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<div class="title">Spline and spline fitting module</div> </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<p>This module provides a simple multi-dimensional spline class while offering most basic functionality to fit a spline to point sets.</p>
<div class="fragment"><div class="line">* #include <unsupported/Eigen/Splines></div>
<div class="line">* </div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Spline.html">Spline< _Scalar, _Dim, _Degree ></a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A class representing multi-dimensional spline curves. <a href="classEigen_1_1Spline.html#details">More...</a><br/></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineFitting.html">SplineFitting< SplineType ></a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves. ">Spline</a> fitting methods. <a href="structEigen_1_1SplineFitting.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01__DerivativeOrder_01_4.html">SplineTraits< Spline< _Scalar, _Dim, _Degree >, _DerivativeOrder ></a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Compile-time attributes of the <a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves. ">Spline</a> class for fixed degree. <a href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01__DerivativeOrder_01_4.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01Dynamic_01_4.html">SplineTraits< Spline< _Scalar, _Dim, _Degree >, Dynamic ></a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Compile-time attributes of the <a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves. ">Spline</a> class for Dynamic degree. <a href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01Dynamic_01_4.html#details">More...</a><br/></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ga1b4cbde5d98411405871accf877552d2"><td class="memTemplParams" colspan="2">template<typename PointArrayType , typename KnotVectorType > </td></tr>
<tr class="memitem:ga1b4cbde5d98411405871accf877552d2"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">ChordLengths</a> (const PointArrayType &pts, KnotVectorType &chord_lengths)</td></tr>
<tr class="memdesc:ga1b4cbde5d98411405871accf877552d2"><td class="mdescLeft"> </td><td class="mdescRight">Computes chord length parameters which are required for spline interpolation. <a href="#ga1b4cbde5d98411405871accf877552d2">More...</a><br/></td></tr>
<tr class="separator:ga1b4cbde5d98411405871accf877552d2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga9474da5ed68bbd9a6788a999330416d6"><td class="memTemplParams" colspan="2">template<typename KnotVectorType > </td></tr>
<tr class="memitem:ga9474da5ed68bbd9a6788a999330416d6"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">KnotAveraging</a> (const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)</td></tr>
<tr class="memdesc:ga9474da5ed68bbd9a6788a999330416d6"><td class="mdescLeft"> </td><td class="mdescRight">Computes knot averages.The knots are computed as </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\begin{align*} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align*}" src="form_90.png"/>
</p>
<p> where <img class="formulaInl" alt="$p$" src="form_87.png"/> is the degree and <img class="formulaInl" alt="$m+1$" src="form_91.png"/> the number knots of the desired interpolating spline. <a href="#ga9474da5ed68bbd9a6788a999330416d6">More...</a><br/></td></tr>
<tr class="separator:ga9474da5ed68bbd9a6788a999330416d6"><td class="memSeparator" colspan="2"> </td></tr>
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<h2 class="groupheader">Function Documentation</h2>
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<td class="memname">void Eigen::ChordLengths </td>
<td>(</td>
<td class="paramtype">const PointArrayType & </td>
<td class="paramname"><em>pts</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">KnotVectorType & </td>
<td class="paramname"><em>chord_lengths</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>Computes chord length parameters which are required for spline interpolation. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">pts</td><td>The data points to which a spline should be fit. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">chord_lengths</td><td>The resulting chord lenggth vector.</td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See Also</dt><dd>Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data </dd></dl>
<p>Referenced by <a class="el" href="structEigen_1_1SplineFitting.html#adff4f85f223a278bc7ebae74e53a8441">SplineFitting< SplineType >::Interpolate()</a>.</p>
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<td class="memname">void Eigen::KnotAveraging </td>
<td>(</td>
<td class="paramtype">const KnotVectorType & </td>
<td class="paramname"><em>parameters</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">DenseIndex </td>
<td class="paramname"><em>degree</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">KnotVectorType & </td>
<td class="paramname"><em>knots</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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<p>Computes knot averages.The knots are computed as </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\begin{align*} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align*}" src="form_90.png"/>
</p>
<p> where <img class="formulaInl" alt="$p$" src="form_87.png"/> is the degree and <img class="formulaInl" alt="$m+1$" src="form_91.png"/> the number knots of the desired interpolating spline. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">parameters</td><td>The input parameters. During interpolation one for each data point. </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">degree</td><td>The spline degree which is used during the interpolation. </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">knots</td><td>The output knot vector.</td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See Also</dt><dd>Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data </dd></dl>
<p>Referenced by <a class="el" href="structEigen_1_1SplineFitting.html#a2a258a77c288288e364bb866814b991f">SplineFitting< SplineType >::Interpolate()</a>.</p>
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