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<div class="title">Spline.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_SPLINE_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_SPLINE_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include "SplineFwd.h"</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>Eigen</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html"> 35</a></span>  <span class="keyword">class </span><a class="code" href="classEigen_1_1Spline.html">Spline</a></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869"> 38</a></span>  <span class="keyword">typedef</span> _Scalar <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>; </div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468"> 39</a></span>  <span class="keyword">enum</span> { <a class="code" href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468">Dimension</a> = _Dim };</div>
<div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2"> 40</a></span>  <span class="keyword">enum</span> { <a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a> = _Degree };</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a name="l00043"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a47316f47c96482079eaeb911b8172d61"> 43</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<Spline>::PointType <a class="code" href="classEigen_1_1Spline.html#a47316f47c96482079eaeb911b8172d61">PointType</a>;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6"> 46</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<Spline>::KnotVectorType <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a>;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  </div>
<div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86"> 49</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<Spline>::BasisVectorType <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">BasisVectorType</a>;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28"> 52</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<Spline>::ControlPointVectorType <a class="code" href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28">ControlPointVectorType</a>;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  </div>
<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#add9cdf708ac9e046dc979bcaff83e600"> 58</a></span>  <a class="code" href="classEigen_1_1Spline.html#add9cdf708ac9e046dc979bcaff83e600">Spline</a>() </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  : m_knots(1, (<a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a>==Dynamic ? 2 : 2*<a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a>+2))</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  , m_ctrls(<a class="code" href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28">ControlPointVectorType</a>::Zero(2,(<a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a>==Dynamic ? 1 : <a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a>+1))) </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// in theory this code can go to the initializer list but it will get pretty</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// much unreadable ...</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">enum</span> { MinDegree = (<a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a>==Dynamic ? 0 : <a class="code" href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Degree</a>) };</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  m_knots.template segment<MinDegree+1>(0) = Array<Scalar,1,MinDegree+1>::Zero();</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  m_knots.template segment<MinDegree+1>(MinDegree+1) = Array<Scalar,1,MinDegree+1>::Ones();</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> OtherVectorType, <span class="keyword">typename</span> OtherArrayType></div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#acc9568b7f7c5c82ccac314515b886c8d"> 75</a></span>  <a class="code" href="classEigen_1_1Spline.html#acc9568b7f7c5c82ccac314515b886c8d">Spline</a>(<span class="keyword">const</span> OtherVectorType& <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>, <span class="keyword">const</span> OtherArrayType& <a class="code" href="classEigen_1_1Spline.html#a1d17a6538090eb7dd12f6c3d366accfe">ctrls</a>) : m_knots(knots), m_ctrls(ctrls) {}</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keyword">template</span> <<span class="keywordtype">int</span> OtherDegree></div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a2aac5d37c74ed3b574f922ef77c7a936"> 82</a></span>  <a class="code" href="classEigen_1_1Spline.html#a2aac5d37c74ed3b574f922ef77c7a936">Spline</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html">Spline<Scalar, Dimension, OtherDegree></a>& spline) : </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  m_knots(spline.<a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>()), m_ctrls(spline.<a class="code" href="classEigen_1_1Spline.html#a1d17a6538090eb7dd12f6c3d366accfe">ctrls</a>()) {}</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf"> 88</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a>& <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_knots; }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div>
<div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a1d17a6538090eb7dd12f6c3d366accfe"> 93</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28">ControlPointVectorType</a>& <a class="code" href="classEigen_1_1Spline.html#a1d17a6538090eb7dd12f6c3d366accfe">ctrls</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_ctrls; }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <a class="code" href="classEigen_1_1Spline.html#a47316f47c96482079eaeb911b8172d61">PointType</a> <a class="code" href="classEigen_1_1Spline.html#a785602b502f082dc3e715ffcb89295b4">operator()</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">typename</span> SplineTraits<Spline>::DerivativeType</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <a class="code" href="classEigen_1_1Spline.html#aa53d1200e3bf388828c21a316c143d49">derivatives</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex order) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keyword">template</span> <<span class="keywordtype">int</span> DerivativeOrder></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">typename</span> SplineTraits<Spline,DerivativeOrder>::DerivativeType</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="code" href="classEigen_1_1Spline.html#aa53d1200e3bf388828c21a316c143d49">derivatives</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex order = DerivativeOrder) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keyword">typename</span> SplineTraits<Spline>::BasisVectorType</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <a class="code" href="classEigen_1_1Spline.html#ae25ee31d76df0cb9f4d07f0c3a02602c">basisFunctions</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keyword">typename</span> SplineTraits<Spline>::BasisDerivativeType</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <a class="code" href="classEigen_1_1Spline.html#a885a771c6c706e970caa3b7244bd02e3">basisFunctionDerivatives</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex order) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keyword">template</span> <<span class="keywordtype">int</span> DerivativeOrder></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">typename</span> SplineTraits<Spline,DerivativeOrder>::BasisDerivativeType</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <a class="code" href="classEigen_1_1Spline.html#a885a771c6c706e970caa3b7244bd02e3">basisFunctionDerivatives</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex order = DerivativeOrder) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942">span</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u) <span class="keyword">const</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">static</span> DenseIndex <a class="code" href="classEigen_1_1Spline.html#ac8dcf3466d6e8e90aacfb1a91ba81bb2">Span</a>(<span class="keyword">typename</span> SplineTraits<Spline>::Scalar u, DenseIndex <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>, <span class="keyword">const</span> <span class="keyword">typename</span> SplineTraits<Spline>::KnotVectorType& <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>);</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keyword">static</span> <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">BasisVectorType</a> <a class="code" href="classEigen_1_1Spline.html#a514f450de91b7ff3cc05d47d8e350e44">BasisFunctions</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>, <span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a>& <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>);</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </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>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a> m_knots; </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <a class="code" href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28">ControlPointVectorType</a> m_ctrls; </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  };</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00213"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#ac8dcf3466d6e8e90aacfb1a91ba81bb2"> 213</a></span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#ac8dcf3466d6e8e90aacfb1a91ba81bb2">Spline<_Scalar, _Dim, _Degree>::Span</a>(</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">typename</span> SplineTraits< <a class="code" href="classEigen_1_1Spline.html">Spline<_Scalar, _Dim, _Degree></a> >::<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u,</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>,</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keyword">const</span> <span class="keyword">typename</span> SplineTraits< <a class="code" href="classEigen_1_1Spline.html">Spline<_Scalar, _Dim, _Degree></a> >::<a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a>& <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>)</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  {</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">// Piegl & Tiller, "The NURBS Book", A2.1 (p. 68)</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">if</span> (u <= <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>(0)) <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>;</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>* pos = std::upper_bound(knots.data()+degree-1, knots.data()+knots.size()-degree-1, u);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">return</span> <span class="keyword">static_cast<</span>DenseIndex<span class="keyword">></span>( std::distance(knots.data(), pos) - 1 );</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</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">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">Spline<_Scalar, _Dim, _Degree>::BasisVectorType</a></div>
<div class="line"><a name="l00226"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a514f450de91b7ff3cc05d47d8e350e44"> 226</a></span>  <a class="code" href="classEigen_1_1Spline.html#a514f450de91b7ff3cc05d47d8e350e44">Spline<_Scalar, _Dim, _Degree>::BasisFunctions</a>(</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Spline<_Scalar, _Dim, _Degree>::Scalar</a> u,</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>,</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keyword">const</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">Spline<_Scalar, _Dim, _Degree>::KnotVectorType</a>& <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>)</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="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">Spline<_Scalar, _Dim, _Degree>::BasisVectorType</a> <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">BasisVectorType</a>;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keyword">const</span> DenseIndex p = <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">const</span> DenseIndex i = <a class="code" href="classEigen_1_1Spline.html#ac8dcf3466d6e8e90aacfb1a91ba81bb2">Spline::Span</a>(u, degree, knots);</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="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a>& U = <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  BasisVectorType left(p+1); left(0) = <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>(0);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  BasisVectorType right(p+1); right(0) = <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>(0); </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>  VectorBlock<BasisVectorType,Degree>(left,1,p) = u - VectorBlock<const KnotVectorType,Degree>(U,i+1-p,p).reverse();</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  VectorBlock<BasisVectorType,Degree>(right,1,p) = VectorBlock<const KnotVectorType,Degree>(U,i+1,p) - u;</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  BasisVectorType N(1,p+1);</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  N(0) = <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>(1);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">for</span> (DenseIndex j=1; j<=p; ++j)</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>  <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> saved = <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>(0);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">for</span> (DenseIndex r=0; r<j; r++)</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>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> tmp = N(r)/(right(r+1)+left(j-r));</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  N[r] = saved + right(r+1)*tmp;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  saved = left(j-r)*tmp;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  }</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  N(j) = saved;</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="keywordflow">return</span> N;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00261"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887"> 261</a></span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">Spline<_Scalar, _Dim, _Degree>::degree</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">if</span> (_Degree == Dynamic)</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordflow">return</span> m_knots.size() - m_ctrls.cols() - 1;</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">return</span> _Degree;</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> </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00270"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942"> 270</a></span>  DenseIndex <a class="code" href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942">Spline<_Scalar, _Dim, _Degree>::span</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u)<span class="keyword"> const</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Spline.html#ac8dcf3466d6e8e90aacfb1a91ba81bb2">Spline::Span</a>(u, <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>(), <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>());</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  }</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00276"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a785602b502f082dc3e715ffcb89295b4"> 276</a></span>  <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Spline.html#a47316f47c96482079eaeb911b8172d61">Spline<_Scalar, _Dim, _Degree>::PointType</a> <a class="code" href="classEigen_1_1Spline.html#a785602b502f082dc3e715ffcb89295b4">Spline<_Scalar, _Dim, _Degree>::operator()</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u)<span class="keyword"> const</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">enum</span> { Order = SplineTraits<Spline>::OrderAtCompileTime };</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keyword">const</span> DenseIndex <a class="code" href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942">span</a> = this-><a class="code" href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942">span</a>(u);</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">const</span> DenseIndex p = <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>();</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">BasisVectorType</a> basis_funcs = <a class="code" href="classEigen_1_1Spline.html#ae25ee31d76df0cb9f4d07f0c3a02602c">basisFunctions</a>(u);</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>  <span class="keyword">const</span> Replicate<BasisVectorType,Dimension,1> ctrl_weights(basis_funcs);</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keyword">const</span> Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(<a class="code" href="classEigen_1_1Spline.html#a1d17a6538090eb7dd12f6c3d366accfe">ctrls</a>(),0,span-p,<a class="code" href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468">Dimension</a>,p+1);</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">return</span> (ctrl_weights * ctrl_pts).rowwise().sum();</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> </div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">/* --------------------------------------------------------------------------------------------- */</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">template</span> <<span class="keyword">typename</span> SplineType, <span class="keyword">typename</span> DerivativeType></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordtype">void</span> derivativesImpl(<span class="keyword">const</span> SplineType& spline, <span class="keyword">typename</span> SplineType::Scalar u, DenseIndex order, DerivativeType& der)</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  { </div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keyword">enum</span> { <a class="code" href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468">Dimension</a> = SplineTraits<SplineType>::Dimension };</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keyword">enum</span> { Order = SplineTraits<SplineType>::OrderAtCompileTime };</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keyword">enum</span> { DerivativeOrder = DerivativeType::ColsAtCompileTime };</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<SplineType>::ControlPointVectorType <a class="code" href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28">ControlPointVectorType</a>;</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<SplineType,DerivativeOrder>::BasisDerivativeType BasisDerivativeType;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> BasisDerivativeType::ConstRowXpr BasisDerivativeRowXpr; </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keyword">const</span> DenseIndex p = spline.degree();</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keyword">const</span> DenseIndex <a class="code" href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942">span</a> = spline.span(u);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keyword">const</span> DenseIndex n = (std::min)(p, order);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  der.resize(<a class="code" href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468">Dimension</a>,n+1);</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> </div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// Retrieve the basis function derivatives up to the desired order... </span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keyword">const</span> BasisDerivativeType basis_func_ders = spline.template basisFunctionDerivatives<DerivativeOrder>(u, n+1);</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="comment">// ... and perform the linear combinations of the control points.</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">for</span> (DenseIndex der_order=0; der_order<n+1; ++der_order)</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  {</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">const</span> Replicate<BasisDerivativeRowXpr,Dimension,1> ctrl_weights( basis_func_ders.row(der_order) );</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keyword">const</span> Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(spline.ctrls(),0,span-p,<a class="code" href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468">Dimension</a>,p+1);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  der.col(der_order) = (ctrl_weights * ctrl_pts).rowwise().sum();</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>  }</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> </div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keyword">typename</span> SplineTraits< Spline<_Scalar, _Dim, _Degree> >::DerivativeType</div>
<div class="line"><a name="l00323"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#aa53d1200e3bf388828c21a316c143d49"> 323</a></span>  <a class="code" href="classEigen_1_1Spline.html#aa53d1200e3bf388828c21a316c143d49">Spline<_Scalar, _Dim, _Degree>::derivatives</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex order)<span class="keyword"> const</span></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keyword">typename</span> SplineTraits< Spline >::DerivativeType res;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  derivativesImpl(*<span class="keyword">this</span>, u, order, res);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  }</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keyword">template</span> <<span class="keywordtype">int</span> DerivativeOrder></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keyword">typename</span> SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::DerivativeType</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <a class="code" href="classEigen_1_1Spline.html#aa53d1200e3bf388828c21a316c143d49">Spline<_Scalar, _Dim, _Degree>::derivatives</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u, DenseIndex order)<span class="keyword"> const</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keyword">typename</span> SplineTraits< Spline, DerivativeOrder >::DerivativeType res;</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  derivativesImpl(*<span class="keyword">this</span>, u, order, res);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  }</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="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keyword">typename</span> SplineTraits< Spline<_Scalar, _Dim, _Degree> ><a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">::BasisVectorType</a></div>
<div class="line"><a name="l00342"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#ae25ee31d76df0cb9f4d07f0c3a02602c"> 342</a></span>  <a class="code" href="classEigen_1_1Spline.html#ae25ee31d76df0cb9f4d07f0c3a02602c">Spline<_Scalar, _Dim, _Degree>::basisFunctions</a>(<a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> u)<span class="keyword"> const</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Spline.html#a514f450de91b7ff3cc05d47d8e350e44">Spline::BasisFunctions</a>(u, <a class="code" href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">degree</a>(), <a class="code" href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">knots</a>());</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> </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="comment">/* --------------------------------------------------------------------------------------------- */</span></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>  <span class="keyword">template</span> <<span class="keyword">typename</span> SplineType, <span class="keyword">typename</span> DerivativeType></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keywordtype">void</span> basisFunctionDerivativesImpl(<span class="keyword">const</span> SplineType& spline, <span class="keyword">typename</span> SplineType::Scalar u, DenseIndex order, DerivativeType& N_)</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  {</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keyword">enum</span> { Order = SplineTraits<SplineType>::OrderAtCompileTime };</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<SplineType>::Scalar <a class="code" href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>;</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<SplineType>::BasisVectorType <a class="code" href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">BasisVectorType</a>;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineTraits<SplineType>::KnotVectorType <a class="code" href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">KnotVectorType</a>;</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> </div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keyword">const</span> KnotVectorType& U = spline.knots();</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> </div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keyword">const</span> DenseIndex p = spline.degree();</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keyword">const</span> DenseIndex span = spline.span(u);</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="keyword">const</span> DenseIndex n = (std::min)(p, order);</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>  N_.resize(n+1, p+1);</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> </div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  BasisVectorType left = BasisVectorType::Zero(p+1);</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  BasisVectorType right = BasisVectorType::Zero(p+1);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  Matrix<Scalar,Order,Order> ndu(p+1,p+1);</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keywordtype">double</span> saved, temp;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  ndu(0,0) = 1.0;</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>  DenseIndex j;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="keywordflow">for</span> (j=1; j<=p; ++j)</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>  left[j] = u-U[span+1-j];</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  right[j] = U[span+j]-u;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  saved = 0.0;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> </div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordflow">for</span> (DenseIndex r=0; r<j; ++r)</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  {</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="comment">/* Lower triangle */</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  ndu(j,r) = right[r+1]+left[j-r];</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  temp = ndu(r,j-1)/ndu(j,r);</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="comment">/* Upper triangle */</span></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  ndu(r,j) = <span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(saved+right[r+1] * temp);</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  saved = left[j-r] * temp;</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  }</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>  ndu(j,j) = <span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(saved);</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  }</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> </div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">for</span> (j = p; j>=0; --j) </div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  N_(0,j) = ndu(j,p);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="comment">// Compute the derivatives</span></div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  DerivativeType a(n+1,p+1);</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  DenseIndex r=0;</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keywordflow">for</span> (; r<=p; ++r)</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>  DenseIndex s1,s2;</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  s1 = 0; s2 = 1; <span class="comment">// alternate rows in array a</span></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  a(0,0) = 1.0;</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>  <span class="comment">// Compute the k-th derivative</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keywordflow">for</span> (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  {</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keywordtype">double</span> d = 0.0;</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  DenseIndex rk,pk,j1,j2;</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  rk = r-k; pk = p-k;</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>  <span class="keywordflow">if</span> (r>=k)</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  {</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  a(s2,0) = a(s1,0)/ndu(pk+1,rk);</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  d = a(s2,0)*ndu(rk,pk);</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="keywordflow">if</span> (rk>=-1) j1 = 1;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="keywordflow">else</span> j1 = -rk;</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keywordflow">if</span> (r-1 <= pk) j2 = k-1;</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keywordflow">else</span> j2 = p-r;</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>  <span class="keywordflow">for</span> (j=j1; j<=j2; ++j)</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  {</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  a(s2,j) = (a(s1,j)-a(s1,j-1))/ndu(pk+1,rk+j);</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  d += a(s2,j)*ndu(rk+j,pk);</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="keywordflow">if</span> (r<=pk)</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  {</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  a(s2,k) = -a(s1,k-1)/ndu(pk+1,r);</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  d += a(s2,k)*ndu(r,pk);</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> </div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  N_(k,r) = <span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(d);</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  j = s1; s1 = s2; s2 = j; <span class="comment">// Switch rows</span></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> </div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <span class="comment">/* Multiply through by the correct factors */</span></div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="comment">/* (Eq. [2.9]) */</span></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  r = p;</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keywordflow">for</span> (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  {</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">for</span> (DenseIndex j=p; j>=0; --j) N_(k,j) *= r;</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  r *= p-k;</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  }</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  }</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> </div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keyword">typename</span> SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisDerivativeType</div>
<div class="line"><a name="l00456"></a><span class="lineno"><a class="line" href="classEigen_1_1Spline.html#a885a771c6c706e970caa3b7244bd02e3"> 456</a></span>  <a class="code" href="classEigen_1_1Spline.html#a885a771c6c706e970caa3b7244bd02e3">Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives</a>(Scalar u, DenseIndex order)<span class="keyword"> const</span></div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keyword">typename</span> SplineTraits< Spline >::BasisDerivativeType der;</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  basisFunctionDerivativesImpl(*<span class="keyword">this</span>, u, order, der);</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="keywordflow">return</span> der;</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  }</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span> </div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Dim, <span class="keywordtype">int</span> _Degree></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keyword">template</span> <<span class="keywordtype">int</span> DerivativeOrder></div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keyword">typename</span> SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::BasisDerivativeType</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <a class="code" href="classEigen_1_1Spline.html#a885a771c6c706e970caa3b7244bd02e3">Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives</a>(Scalar u, DenseIndex order)<span class="keyword"> const</span></div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="keyword">typename</span> SplineTraits< Spline, DerivativeOrder >::BasisDerivativeType der;</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  basisFunctionDerivativesImpl(*<span class="keyword">this</span>, u, order, der);</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keywordflow">return</span> der;</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="l00473"></a><span class="lineno"> 473</span> </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="preprocessor">#endif // EIGEN_SPLINE_H</span></div>
<div class="ttc" id="classEigen_1_1Spline_html"><div class="ttname"><a href="classEigen_1_1Spline.html">Eigen::Spline</a></div><div class="ttdoc">A class representing multi-dimensional spline curves. </div><div class="ttdef"><b>Definition:</b> Spline.h:35</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_aea29b63b6c32046ae9a471d82c5cf869"><div class="ttname"><a href="classEigen_1_1Spline.html#aea29b63b6c32046ae9a471d82c5cf869">Eigen::Spline::Scalar</a></div><div class="ttdeci">_Scalar Scalar</div><div class="ttdef"><b>Definition:</b> Spline.h:38</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a9400cd9f6e3863b84a40d08fe18434b6"><div class="ttname"><a href="classEigen_1_1Spline.html#a9400cd9f6e3863b84a40d08fe18434b6">Eigen::Spline::KnotVectorType</a></div><div class="ttdeci">SplineTraits< Spline >::KnotVectorType KnotVectorType</div><div class="ttdoc">The data type used to store knot vectors. </div><div class="ttdef"><b>Definition:</b> Spline.h:46</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a885a771c6c706e970caa3b7244bd02e3"><div class="ttname"><a href="classEigen_1_1Spline.html#a885a771c6c706e970caa3b7244bd02e3">Eigen::Spline::basisFunctionDerivatives</a></div><div class="ttdeci">SplineTraits< Spline >::BasisDerivativeType basisFunctionDerivatives(Scalar u, DenseIndex order) const </div><div class="ttdoc">Computes the non-zero spline basis function derivatives up to given order. </div><div class="ttdef"><b>Definition:</b> Spline.h:456</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_ab7b2d980c535975a69e01687c8277f28"><div class="ttname"><a href="classEigen_1_1Spline.html#ab7b2d980c535975a69e01687c8277f28">Eigen::Spline::ControlPointVectorType</a></div><div class="ttdeci">SplineTraits< Spline >::ControlPointVectorType ControlPointVectorType</div><div class="ttdoc">The data type representing the spline&#39;s control points. </div><div class="ttdef"><b>Definition:</b> Spline.h:52</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_aa53d1200e3bf388828c21a316c143d49"><div class="ttname"><a href="classEigen_1_1Spline.html#aa53d1200e3bf388828c21a316c143d49">Eigen::Spline::derivatives</a></div><div class="ttdeci">SplineTraits< Spline >::DerivativeType derivatives(Scalar u, DenseIndex order) const </div><div class="ttdoc">Evaluation of spline derivatives of up-to given order. </div><div class="ttdef"><b>Definition:</b> Spline.h:323</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_acc9568b7f7c5c82ccac314515b886c8d"><div class="ttname"><a href="classEigen_1_1Spline.html#acc9568b7f7c5c82ccac314515b886c8d">Eigen::Spline::Spline</a></div><div class="ttdeci">Spline(const OtherVectorType &knots, const OtherArrayType &ctrls)</div><div class="ttdoc">Creates a spline from a knot vector and control points. </div><div class="ttdef"><b>Definition:</b> Spline.h:75</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468"><div class="ttname"><a href="classEigen_1_1Spline.html#aac34dfe6c6b73b43a4656c9dce041034a33cede6b934046a29e456d31efa91468">Eigen::Spline::Dimension</a></div><div class="ttdef"><b>Definition:</b> Spline.h:39</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2"><div class="ttname"><a href="classEigen_1_1Spline.html#a0ed680fdb405e7195d9f14032851eebbabb19dc249d37afc2ee77d19133fb68d2">Eigen::Spline::Degree</a></div><div class="ttdef"><b>Definition:</b> Spline.h:40</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a514f450de91b7ff3cc05d47d8e350e44"><div class="ttname"><a href="classEigen_1_1Spline.html#a514f450de91b7ff3cc05d47d8e350e44">Eigen::Spline::BasisFunctions</a></div><div class="ttdeci">static BasisVectorType BasisFunctions(Scalar u, DenseIndex degree, const KnotVectorType &knots)</div><div class="ttdoc">Returns the spline&#39;s non-zero basis functions. </div><div class="ttdef"><b>Definition:</b> Spline.h:226</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a98dc7c576ebbd7017726f5937eecc942"><div class="ttname"><a href="classEigen_1_1Spline.html#a98dc7c576ebbd7017726f5937eecc942">Eigen::Spline::span</a></div><div class="ttdeci">DenseIndex span(Scalar u) const </div><div class="ttdoc">Returns the span within the knot vector in which u is falling. </div><div class="ttdef"><b>Definition:</b> Spline.h:270</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a47316f47c96482079eaeb911b8172d61"><div class="ttname"><a href="classEigen_1_1Spline.html#a47316f47c96482079eaeb911b8172d61">Eigen::Spline::PointType</a></div><div class="ttdeci">SplineTraits< Spline >::PointType PointType</div><div class="ttdoc">The point type the spline is representing. </div><div class="ttdef"><b>Definition:</b> Spline.h:43</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a660f20e92cb1ee49b3fb9a5e70c7fa86"><div class="ttname"><a href="classEigen_1_1Spline.html#a660f20e92cb1ee49b3fb9a5e70c7fa86">Eigen::Spline::BasisVectorType</a></div><div class="ttdeci">SplineTraits< Spline >::BasisVectorType BasisVectorType</div><div class="ttdoc">The data type used to store non-zero basis functions. </div><div class="ttdef"><b>Definition:</b> Spline.h:49</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a01716591756c5c0474d0b6c156da8887"><div class="ttname"><a href="classEigen_1_1Spline.html#a01716591756c5c0474d0b6c156da8887">Eigen::Spline::degree</a></div><div class="ttdeci">DenseIndex degree() const </div><div class="ttdoc">Returns the spline degree. </div><div class="ttdef"><b>Definition:</b> Spline.h:261</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a1d17a6538090eb7dd12f6c3d366accfe"><div class="ttname"><a href="classEigen_1_1Spline.html#a1d17a6538090eb7dd12f6c3d366accfe">Eigen::Spline::ctrls</a></div><div class="ttdeci">const ControlPointVectorType & ctrls() const </div><div class="ttdoc">Returns the knots of the underlying spline. </div><div class="ttdef"><b>Definition:</b> Spline.h:93</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a785602b502f082dc3e715ffcb89295b4"><div class="ttname"><a href="classEigen_1_1Spline.html#a785602b502f082dc3e715ffcb89295b4">Eigen::Spline::operator()</a></div><div class="ttdeci">PointType operator()(Scalar u) const </div><div class="ttdoc">Returns the spline value at a given site . </div><div class="ttdef"><b>Definition:</b> Spline.h:276</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_a2aac5d37c74ed3b574f922ef77c7a936"><div class="ttname"><a href="classEigen_1_1Spline.html#a2aac5d37c74ed3b574f922ef77c7a936">Eigen::Spline::Spline</a></div><div class="ttdeci">Spline(const Spline< Scalar, Dimension, OtherDegree > &spline)</div><div class="ttdoc">Copy constructor for splines. </div><div class="ttdef"><b>Definition:</b> Spline.h:82</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_add9cdf708ac9e046dc979bcaff83e600"><div class="ttname"><a href="classEigen_1_1Spline.html#add9cdf708ac9e046dc979bcaff83e600">Eigen::Spline::Spline</a></div><div class="ttdeci">Spline()</div><div class="ttdoc">Creates a (constant) zero spline. For Splines with dynamic degree, the resulting degree will be 0...</div><div class="ttdef"><b>Definition:</b> Spline.h:58</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_ae25ee31d76df0cb9f4d07f0c3a02602c"><div class="ttname"><a href="classEigen_1_1Spline.html#ae25ee31d76df0cb9f4d07f0c3a02602c">Eigen::Spline::basisFunctions</a></div><div class="ttdeci">SplineTraits< Spline >::BasisVectorType basisFunctions(Scalar u) const </div><div class="ttdoc">Computes the non-zero basis functions at the given site. </div><div class="ttdef"><b>Definition:</b> Spline.h:342</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_adcb07c9a66c0a8a1ec577e49a39baeaf"><div class="ttname"><a href="classEigen_1_1Spline.html#adcb07c9a66c0a8a1ec577e49a39baeaf">Eigen::Spline::knots</a></div><div class="ttdeci">const KnotVectorType & knots() const </div><div class="ttdoc">Returns the knots of the underlying spline. </div><div class="ttdef"><b>Definition:</b> Spline.h:88</div></div>
<div class="ttc" id="classEigen_1_1Spline_html_ac8dcf3466d6e8e90aacfb1a91ba81bb2"><div class="ttname"><a href="classEigen_1_1Spline.html#ac8dcf3466d6e8e90aacfb1a91ba81bb2">Eigen::Spline::Span</a></div><div class="ttdeci">static DenseIndex Span(typename SplineTraits< Spline >::Scalar u, DenseIndex degree, const typename SplineTraits< Spline >::KnotVectorType &knots)</div><div class="ttdoc">Computes the spang within the provided knot vector in which u is falling. </div><div class="ttdef"><b>Definition:</b> Spline.h:213</div></div>
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