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<div class="title">al_Interpolation.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_MATH_INTERPOLATION_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define INCLUDE_AL_MATH_INTERPOLATION_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"> A collection of generic interpolation functions</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"></span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> File author(s):</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> Lance Putnam, 2006, [email protected]</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">namespace </span><a class="code" href="namespaceal.html">al</a> {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
<div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="namespaceal_1_1ipl.html"> 48</a></span> <span class="keyword">namespace </span>ipl {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> Tv <a class="code" href="group___math.html#gae25a56e2e68e9cddb8a8d59e56f8288d">bezier</a>(Tf frac, <span class="keyword">const</span> Tv& x2, <span class="keyword">const</span> Tv& x1, <span class="keyword">const</span> Tv& x0);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> Tv <a class="code" href="group___math.html#gae25a56e2e68e9cddb8a8d59e56f8288d">bezier</a>(Tf frac, <span class="keyword">const</span> Tv& x3, <span class="keyword">const</span> Tv& x2, <span class="keyword">const</span> Tv& x1, <span class="keyword">const</span> Tv& x0);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> Tv <a class="code" href="group___math.html#ga465b8747dbef55281301ee3801c36abe">casteljau</a>(<span class="keyword">const</span> Tf& frac, <span class="keyword">const</span> Tv& a, <span class="keyword">const</span> Tv& b, <span class="keyword">const</span> Tv& c,</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keyword">const</span> Tv& d);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tp, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> Tv <a class="code" href="group___math.html#ga36105e344104166b97f0a6f51560fd76">hermite</a>(Tp f, <span class="keyword">const</span> Tv& w, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z, Tp tension,</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  Tp bias);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gac34b241d907c8471c7bfa09207bd18b3">lagrange</a>(T* h, T delay, <span class="keywordtype">int</span> order);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga91fc7337dd163ffca419bbcf917bfab7">lagrange1</a>(T* h, T delay);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga62a32a386d799491b42c8d0089ad19c8">lagrange2</a>(T* h, T delay);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga9fbe7b22099ead82a30b5b04255ea9e3">lagrange3</a>(T* h, T delay);</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> <span class="comment">// Various functions to perform Waring-Lagrange interpolation.</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// These are much faster than using a general purpose FIR filter since</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// the coefs are computed directly and nested multiplication is used</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// rather than directly evaluating the polynomial (FIR).</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gaa941590d601a613962a98888c68a91bd">cardinalSpline</a>(Tv* w, <span class="keyword">const</span> Tv* x, <span class="keyword">const</span> Tf& f, <span class="keywordtype">double</span> b);</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> Tv <a class="code" href="group___math.html#ga26ffc66ac3be99197f46819c3dc33ce4">cubic</a>(Tf frac, <span class="keyword">const</span> Tv& w, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> Tv <a class="code" href="group___math.html#gaffdd572217deee07e2f811a545eaffe3">cubic2</a>(Tf frac, <span class="keyword">const</span> Tv& w, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  </div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> Tv <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(Tf frac, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> Tv <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(Tf frac, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> Tv <a class="code" href="group___math.html#ga8c05a1ef112a3ea36ab5d0a599102d65">linearCyclic</a>(Tf frac, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(Tv* dst, <span class="keyword">const</span> Tv* xs, <span class="keyword">const</span> Tv* xp1s, <span class="keywordtype">int</span> len, <span class="keyword">const</span> Tf& frac);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> Tv <a class="code" href="group___math.html#ga4f50b6d0ce1c4c7137a853a879ffd92b">nearest</a>(Tf frac, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00182"></a><span class="lineno"><a class="line" href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65"> 182</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65">bilinear</a>(<span class="keyword">const</span> Tf& fracX, <span class="keyword">const</span> Tf& fracY, <span class="keyword">const</span> Tv& xy, <span class="keyword">const</span> Tv& Xy,</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keyword">const</span> Tv& xY, <span class="keyword">const</span> Tv& XY) {</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(fracY, <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(fracX, xy, Xy), <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(fracX, xY, XY));</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf2, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00191"></a><span class="lineno"><a class="line" href="group___math.html#gaddd306398322157429607317d901c18f"> 191</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65">bilinear</a>(<span class="keyword">const</span> Tf2& f, <span class="keyword">const</span> Tv& xy, <span class="keyword">const</span> Tv& Xy, <span class="keyword">const</span> Tv& xY,</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keyword">const</span> Tv& XY) {</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65">bilinear</a>(f[0], f[1], xy, Xy, xY, XY);</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="l00199"></a><span class="lineno"> 199</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00200"></a><span class="lineno"><a class="line" href="group___math.html#ga623773336d6de114661f18ee79168886"> 200</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#ga623773336d6de114661f18ee79168886">trilinear</a>(<span class="keyword">const</span> Tf& fracX, <span class="keyword">const</span> Tf& fracY, <span class="keyword">const</span> Tf& fracZ,</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">const</span> Tv& xyz, <span class="keyword">const</span> Tv& Xyz, <span class="keyword">const</span> Tv& xYz, <span class="keyword">const</span> Tv& XYz,</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">const</span> Tv& xyZ, <span class="keyword">const</span> Tv& XyZ, <span class="keyword">const</span> Tv& xYZ,</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">const</span> Tv& XYZ) {</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(fracZ, <a class="code" href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65">bilinear</a>(fracX, fracY, xyz, Xyz, xYz, XYz),</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <a class="code" href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65">bilinear</a>(fracX, fracY, xyZ, XyZ, xYZ, XYZ));</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> }</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  </div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf3, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00214"></a><span class="lineno"><a class="line" href="group___math.html#ga0d390de762169619f0ac6f33ca1fabbf"> 214</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#ga623773336d6de114661f18ee79168886">trilinear</a>(<span class="keyword">const</span> Tf3& f, <span class="keyword">const</span> Tv& xyz, <span class="keyword">const</span> Tv& Xyz, <span class="keyword">const</span> Tv& xYz,</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">const</span> Tv& XYz, <span class="keyword">const</span> Tv& xyZ, <span class="keyword">const</span> Tv& XyZ, <span class="keyword">const</span> Tv& xYZ,</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keyword">const</span> Tv& XYZ) {</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga623773336d6de114661f18ee79168886">trilinear</a>(f[0], f[1], f[2], xyz, Xyz, xYz, XYz, xyZ, XyZ, xYZ, XYZ);</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment">//------------------------------------------------------------------------------</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment">// Implementation</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment">//------------------------------------------------------------------------------</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  </div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00225"></a><span class="lineno"><a class="line" href="group___math.html#gae25a56e2e68e9cddb8a8d59e56f8288d"> 225</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gae25a56e2e68e9cddb8a8d59e56f8288d">bezier</a>(Tf d, <span class="keyword">const</span> Tv& x2, <span class="keyword">const</span> Tv& x1, <span class="keyword">const</span> Tv& x0) {</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  Tf d2 = d * d;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  Tf dm1 = Tf(1) - d;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  Tf dm12 = dm1 * dm1;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">return</span> dm12 * x2 + Tf(2) * dm1 * d * x1 + d2 * x0;</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="comment">// x2 (1-d)(1-d) + 2 x1 (1-d) d + x0 d d</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">// x2 - d 2 x2 + d d x2 + d 2 x1 - d d 2 x1 + d d x0</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">// x2 - d (2 x2 + d x2 + 2 x1 - d 2 x1 + d x0)</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="comment">// x2 - d (2 (x2 + x1) + d (x2 - 2 x1 + x0))</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">// float c2 = x2 - 2.f * x1 + x0;</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">// float c1 = 2.f * (x2 + x1);</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// return x2 - (d * c2 + c1) * d;</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> }</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  </div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00242"></a><span class="lineno"><a class="line" href="group___math.html#gae90ea402a897a3cd9de4ef8569521ca1"> 242</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gae25a56e2e68e9cddb8a8d59e56f8288d">bezier</a>(Tf d, <span class="keyword">const</span> Tv& x3, <span class="keyword">const</span> Tv& x2, <span class="keyword">const</span> Tv& x1, <span class="keyword">const</span> Tv& x0) {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  Tv c1 = Tf(3) * (x2 - x3);</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  Tv c2 = Tf(3) * (x1 - x2) - c1;</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  Tv c3 = x0 - x3 - c1 - c2;</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">return</span> ((c3 * d + c2) * d + c1) * d + x3;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> }</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00250"></a><span class="lineno"><a class="line" href="group___math.html#ga465b8747dbef55281301ee3801c36abe"> 250</a></span> Tv <a class="code" href="group___math.html#ga465b8747dbef55281301ee3801c36abe">casteljau</a>(<span class="keyword">const</span> Tf& f, <span class="keyword">const</span> Tv& a, <span class="keyword">const</span> Tv& b, <span class="keyword">const</span> Tv& c, <span class="keyword">const</span> Tv& d) {</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  Tv ab = <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, a, b);</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  Tv bc = <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, b, c);</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  Tv cd = <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, c, d);</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, ab, bc), <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, bc, cd));</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> }</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  </div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="group___math.html#gaa941590d601a613962a98888c68a91bd"> 258</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gaa941590d601a613962a98888c68a91bd">cardinalSpline</a>(Tv* w, <span class="keyword">const</span> Tv* x, <span class="keyword">const</span> Tf& f, <span class="keywordtype">double</span> b) {</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="comment">// c = (1-b); // tension</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  b *= (x[2] - x[1]); <span class="comment">// make domain [t[1], t[2]]</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="comment">// evaluate the Hermite basis functions</span></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  Tf h00 = (1 + 2 * f) * (f - 1) * (f - 1);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  Tf h10 = f * (f - 1) * (f - 1);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  Tf h01 = f * f * (3 - 2 * f);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  Tf h11 = f * f * (f - 1);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  </div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="comment">/*</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"> The general cubic Hermite spline is</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment"> p(f) = h00 * p0 + h10 * m0 + h01 * p1 + h11 * m1</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"></span> </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> For a cardinal spline, the tangent at point k is</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment"> m[k] = (1-c) * (p[k+1] - p[k-1]) / (x[k+1] - x[k-1])</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment"></span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment"> To get the weights for each point, we plug the tangents into the general</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment"> spline equation and factor out the p[k].</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  </div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  w[0] = (-b * h10 / (x[2] - x[0]));</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  w[1] = (h00 - b * h11 / (x[3] - x[1]));</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  w[2] = (h01 + b * h10 / (x[2] - x[0]));</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  w[3] = (+b * h11 / (x[3] - x[1]));</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> }</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  </div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00286"></a><span class="lineno"><a class="line" href="group___math.html#ga26ffc66ac3be99197f46819c3dc33ce4"> 286</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#ga26ffc66ac3be99197f46819c3dc33ce4">cubic</a>(Tf f, <span class="keyword">const</span> Tv& w, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z) {</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="comment">// Tv c3 = (x - y)*(Tf)1.5 + (z - w)*(Tf)0.5;</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// Tv c2 = w - x*(Tf)2.5 + y*(Tf)2. - z*(Tf)0.5;</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// Tv c1 = (y - w)*(Tf)0.5;</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="comment">// return ((c3 * f + c2) * f + c1) * f + x;</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="comment">// -w + 3x - 3y + z</span></div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="comment">// 2w - 5x + 4y - z</span></div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="comment">// c2 = w - 2x + y - c3</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="comment">// Tv c3 = (x - y)*(Tf)3 + z - w;</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="comment">// Tv c2 = w - x*(Tf)2 + y - c3;</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// Tv c1 = y - w;</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">// return (((c3 * f + c2) * f + c1)) * f * (Tf)0.5 + x;</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="comment">// Tv c3 = (x - y)*(Tf)1.5 + (z - w)*(Tf)0.5;</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="comment">// Tv c2 = (y + w)*(Tf)0.5 - x - c3;</span></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="comment">// Tv c1 = (y - w)*(Tf)0.5;</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">// return ((c3 * f + c2) * f + c1) * f + x;</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  </div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  Tv c1 = (y - w) * Tf(0.5);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  Tv c3 = (x - y) * Tf(1.5) + (z - w) * Tf(0.5);</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  Tv c2 = c1 + w - x - c3;</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">return</span> ((c3 * f + c2) * f + c1) * f + x;</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> }</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  </div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga26ffc66ac3be99197f46819c3dc33ce4">cubic</a>(T* dst, <span class="keyword">const</span> T* xm1s, <span class="keyword">const</span> T* xs, <span class="keyword">const</span> T* xp1s, <span class="keyword">const</span> T* xp2s,</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordtype">int</span> len, T f) {</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < len; ++i)</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  dst[i] = <a class="code" href="group___math.html#ga26ffc66ac3be99197f46819c3dc33ce4">cubic</a>(f, xm1s[i], xs[i], xp1s[i], xp2s[i]);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> }</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  </div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment">// From http://astronomy.swin.edu.au/~pbourke/other/interpolation/ (Paul Bourke)</span></div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00321"></a><span class="lineno"><a class="line" href="group___math.html#gaffdd572217deee07e2f811a545eaffe3"> 321</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gaffdd572217deee07e2f811a545eaffe3">cubic2</a>(Tf f, <span class="keyword">const</span> Tv& w, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z) {</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  Tv c3 = z - y - w + x;</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  Tv c2 = w - x - c3;</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  Tv c1 = y - w;</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">return</span> ((c3 * f + c2) * f + c1) * f + x;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> }</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  </div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="comment">// From http://astronomy.swin.edu.au/~pbourke/other/interpolation/ (Paul Bourke)</span></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="comment"> Tension: 1 is high, 0 normal, -1 is low</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="comment"> Bias: 0 is even,</span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="comment"> positive is towards first segment,</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment"> negative towards the other</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tp, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00336"></a><span class="lineno"><a class="line" href="group___math.html#ga36105e344104166b97f0a6f51560fd76"> 336</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#ga36105e344104166b97f0a6f51560fd76">hermite</a>(Tp f, <span class="keyword">const</span> Tv& w, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z,</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  Tp tension, Tp bias) {</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  tension = (Tp(1) - tension) * Tp(0.5);</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="comment">// compute endpoint tangents</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="comment">// Tv m0 = ((x-w)*(1+bias) + (y-x)*(1-bias))*tension;</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="comment">// Tv m1 = ((y-x)*(1+bias) + (z-y)*(1-bias))*tension;</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  Tv m0 = ((x * Tv(2) - w - y) * bias + y - w) * tension;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  Tv m1 = ((y * Tv(2) - x - z) * bias + z - x) * tension;</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  </div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="comment">// x - w + x b - w b + y - x - y b + x b</span></div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="comment">// -w + 2x b - w b + y - y b</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// b(2x - w - y) + y - w</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="comment">// y - x + y b - x b + z - y - z b + y b</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="comment">// -x + 2y b - x b + z - z b</span></div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="comment">// b(2y - x - z) + z - x</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  </div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  Tp f2 = f * f;</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  Tp f3 = f2 * f;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="comment">// compute hermite basis functions</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  Tp a3 = Tp(-2) * f3 + Tp(3) * f2;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  Tp a0 = Tp(1) - a3;</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  Tp a2 = f3 - f2;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  Tp a1 = f3 - Tp(2) * f2 + f;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  </div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="keywordflow">return</span> x * a0 + m0 * a1 + m1 * a2 + y * a3;</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> }</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  </div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00367"></a><span class="lineno"><a class="line" href="group___math.html#gac34b241d907c8471c7bfa09207bd18b3"> 367</a></span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gac34b241d907c8471c7bfa09207bd18b3">lagrange</a>(T* a, T delay, <span class="keywordtype">int</span> order) {</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i <= order; ++i) {</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  T coef = T(1);</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  T i_f = T(i);</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j <= order; ++j) {</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keywordflow">if</span> (j != i) {</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  T j_f = (T)j;</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  coef *= (delay - j_f) / (i_f - j_f);</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>  *a++ = coef;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  }</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> }</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  </div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00382"></a><span class="lineno"><a class="line" href="group___math.html#ga91fc7337dd163ffca419bbcf917bfab7"> 382</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga91fc7337dd163ffca419bbcf917bfab7">lagrange1</a>(T* h, T d) {</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  h[0] = T(1) - d;</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  h[1] = d;</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> }</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  </div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00388"></a><span class="lineno"><a class="line" href="group___math.html#ga62a32a386d799491b42c8d0089ad19c8"> 388</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga62a32a386d799491b42c8d0089ad19c8">lagrange2</a>(T* h, T d) {</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  h[0] = (d - T(1)) * (d - T(2)) * T(0.5);</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  h[1] = -d * (d - T(2));</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  h[2] = d * (d - T(1)) * T(0.5);</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> }</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  </div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00395"></a><span class="lineno"><a class="line" href="group___math.html#ga9fbe7b22099ead82a30b5b04255ea9e3"> 395</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga9fbe7b22099ead82a30b5b04255ea9e3">lagrange3</a>(T* h, T d) {</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  T d1 = d - T(1);</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  T d2 = d - T(2);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  T d3 = d - T(3);</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  h[0] = -d1 * d2 * d3 * T(1. / 6.);</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  h[1] = d * d2 * d3 * T(0.5);</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  h[2] = -d * d1 * d3 * T(0.5);</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  h[3] = d * d1 * d2 * T(1. / 6.);</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span> }</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment">x1 (1 - d) + x0 d</span></div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment">x1 - x1 d + x0 d</span></div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment">x1 + (x0 - x1) d</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment"></span> </div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="comment">x2 (d - 1) (d - 2) /2 - x1 d (d - 2) + x0 d (d - 1) /2</span></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment">d d /2 x2 - d 3/2 x2 + x2 - d d x1 + d 2 x1 + d d /2 x0 - d /2 x0</span></div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment">d d /2 x2 - d d x1 + d d /2 x0 - d 3/2 x2 + d 2 x1 - d /2 x0 + x2</span></div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment">d (d (/2 x2 - x1 + /2 x0) - 3/2 x2 + 2 x1 - /2 x0) + x2</span></div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  </div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00417"></a><span class="lineno"><a class="line" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc"> 417</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(Tf f, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y) {</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <span class="keywordflow">return</span> (y - x) * f + x;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span> }</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00422"></a><span class="lineno"><a class="line" href="group___math.html#ga7fa68a8a46a445ba94aca690b577091f"> 422</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(Tf frac, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z) {</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  frac *= Tf(2);</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keywordflow">if</span> (frac < Tf(1)) <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">ipl::linear</a>(frac, x, y);</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">ipl::linear</a>(frac - Tf(1), y, z);</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> }</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  </div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00429"></a><span class="lineno"><a class="line" href="group___math.html#gaae9bb28b21a5b2f6340dca3e40a0f734"> 429</a></span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(Tv* dst, <span class="keyword">const</span> Tv* xs, <span class="keyword">const</span> Tv* xp1s, <span class="keywordtype">int</span> len, <span class="keyword">const</span> Tf& f) {</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < len; ++i) dst[i] = <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">linear</a>(f, xs[i], xp1s[i]);</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> }</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> <span class="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00434"></a><span class="lineno"><a class="line" href="group___math.html#ga8c05a1ef112a3ea36ab5d0a599102d65"> 434</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#ga8c05a1ef112a3ea36ab5d0a599102d65">linearCyclic</a>(Tf frac, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y, <span class="keyword">const</span> Tv& z) {</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  frac *= Tf(3);</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">if</span> (frac <= Tf(1))</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">ipl::linear</a>(frac, x, y);</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (frac >= Tf(2))</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">ipl::linear</a>(frac - Tf(2), z, x);</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">ipl::linear</a>(frac - Tf(1), y, z);</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> }</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="keyword">template</span> <<span class="keyword">class</span> Tf, <span class="keyword">class</span> Tv></div>
<div class="line"><a name="l00444"></a><span class="lineno"><a class="line" href="group___math.html#ga4f50b6d0ce1c4c7137a853a879ffd92b"> 444</a></span> <span class="keyword">inline</span> Tv <a class="code" href="group___math.html#ga4f50b6d0ce1c4c7137a853a879ffd92b">nearest</a>(Tf f, <span class="keyword">const</span> Tv& x, <span class="keyword">const</span> Tv& y) {</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="keywordflow">return</span> (f < Tf(0.5)) ? x : y;</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> }</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  </div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> } <span class="comment">// namespace ipl</span></div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> } <span class="comment">// namespace al</span></div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="agroup___math_html_ga26ffc66ac3be99197f46819c3dc33ce4"><div class="ttname"><a href="group___math.html#ga26ffc66ac3be99197f46819c3dc33ce4">al::ipl::cubic</a></div><div class="ttdeci">Tv cubic(Tf frac, const Tv &w, const Tv &x, const Tv &y, const Tv &z)</div><div class="ttdoc">Cubic interpolation.</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00286">al_Interpolation.hpp:286</a></div></div>
<div class="ttc" id="agroup___math_html_ga36105e344104166b97f0a6f51560fd76"><div class="ttname"><a href="group___math.html#ga36105e344104166b97f0a6f51560fd76">al::ipl::hermite</a></div><div class="ttdeci">Tv hermite(Tp f, const Tv &w, const Tv &x, const Tv &y, const Tv &z, Tp tension, Tp bias)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00336">al_Interpolation.hpp:336</a></div></div>
<div class="ttc" id="agroup___math_html_ga465b8747dbef55281301ee3801c36abe"><div class="ttname"><a href="group___math.html#ga465b8747dbef55281301ee3801c36abe">al::ipl::casteljau</a></div><div class="ttdeci">Tv casteljau(const Tf &frac, const Tv &a, const Tv &b, const Tv &c, const Tv &d)</div><div class="ttdoc">de Casteljau algorithm for four point interpolation</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00250">al_Interpolation.hpp:250</a></div></div>
<div class="ttc" id="agroup___math_html_ga4f50b6d0ce1c4c7137a853a879ffd92b"><div class="ttname"><a href="group___math.html#ga4f50b6d0ce1c4c7137a853a879ffd92b">al::ipl::nearest</a></div><div class="ttdeci">Tv nearest(Tf frac, const Tv &x, const Tv &y)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00444">al_Interpolation.hpp:444</a></div></div>
<div class="ttc" id="agroup___math_html_ga623773336d6de114661f18ee79168886"><div class="ttname"><a href="group___math.html#ga623773336d6de114661f18ee79168886">al::ipl::trilinear</a></div><div class="ttdeci">Tv trilinear(const Tf &fracX, const Tf &fracY, const Tf &fracZ, const Tv &xyz, const Tv &Xyz, const Tv &xYz, const Tv &XYz, const Tv &xyZ, const Tv &XyZ, const Tv &xYZ, const Tv &XYZ)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00200">al_Interpolation.hpp:200</a></div></div>
<div class="ttc" id="agroup___math_html_ga62a32a386d799491b42c8d0089ad19c8"><div class="ttname"><a href="group___math.html#ga62a32a386d799491b42c8d0089ad19c8">al::ipl::lagrange2</a></div><div class="ttdeci">void lagrange2(T *h, T delay)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00388">al_Interpolation.hpp:388</a></div></div>
<div class="ttc" id="agroup___math_html_ga8c05a1ef112a3ea36ab5d0a599102d65"><div class="ttname"><a href="group___math.html#ga8c05a1ef112a3ea36ab5d0a599102d65">al::ipl::linearCyclic</a></div><div class="ttdeci">Tv linearCyclic(Tf frac, const Tv &x, const Tv &y, const Tv &z)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00434">al_Interpolation.hpp:434</a></div></div>
<div class="ttc" id="agroup___math_html_ga91fc7337dd163ffca419bbcf917bfab7"><div class="ttname"><a href="group___math.html#ga91fc7337dd163ffca419bbcf917bfab7">al::ipl::lagrange1</a></div><div class="ttdeci">void lagrange1(T *h, T delay)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00382">al_Interpolation.hpp:382</a></div></div>
<div class="ttc" id="agroup___math_html_ga9fbe7b22099ead82a30b5b04255ea9e3"><div class="ttname"><a href="group___math.html#ga9fbe7b22099ead82a30b5b04255ea9e3">al::ipl::lagrange3</a></div><div class="ttdeci">void lagrange3(T *h, T delay)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00395">al_Interpolation.hpp:395</a></div></div>
<div class="ttc" id="agroup___math_html_gaa941590d601a613962a98888c68a91bd"><div class="ttname"><a href="group___math.html#gaa941590d601a613962a98888c68a91bd">al::ipl::cardinalSpline</a></div><div class="ttdeci">void cardinalSpline(Tv *w, const Tv *x, const Tf &f, double b)</div><div class="ttdoc">Compute weights for cubic cardinal spline.</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00258">al_Interpolation.hpp:258</a></div></div>
<div class="ttc" id="agroup___math_html_gac34b241d907c8471c7bfa09207bd18b3"><div class="ttname"><a href="group___math.html#gac34b241d907c8471c7bfa09207bd18b3">al::ipl::lagrange</a></div><div class="ttdeci">void lagrange(T *h, T delay, int order)</div><div class="ttdoc">Computes FIR coefficients for Waring-Lagrange interpolation.</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00367">al_Interpolation.hpp:367</a></div></div>
<div class="ttc" id="agroup___math_html_gad02983ca0c42cf32a7c8fcd44babe7bc"><div class="ttname"><a href="group___math.html#gad02983ca0c42cf32a7c8fcd44babe7bc">al::ipl::linear</a></div><div class="ttdeci">Tv linear(Tf frac, const Tv &x, const Tv &y)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00417">al_Interpolation.hpp:417</a></div></div>
<div class="ttc" id="agroup___math_html_gae25a56e2e68e9cddb8a8d59e56f8288d"><div class="ttname"><a href="group___math.html#gae25a56e2e68e9cddb8a8d59e56f8288d">al::ipl::bezier</a></div><div class="ttdeci">Tv bezier(Tf frac, const Tv &x2, const Tv &x1, const Tv &x0)</div><div class="ttdoc">Bezier curve, 3-point quadratic.</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00225">al_Interpolation.hpp:225</a></div></div>
<div class="ttc" id="agroup___math_html_gae76cff2ba7520b09f6ada0a1734e1f65"><div class="ttname"><a href="group___math.html#gae76cff2ba7520b09f6ada0a1734e1f65">al::ipl::bilinear</a></div><div class="ttdeci">Tv bilinear(const Tf &fracX, const Tf &fracY, const Tv &xy, const Tv &Xy, const Tv &xY, const Tv &XY)</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00182">al_Interpolation.hpp:182</a></div></div>
<div class="ttc" id="agroup___math_html_gaffdd572217deee07e2f811a545eaffe3"><div class="ttname"><a href="group___math.html#gaffdd572217deee07e2f811a545eaffe3">al::ipl::cubic2</a></div><div class="ttdeci">Tv cubic2(Tf frac, const Tv &w, const Tv &x, const Tv &y, const Tv &z)</div><div class="ttdoc">Cubic interpolation.</div><div class="ttdef"><b>Definition:</b> <a href="al___interpolation_8hpp_source.html#l00321">al_Interpolation.hpp:321</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>
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