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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_FITTING_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_FITTING_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 <numeric></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="preprocessor">#include "SplineFwd.h"</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <Eigen/QR></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span>Eigen</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> KnotVectorType></div>
<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6"> 41</a></span>  <span class="keywordtype">void</span> <a class="code" href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">KnotAveraging</a>(<span class="keyword">const</span> KnotVectorType& parameters, DenseIndex degree, KnotVectorType& knots)</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  knots.resize(parameters.size()+degree+1); </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="keywordflow">for</span> (DenseIndex j=1; j<parameters.size()-degree; ++j)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  knots(j+degree) = parameters.segment(j,degree).mean();</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  knots.segment(0,degree+1) = KnotVectorType::Zero(degree+1);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  knots.segment(knots.size()-degree-1,degree+1) = KnotVectorType::Ones(degree+1);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Po<span class="keywordtype">int</span>ArrayType, <span class="keyword">typename</span> KnotVectorType></div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2"> 62</a></span>  <span class="keywordtype">void</span> <a class="code" href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">ChordLengths</a>(<span class="keyword">const</span> PointArrayType& pts, KnotVectorType& chord_lengths)</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> KnotVectorType::Scalar Scalar;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">const</span> DenseIndex n = pts.cols();</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>  <span class="comment">// 1. compute the column-wise norms</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  chord_lengths.resize(pts.cols());</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  chord_lengths[0] = 0;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  chord_lengths.rightCols(n-1) = (pts.array().leftCols(n-1) - pts.array().rightCols(n-1)).matrix().colwise().norm();</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// 2. compute the partial sums</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  std::partial_sum(chord_lengths.data(), chord_lengths.data()+n, chord_lengths.data());</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// 3. normalize the data</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  chord_lengths /= chord_lengths(n-1);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  chord_lengths(n-1) = Scalar(1);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SplineType></div>
<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="structEigen_1_1SplineFitting.html"> 86</a></span>  <span class="keyword">struct </span><a class="code" href="structEigen_1_1SplineFitting.html">SplineFitting</a></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  {</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineType::KnotVectorType KnotVectorType;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Po<span class="keywordtype">int</span>ArrayType></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">static</span> SplineType <a class="code" href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441">Interpolate</a>(<span class="keyword">const</span> PointArrayType& pts, DenseIndex degree);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Po<span class="keywordtype">int</span>ArrayType></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">static</span> SplineType <a class="code" href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441">Interpolate</a>(<span class="keyword">const</span> PointArrayType& pts, DenseIndex degree, <span class="keyword">const</span> KnotVectorType& knot_parameters);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  };</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SplineType></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Po<span class="keywordtype">int</span>ArrayType></div>
<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="structEigen_1_1SplineFitting.html#a2a258a77c288288e364bb866814b991f"> 116</a></span>  SplineType <a class="code" href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441">SplineFitting<SplineType>::Interpolate</a>(<span class="keyword">const</span> PointArrayType& pts, DenseIndex degree, <span class="keyword">const</span> KnotVectorType& knot_parameters)</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineType::KnotVectorType::Scalar Scalar; </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SplineType::ControlPointVectorType ControlPointVectorType; </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,Dynamic> MatrixType;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  KnotVectorType knots;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <a class="code" href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">KnotAveraging</a>(knot_parameters, degree, knots);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  DenseIndex n = pts.cols();</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  MatrixType A = MatrixType::Zero(n,n);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">for</span> (DenseIndex i=1; i<n-1; ++i)</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  {</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> DenseIndex span = SplineType::Span(knot_parameters[i], degree, knots);</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// The segment call should somehow be told the spline order at compile time.</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  A.row(i).segment(span-degree, degree+1) = SplineType::BasisFunctions(knot_parameters[i], degree, knots);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  A(0,0) = 1.0;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  A(n-1,n-1) = 1.0;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  HouseholderQR<MatrixType> qr(A);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">// Here, we are creating a temporary due to an Eigen issue.</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  ControlPointVectorType ctrls = qr.solve(MatrixType(pts.transpose())).transpose();</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">return</span> SplineType(knots, ctrls);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SplineType></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Po<span class="keywordtype">int</span>ArrayType></div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441"> 148</a></span>  SplineType <a class="code" href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441">SplineFitting<SplineType>::Interpolate</a>(<span class="keyword">const</span> PointArrayType& pts, DenseIndex degree)</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  {</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  KnotVectorType chord_lengths; <span class="comment">// knot parameters</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <a class="code" href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">ChordLengths</a>(pts, chord_lengths);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">return</span> Interpolate(pts, degree, chord_lengths);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> }</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="preprocessor">#endif // EIGEN_SPLINE_FITTING_H</span></div>
<div class="ttc" id="structEigen_1_1SplineFitting_html"><div class="ttname"><a href="structEigen_1_1SplineFitting.html">Eigen::SplineFitting</a></div><div class="ttdoc">Spline fitting methods. </div><div class="ttdef"><b>Definition:</b> SplineFitting.h:86</div></div>
<div class="ttc" id="group__Splines__Module_html_ga1b4cbde5d98411405871accf877552d2"><div class="ttname"><a href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">Eigen::ChordLengths</a></div><div class="ttdeci">void ChordLengths(const PointArrayType &pts, KnotVectorType &chord_lengths)</div><div class="ttdoc">Computes chord length parameters which are required for spline interpolation. </div><div class="ttdef"><b>Definition:</b> SplineFitting.h:62</div></div>
<div class="ttc" id="group__Splines__Module_html_ga9474da5ed68bbd9a6788a999330416d6"><div class="ttname"><a href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">Eigen::KnotAveraging</a></div><div class="ttdeci">void KnotAveraging(const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)</div><div class="ttdoc">Computes knot averages.The knots are computed as where is the degree and the number knots of the d...</div><div class="ttdef"><b>Definition:</b> SplineFitting.h:41</div></div>
<div class="ttc" id="structEigen_1_1SplineFitting_html_adff4f85f223a278bc7ebae74e53a8441"><div class="ttname"><a href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441">Eigen::SplineFitting::Interpolate</a></div><div class="ttdeci">static SplineType Interpolate(const PointArrayType &pts, DenseIndex degree)</div><div class="ttdoc">Fits an interpolating Spline to the given data points. </div><div class="ttdef"><b>Definition:</b> SplineFitting.h:148</div></div>
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