8c7cbd2e6b3720f394ca3fe439bb">lookAtRight</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& ux, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uy,</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uz, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& pos,</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordtype">double</span> eyeSep) {</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a43fee81f5d41e0652c0b2c3d14abc30d">lookAtOffAxis</a>(ux, uy, uz, pos, 0.5 * eyeSep);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  }</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  </div>
<div class="line"><a name="l00410"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a43fee81f5d41e0652c0b2c3d14abc30d"> 410</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a43fee81f5d41e0652c0b2c3d14abc30d">lookAtOffAxis</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& ux, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uy,</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& uz, <span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& pos,</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordtype">double</span> eyeShift) {</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#af33c8412c17906013a6e2cf2c9d682fe">lookAt</a>(ux, uy, uz, pos + (ux * -eyeShift));</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  }</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  </div>
<div class="line"><a name="l00420"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a5a184ddd53688e856e8f25db313b1eae"> 420</a></span>  <a class="code" href="classal_1_1_vec.html">Vec<4, T></a> <a class="code" href="classal_1_1_matrix4.html#a5a184ddd53688e856e8f25db313b1eae">transform</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<4, T></a>& vCol)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> *<span class="keyword">this</span> * vCol; }</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  </div>
<div class="line"><a name="l00423"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a5b1259152768e2f51cb5d671d8f0da5e"> 423</a></span>  <a class="code" href="classal_1_1_vec.html">Vec<4, T></a> <a class="code" href="classal_1_1_matrix4.html#a5b1259152768e2f51cb5d671d8f0da5e">transform</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_vec.html">Vec<3, T></a>& vCol)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_matrix4.html#a5a184ddd53688e856e8f25db313b1eae">transform</a>(<a class="code" href="classal_1_1_vec.html">Vec<4, T></a>(vCol, T(1)));</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  }</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  </div>
<div class="line"><a name="l00428"></a><span class="lineno"><a class="line" href="classal_1_1_matrix4.html#a43f25693db09358f006f5b02c7c63fe2"> 428</a></span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> <a class="code" href="classal_1_1_matrix4.html#a43f25693db09358f006f5b02c7c63fe2">inverse</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a>& m) {</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> res(m);</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <a class="code" href="namespaceal.html#a01e6ff37545e24d45fe18c45c526a06b">invert</a>(res);</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  }</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  </div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  <span class="comment">// \deprecated Use Mat::translation</span></div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html">Matrix4</a> translate(T x, T y, T z) {</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a3c4409eb7c87f2041538baec741dd66d">translation</a>(<a class="code" href="classal_1_1_vec.html">Vec<3, T></a>(x, y, z));</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  }</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="comment">// \deprecated Use Mat::translation</span></div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> V></div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> translate(<span class="keyword">const</span> Vec<3, V>& v) {</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a3c4409eb7c87f2041538baec741dd66d">translation</a>(v);</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  }</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="comment">// \deprecated Use Mat::scaling</span></div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> scale(T x, T y, T z) { <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a3ab804e4cf805f1a92ae4ee2164ff745">scaling</a>(x, y, z); }</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="comment">// \deprecated Use Mat::scaling</span></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> V></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> scale(<span class="keyword">const</span> Vec<3, V>& v) {</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a3ab804e4cf805f1a92ae4ee2164ff745">scaling</a>(v);</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  }</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <span class="comment">// \deprecated Use Mat::scaling</span></div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> V></div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> scale(<span class="keyword">const</span> V& v) {</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a3ab804e4cf805f1a92ae4ee2164ff745">scaling</a>(v);</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  }</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="comment">// \deprecated Use Mat::rotation</span></div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> rotateXY(T theta) { <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a469d2249af79eddad941c3aea7f62dfe">rotation</a>(theta, 0, 1); }</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> rotateYZ(T theta) { <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a469d2249af79eddad941c3aea7f62dfe">rotation</a>(theta, 1, 2); }</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keyword">static</span> <a class="code" href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">Matrix4</a> rotateZX(T theta) { <span class="keywordflow">return</span> <a class="code" href="classal_1_1_mat.html#a469d2249af79eddad941c3aea7f62dfe">rotation</a>(theta, 2, 0); }</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> };</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00463"></a><span class="lineno"><a class="line" href="namespaceal.html#a980d8afb59ec2aa6e1097bae6d1c138d"> 463</a></span> <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a980d8afb59ec2aa6e1097bae6d1c138d">frustumFar</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a>& proj) {</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keywordflow">return</span> proj[14] / (proj[10] + T(1));</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> }</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  </div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00469"></a><span class="lineno"><a class="line" href="namespaceal.html#a282fb9ab041dcb0215a4db50c343e2ea"> 469</a></span> <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a282fb9ab041dcb0215a4db50c343e2ea">frustumNear</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a>& proj) {</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keywordflow">return</span> proj[14] / (proj[10] - T(1));</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> }</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00475"></a><span class="lineno"><a class="line" href="namespaceal.html#aed78f28e0bf2fa336f05684d515feefe"> 475</a></span> <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#aed78f28e0bf2fa336f05684d515feefe">frustumDepth</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a>& proj) {</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keywordflow">return</span> (T(-2) * proj[14]) / (proj[10] * proj[10] - T(1));</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> }</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  </div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00481"></a><span class="lineno"><a class="line" href="namespaceal.html#a3bf314d5cf2586cd163ad52e72f6cc27"> 481</a></span> <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a3bf314d5cf2586cd163ad52e72f6cc27">frustumAspect</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_mat.html">Mat<4, T></a>& proj) {</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="keywordflow">return</span> proj[5] / proj[0];</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> }</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  </div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> } <span class="comment">// namespace al</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  </div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="preprocessor">#endif </span><span class="comment">/* include guard */</span><span class="preprocessor"></span></div>
<div class="ttc" id="aclassal_1_1_mat_html"><div class="ttname"><a href="classal_1_1_mat.html">al::Mat</a></div><div class="ttdoc">Fixed-size n-by-n square matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___mat_8hpp_source.html#l00078">al_Mat.hpp:78</a></div></div>
<div class="ttc" id="aclassal_1_1_mat_html_a289ba4b7f55059fab225e368551c2004"><div class="ttname"><a href="classal_1_1_mat.html#a289ba4b7f55059fab225e368551c2004">al::Mat::elems</a></div><div class="ttdeci">const T * elems() const</div><div class="ttdoc">Get read-only pointer to elements.</div><div class="ttdef"><b>Definition:</b> <a href="al___mat_8hpp_source.html#l00191">al_Mat.hpp:191</a></div></div>
<div class="ttc" id="aclassal_1_1_mat_html_a3ab804e4cf805f1a92ae4ee2164ff745"><div class="ttname"><a href="classal_1_1_mat.html#a3ab804e4cf805f1a92ae4ee2164ff745">al::Mat< 4, double >::scaling</a></div><div class="ttdeci">static Mat scaling(const Vec< N - 1, V > &v)</div><div class="ttdoc">Get a scaling transform matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___mat_8hpp_source.html#l00146">al_Mat.hpp:146</a></div></div>
<div class="ttc" id="aclassal_1_1_mat_html_a3c4409eb7c87f2041538baec741dd66d"><div class="ttname"><a href="classal_1_1_mat.html#a3c4409eb7c87f2041538baec741dd66d">al::Mat< 4, double >::translation</a></div><div class="ttdeci">static Mat translation(const Vec< N - 1, V > &v)</div><div class="ttdoc">Get a translation transform matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___mat_8hpp_source.html#l00167">al_Mat.hpp:167</a></div></div>
<div class="ttc" id="aclassal_1_1_mat_html_a469d2249af79eddad941c3aea7f62dfe"><div class="ttname"><a href="classal_1_1_mat.html#a469d2249af79eddad941c3aea7f62dfe">al::Mat< 4, double >::rotation</a></div><div class="ttdeci">static Mat rotation(double angle, int dim1, int dim2)</div><div class="ttdoc">Get a rotation transform matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___mat_8hpp_source.html#l00131">al_Mat.hpp:131</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html"><div class="ttname"><a href="classal_1_1_matrix4.html">al::Matrix4</a></div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00063">al_Matrix4.hpp:63</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a013398f378bdaca67c911fa21c796427"><div class="ttname"><a href="classal_1_1_matrix4.html#a013398f378bdaca67c911fa21c796427">al::Matrix4::perspective</a></div><div class="ttdeci">static Matrix4 perspective(const Vec< 3, T > &nearBL, const Vec< 3, T > &nearBR, const Vec< 3, T > &nearTL, const Vec< 3, T > &eye, T near, T far)</div><div class="ttdoc">Calculate perspective projection from near plane and eye coordinates.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00208">al_Matrix4.hpp:208</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a03cf4259bb47590eed26b183d836d0f9"><div class="ttname"><a href="classal_1_1_matrix4.html#a03cf4259bb47590eed26b183d836d0f9">al::Matrix4::lookAtLeft</a></div><div class="ttdeci">static Matrix4 lookAtLeft(const Vec< 3, T > &ux, const Vec< 3, T > &uy, const Vec< 3, T > &uz, const Vec< 3, T > &pos, double eyeSep)</div><div class="ttdoc">Get a left-eye viewing matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00396">al_Matrix4.hpp:396</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a0ec875fcd68db0642906059e9c7a1ea6"><div class="ttname"><a href="classal_1_1_matrix4.html#a0ec875fcd68db0642906059e9c7a1ea6">al::Matrix4::fromQuat</a></div><div class="ttdeci">Matrix4 & fromQuat(Quat< T > &q)</div><div class="ttdoc">Set from quaternion.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00108">al_Matrix4.hpp:108</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a18c4e3451b2dfcf15a9cbcde214e7b3f"><div class="ttname"><a href="classal_1_1_matrix4.html#a18c4e3451b2dfcf15a9cbcde214e7b3f">al::Matrix4::ortho2D</a></div><div class="ttdeci">static Matrix4 ortho2D(T l, T r, T b, T t)</div><div class="ttdoc">Get a two-dimensional orthographic projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00341">al_Matrix4.hpp:341</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a1b9f9f5cc7b578b62e0244cc1884de72"><div class="ttname"><a href="classal_1_1_matrix4.html#a1b9f9f5cc7b578b62e0244cc1884de72">al::Matrix4::perspectiveOffAxis</a></div><div class="ttdeci">static Matrix4 perspectiveOffAxis(T fovy, T aspect, T near, T far, T xShift, T yShift, T focal)</div><div class="ttdoc">Get an off-axis perspective projection matrix (for stereographics)</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00273">al_Matrix4.hpp:273</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a1eed8c476d4a80dcfc4bdc87d78fb513"><div class="ttname"><a href="classal_1_1_matrix4.html#a1eed8c476d4a80dcfc4bdc87d78fb513">al::Matrix4::Matrix4</a></div><div class="ttdeci">Matrix4()</div><div class="ttdoc">Default constructor creates an identity matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00068">al_Matrix4.hpp:68</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a2a5a266029011521b1d0ebe455720851"><div class="ttname"><a href="classal_1_1_matrix4.html#a2a5a266029011521b1d0ebe455720851">al::Matrix4::perspectiveOffAxis</a></div><div class="ttdeci">static Matrix4 perspectiveOffAxis(T fovy, T aspect, T near, T far, T xShift, T focal)</div><div class="ttdoc">Get an off-axis perspective projection matrix (for stereographics)</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00253">al_Matrix4.hpp:253</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a2d22a3042933340e391d8a25df8a5bc8"><div class="ttname"><a href="classal_1_1_matrix4.html#a2d22a3042933340e391d8a25df8a5bc8">al::Matrix4::perspective</a></div><div class="ttdeci">static Matrix4 perspective(T fovy, T aspect, T near, T far)</div><div class="ttdoc">Get a perspective projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00187">al_Matrix4.hpp:187</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a35e08a87da86bda23ea3fd0a47426250"><div class="ttname"><a href="classal_1_1_matrix4.html#a35e08a87da86bda23ea3fd0a47426250">al::Matrix4::perspectiveLeft</a></div><div class="ttdeci">static Matrix4 perspectiveLeft(T fovy, T aspect, T near, T far, T eyeSep, T focal)</div><div class="ttdoc">Get a left-eye perspective projection matrix (for stereographics)</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00241">al_Matrix4.hpp:241</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a3762d032592d19af4958ad45c20033e0"><div class="ttname"><a href="classal_1_1_matrix4.html#a3762d032592d19af4958ad45c20033e0">al::Matrix4::shearYZ</a></div><div class="ttdeci">static Matrix4 shearYZ(T y, T z)</div><div class="ttdoc">Get a shear transformation matrix on the yz plane.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00151">al_Matrix4.hpp:151</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a43f25693db09358f006f5b02c7c63fe2"><div class="ttname"><a href="classal_1_1_matrix4.html#a43f25693db09358f006f5b02c7c63fe2">al::Matrix4::inverse</a></div><div class="ttdeci">static Matrix4 inverse(const Mat< 4, T > &m)</div><div class="ttdoc">Get the inverse of a matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00428">al_Matrix4.hpp:428</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a43fee81f5d41e0652c0b2c3d14abc30d"><div class="ttname"><a href="classal_1_1_matrix4.html#a43fee81f5d41e0652c0b2c3d14abc30d">al::Matrix4::lookAtOffAxis</a></div><div class="ttdeci">static Matrix4 lookAtOffAxis(const Vec< 3, T > &ux, const Vec< 3, T > &uy, const Vec< 3, T > &uz, const Vec< 3, T > &pos, double eyeShift)</div><div class="ttdoc">Get an off-axis viewing matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00410">al_Matrix4.hpp:410</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a4ac074812fdb8e439443e16c80416da5"><div class="ttname"><a href="classal_1_1_matrix4.html#a4ac074812fdb8e439443e16c80416da5">al::Matrix4::perspectiveRight</a></div><div class="ttdeci">static Matrix4 perspectiveRight(T fovy, T aspect, T near, T far, T eyeSep, T focal)</div><div class="ttdoc">Get a right-eye perspective projection matrix (for stereographics)</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00247">al_Matrix4.hpp:247</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a4b648d23d4b8f60f9eb72c1e460b870a"><div class="ttname"><a href="classal_1_1_matrix4.html#a4b648d23d4b8f60f9eb72c1e460b870a">al::Matrix4::ortho</a></div><div class="ttdeci">static Matrix4 ortho(T l, T r, T b, T t, T n, T f)</div><div class="ttdoc">Get an orthographic projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00312">al_Matrix4.hpp:312</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a5a184ddd53688e856e8f25db313b1eae"><div class="ttname"><a href="classal_1_1_matrix4.html#a5a184ddd53688e856e8f25db313b1eae">al::Matrix4::transform</a></div><div class="ttdeci">Vec< 4, T > transform(const Vec< 4, T > &vCol) const</div><div class="ttdoc">Computes product of matrix multiplied by column vector, r = m * vCol.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00420">al_Matrix4.hpp:420</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a5b1259152768e2f51cb5d671d8f0da5e"><div class="ttname"><a href="classal_1_1_matrix4.html#a5b1259152768e2f51cb5d671d8f0da5e">al::Matrix4::transform</a></div><div class="ttdeci">Vec< 4, T > transform(const Vec< 3, T > &vCol) const</div><div class="ttdoc">Computes product of matrix multiplied by column vector, r = m * vCol.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00423">al_Matrix4.hpp:423</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a6a0d3df8f114343d2c83023b7c062c90"><div class="ttname"><a href="classal_1_1_matrix4.html#a6a0d3df8f114343d2c83023b7c062c90">al::Matrix4::shearZX</a></div><div class="ttdeci">static Matrix4 shearZX(T z, T x)</div><div class="ttdoc">Get a shear transformation matrix on the zx plane.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00156">al_Matrix4.hpp:156</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a75fbce67ec6620b64347b76d13322814"><div class="ttname"><a href="classal_1_1_matrix4.html#a75fbce67ec6620b64347b76d13322814">al::Matrix4::lookAt</a></div><div class="ttdeci">static Matrix4 lookAt(const Vec< 3, T > &eyePos, const Vec< 3, T > &at, const Vec< 3, T > &up)</div><div class="ttdoc">Get a viewing matrix based on look-at parameters.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00368">al_Matrix4.hpp:368</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a7a02e36e11cd247d6b8dba65fd58fcb6"><div class="ttname"><a href="classal_1_1_matrix4.html#a7a02e36e11cd247d6b8dba65fd58fcb6">al::Matrix4::Matrix4</a></div><div class="ttdeci">Matrix4(const Mat< 4, T > &src)</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00102">al_Matrix4.hpp:102</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a904c343eabcd544fa11b9f659594faf6"><div class="ttname"><a href="classal_1_1_matrix4.html#a904c343eabcd544fa11b9f659594faf6">al::Matrix4::perspective</a></div><div class="ttdeci">static Matrix4 perspective(T l, T r, T b, T t, T n, T f)</div><div class="ttdoc">Get a perspective projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00168">al_Matrix4.hpp:168</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_a9d5e8c7cbd2e6b3720f394ca3fe439bb"><div class="ttname"><a href="classal_1_1_matrix4.html#a9d5e8c7cbd2e6b3720f394ca3fe439bb">al::Matrix4::lookAtRight</a></div><div class="ttdeci">static Matrix4 lookAtRight(const Vec< 3, T > &ux, const Vec< 3, T > &uy, const Vec< 3, T > &uz, const Vec< 3, T > &pos, double eyeSep)</div><div class="ttdoc">Get a right-eye viewing matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00403">al_Matrix4.hpp:403</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_ab733d545f97a2db7c36a227fd5db3930"><div class="ttname"><a href="classal_1_1_matrix4.html#ab733d545f97a2db7c36a227fd5db3930">al::Matrix4::shearXY</a></div><div class="ttdeci">static Matrix4 shearXY(T x, T y)</div><div class="ttdoc">Get a shear transformation matrix on the xy plane.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00146">al_Matrix4.hpp:146</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_acdb19ebd1f752bc3a7d8cd7c3ef099be"><div class="ttname"><a href="classal_1_1_matrix4.html#acdb19ebd1f752bc3a7d8cd7c3ef099be">al::Matrix4::Matrix4</a></div><div class="ttdeci">Matrix4(const T *src)</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00099">al_Matrix4.hpp:99</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_adce4e41e81e94612748487e9b7a50206"><div class="ttname"><a href="classal_1_1_matrix4.html#adce4e41e81e94612748487e9b7a50206">al::Matrix4::toQuat</a></div><div class="ttdeci">Quat< T > toQuat() const</div><div class="ttdoc">Get a quaternion representation.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00105">al_Matrix4.hpp:105</a></div></div>
<div class="ttc" id="aclassal_1_1_matrix4_html_af33c8412c17906013a6e2cf2c9d682fe"><div class="ttname"><a href="classal_1_1_matrix4.html#af33c8412c17906013a6e2cf2c9d682fe">al::Matrix4::lookAt</a></div><div class="ttdeci">static Matrix4 lookAt(const Vec< 3, T > &ur, const Vec< 3, T > &uu, const Vec< 3, T > &uf, const Vec< 3, T > &eyePos)</div><div class="ttdoc">Get a viewing matrix based on an eye reference frame.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00356">al_Matrix4.hpp:356</a></div></div>
<div class="ttc" id="aclassal_1_1_quat_html"><div class="ttname"><a href="classal_1_1_quat.html">al::Quat</a></div><div class="ttdef"><b>Definition:</b> <a href="al___quat_8hpp_source.html#l00063">al_Quat.hpp:63</a></div></div>
<div class="ttc" id="aclassal_1_1_quat_html_a49e8ad00ebd60347af2d671260e39cbd"><div class="ttname"><a href="classal_1_1_quat.html#a49e8ad00ebd60347af2d671260e39cbd">al::Quat::fromMatrix</a></div><div class="ttdeci">Quat & fromMatrix(const T *matrix)</div><div class="ttdef"><b>Definition:</b> <a href="al___quat_8hpp_source.html#l00579">al_Quat.hpp:579</a></div></div>
<div class="ttc" id="aclassal_1_1_quat_html_a63cc4051e9aa05de6356bb1b547f8c81"><div class="ttname"><a href="classal_1_1_quat.html#a63cc4051e9aa05de6356bb1b547f8c81">al::Quat::toMatrix</a></div><div class="ttdeci">void toMatrix(T2 *matrix) const</div><div class="ttdoc">Convert to column-major 4-by-4 projective space transformation matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___quat_8hpp_source.html#l00764">al_Quat.hpp:764</a></div></div>
<div class="ttc" id="aclassal_1_1_quat_html_a8688ba3bf4737c8541a9e73c42852514"><div class="ttname"><a href="classal_1_1_quat.html#a8688ba3bf4737c8541a9e73c42852514">al::Quat::toMatrixTransposed</a></div><div class="ttdeci">void toMatrixTransposed(T2 *matrix) const</div><div class="ttdoc">Convert to row-major 4-by-4 projective space transformation matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___quat_8hpp_source.html#l00789">al_Quat.hpp:789</a></div></div>
<div class="ttc" id="aclassal_1_1_vec_html"><div class="ttname"><a href="classal_1_1_vec.html">al::Vec< 3, T ></a></div></div>
<div class="ttc" id="aclassal_1_1_vec_html_a2737e88df374bcf0874ecf24bd72ed64"><div class="ttname"><a href="classal_1_1_vec.html#a2737e88df374bcf0874ecf24bd72ed64">al::Vec::normalize</a></div><div class="ttdeci">Vec & normalize(T scale=T(1))</div><div class="ttdoc">Set magnitude to one without changing direction.</div><div class="ttdef"><b>Definition:</b> <a href="al___vec_8hpp_source.html#l00729">al_Vec.hpp:729</a></div></div>
<div class="ttc" id="aclassal_1_1_vec_html_aa5fee82d55d3f5cc48443e1f19903aad"><div class="ttname"><a href="classal_1_1_vec.html#aa5fee82d55d3f5cc48443e1f19903aad">al::Vec::dot</a></div><div class="ttdeci">T dot(const Vec< N, U > &v) const</div><div class="ttdoc">Returns dot (inner) product between vectors.</div><div class="ttdef"><b>Definition:</b> <a href="al___vec_8hpp_source.html#l00406">al_Vec.hpp:406</a></div></div>
<div class="ttc" id="anamespaceal_html"><div class="ttname"><a href="namespaceal.html">al</a></div><div class="ttdef"><b>Definition:</b> <a href="al___app_8hpp_source.html#l00023">al_App.hpp:23</a></div></div>
<div class="ttc" id="anamespaceal_html_a01e6ff37545e24d45fe18c45c526a06b"><div class="ttname"><a href="namespaceal.html#a01e6ff37545e24d45fe18c45c526a06b">al::invert</a></div><div class="ttdeci">bool invert(Mat< 1, T > &m)</div><div class="ttdef"><b>Definition:</b> <a href="al___mat_8hpp_source.html#l00643">al_Mat.hpp:643</a></div></div>
<div class="ttc" id="anamespaceal_html_a282fb9ab041dcb0215a4db50c343e2ea"><div class="ttname"><a href="namespaceal.html#a282fb9ab041dcb0215a4db50c343e2ea">al::frustumNear</a></div><div class="ttdeci">T frustumNear(const Mat< 4, T > &proj)</div><div class="ttdoc">Get frustum near plane distance from a projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00469">al_Matrix4.hpp:469</a></div></div>
<div class="ttc" id="anamespaceal_html_a2c986862410061adeaba684e7fffb06b"><div class="ttname"><a href="namespaceal.html#a2c986862410061adeaba684e7fffb06b">al::Vec3d</a></div><div class="ttdeci">Vec< 3, double > Vec3d</div><div class="ttdoc">double 3-vector</div><div class="ttdef"><b>Definition:</b> <a href="al___vec_8hpp_source.html#l00060">al_Vec.hpp:60</a></div></div>
<div class="ttc" id="anamespaceal_html_a3bf314d5cf2586cd163ad52e72f6cc27"><div class="ttname"><a href="namespaceal.html#a3bf314d5cf2586cd163ad52e72f6cc27">al::frustumAspect</a></div><div class="ttdeci">T frustumAspect(const Mat< 4, T > &proj)</div><div class="ttdoc">Get frustum aspect ratio from a projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00481">al_Matrix4.hpp:481</a></div></div>
<div class="ttc" id="anamespaceal_html_a4b47c3c871060f3a288d5066b452586a"><div class="ttname"><a href="namespaceal.html#a4b47c3c871060f3a288d5066b452586a">al::Matrix4f</a></div><div class="ttdeci">Matrix4< float > Matrix4f</div><div class="ttdoc">Single-precision 4-by-4 matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00057">al_Matrix4.hpp:57</a></div></div>
<div class="ttc" id="anamespaceal_html_a7be5747e8d4348af7f9dda1bbf480ee4"><div class="ttname"><a href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">al::angle</a></div><div class="ttdeci">T angle(const Vec< N, T > &a, const Vec< N, T > &b)</div><div class="ttdoc">Returns angle, in interval [0, pi], between two vectors.</div><div class="ttdef"><b>Definition:</b> <a href="al___vec_8hpp_source.html#l00634">al_Vec.hpp:634</a></div></div>
<div class="ttc" id="anamespaceal_html_a980d8afb59ec2aa6e1097bae6d1c138d"><div class="ttname"><a href="namespaceal.html#a980d8afb59ec2aa6e1097bae6d1c138d">al::frustumFar</a></div><div class="ttdeci">T frustumFar(const Mat< 4, T > &proj)</div><div class="ttdoc">Get frustum far plane distance from a projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00463">al_Matrix4.hpp:463</a></div></div>
<div class="ttc" id="anamespaceal_html_ad14a4f234c06e599950cccc84adaab80"><div class="ttname"><a href="namespaceal.html#ad14a4f234c06e599950cccc84adaab80">al::cross</a></div><div class="ttdeci">void cross(Vec< 3, T > &r, const Vec< 3, T > &a, const Vec< 3, T > &b)</div><div class="ttdoc">Sets r to cross product, a x b.</div><div class="ttdef"><b>Definition:</b> <a href="al___vec_8hpp_source.html#l00574">al_Vec.hpp:574</a></div></div>
<div class="ttc" id="anamespaceal_html_ad2d48f8ee7cfa29f2c8be8c0fb118b28"><div class="ttname"><a href="namespaceal.html#ad2d48f8ee7cfa29f2c8be8c0fb118b28">al::Matrix4d</a></div><div class="ttdeci">Matrix4< double > Matrix4d</div><div class="ttdoc">Double-precision 4-by-4 matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00056">al_Matrix4.hpp:54</a></div></div>
<div class="ttc" id="anamespaceal_html_aed78f28e0bf2fa336f05684d515feefe"><div class="ttname"><a href="namespaceal.html#aed78f28e0bf2fa336f05684d515feefe">al::frustumDepth</a></div><div class="ttdeci">T frustumDepth(const Mat< 4, T > &proj)</div><div class="ttdoc">Get frustum depth from a projection matrix.</div><div class="ttdef"><b>Definition:</b> <a href="al___matrix4_8hpp_source.html#l00475">al_Matrix4.hpp:475</a></div></div>
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