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<div class="title">ParametrizedLine< _Scalar, _AmbientDim, Options > Class Template Reference<div class="ingroups"><a class="el" href="group__Geometry__Module.html">Geometry module</a></div></div> </div>
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<div class="textblock"><h3>template<typename _Scalar, int _AmbientDim, int Options = AutoAlign><br/>
class Eigen::ParametrizedLine< _Scalar, _AmbientDim, Options ></h3>
<p>A parametrized line. </p>
<p>This is defined in the Geometry module.</p>
<div class="fragment"><div class="line"><span class="preprocessor">#include <Eigen/Geometry></span> </div>
</div><!-- fragment --><p>A parametrized line is defined by an origin point <img class="formulaInl" alt="$ \mathbf{o} $" src="form_104.png"/> and a unit direction vector <img class="formulaInl" alt="$ \mathbf{d} $" src="form_105.png"/> such that the line corresponds to the set <img class="formulaInl" alt="$ l(t) = \mathbf{o} + t \mathbf{d} $" src="form_106.png"/>, <img class="formulaInl" alt="$ t \in \mathbf{R} $" src="form_107.png"/>.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">_Scalar</td><td>the scalar type, i.e., the type of the coefficients </td></tr>
<tr><td class="paramname">_AmbientDim</td><td>the dimension of the ambient space, can be a compile time value or Dynamic. </td></tr>
</table>
</dd>
</dl>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a1c65a5e9e83b2ba93c71739cad4a6c94"><td class="memTemplParams" colspan="2">template<typename NewScalarType > </td></tr>
<tr class="memitem:a1c65a5e9e83b2ba93c71739cad4a6c94"><td class="memTemplItemLeft" align="right" valign="top">internal::cast_return_type<br class="typebreak"/>
< <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>, <br class="typebreak"/>
<a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a><br class="typebreak"/>
< NewScalarType, <br class="typebreak"/>
AmbientDimAtCompileTime, <br class="typebreak"/>
Options > >::type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a1c65a5e9e83b2ba93c71739cad4a6c94">cast</a> () const </td></tr>
<tr class="separator:a1c65a5e9e83b2ba93c71739cad4a6c94"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8809dd8f7c45e11b3f62c3fcf0175e68"><td class="memItemLeft" align="right" valign="top">Index </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a8809dd8f7c45e11b3f62c3fcf0175e68">dim</a> () const </td></tr>
<tr class="separator:a8809dd8f7c45e11b3f62c3fcf0175e68"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a07e68c35a13ec165902e8f5e670acd26"><td class="memItemLeft" align="right" valign="top">RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a07e68c35a13ec165902e8f5e670acd26">distance</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p) const </td></tr>
<tr class="separator:a07e68c35a13ec165902e8f5e670acd26"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5332a558e67b203eddb54856f7609ff9"><td class="memTemplParams" colspan="2">template<int OtherOptions> </td></tr>
<tr class="memitem:a5332a558e67b203eddb54856f7609ff9"><td class="memTemplItemLeft" align="right" valign="top">_Scalar </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a5332a558e67b203eddb54856f7609ff9">intersection</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const </td></tr>
<tr class="separator:a5332a558e67b203eddb54856f7609ff9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a122c56306b853cf5128f5cc8c480afb1"><td class="memTemplParams" colspan="2">template<int OtherOptions> </td></tr>
<tr class="memitem:a122c56306b853cf5128f5cc8c480afb1"><td class="memTemplItemLeft" align="right" valign="top">_Scalar </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a122c56306b853cf5128f5cc8c480afb1">intersectionParameter</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const </td></tr>
<tr class="separator:a122c56306b853cf5128f5cc8c480afb1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1549464241a7d8d863e5e9cad32688c2"><td class="memTemplParams" colspan="2">template<int OtherOptions> </td></tr>
<tr class="memitem:a1549464241a7d8d863e5e9cad32688c2"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>< _Scalar, <br class="typebreak"/>
_AmbientDim, _Options ><br class="typebreak"/>
::<a class="el" href="classEigen_1_1Matrix.html">VectorType</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a1549464241a7d8d863e5e9cad32688c2">intersectionPoint</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const </td></tr>
<tr class="separator:a1549464241a7d8d863e5e9cad32688c2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a696096bc0f2b23dbee9f800cd89ace73"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a696096bc0f2b23dbee9f800cd89ace73">isApprox</a> (const <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a> &other, typename <a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>< Scalar >::Real prec=<a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>< Scalar >::dummy_precision()) const </td></tr>
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<tr class="memitem:ac5c2ec38035eb882c02df80d7e94c2a9"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#ac5c2ec38035eb882c02df80d7e94c2a9">ParametrizedLine</a> ()</td></tr>
<tr class="separator:ac5c2ec38035eb882c02df80d7e94c2a9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5e7bf37eebc5f6f8fd9eb0d505cad45d"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a5e7bf37eebc5f6f8fd9eb0d505cad45d">ParametrizedLine</a> (Index _dim)</td></tr>
<tr class="separator:a5e7bf37eebc5f6f8fd9eb0d505cad45d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aaaa6ea65c420bb90c2a98719ea17074f"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#aaaa6ea65c420bb90c2a98719ea17074f">ParametrizedLine</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &origin, const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &direction)</td></tr>
<tr class="separator:aaaa6ea65c420bb90c2a98719ea17074f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a585e0885f09c39b72d99791e8de387b6"><td class="memTemplParams" colspan="2">template<int OtherOptions> </td></tr>
<tr class="memitem:a585e0885f09c39b72d99791e8de387b6"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a585e0885f09c39b72d99791e8de387b6">ParametrizedLine</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > &hyperplane)</td></tr>
<tr class="separator:a585e0885f09c39b72d99791e8de387b6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a317dec95e2fb2bfef6b63b6b7bc10d4e"><td class="memTemplParams" colspan="2">template<typename OtherScalarType , int OtherOptions> </td></tr>
<tr class="memitem:a317dec95e2fb2bfef6b63b6b7bc10d4e"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a317dec95e2fb2bfef6b63b6b7bc10d4e">ParametrizedLine</a> (const <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)</td></tr>
<tr class="separator:a317dec95e2fb2bfef6b63b6b7bc10d4e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0dfdd3abc1d123cfd6da5deba6ac51ac"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Matrix.html">VectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#a0dfdd3abc1d123cfd6da5deba6ac51ac">pointAt</a> (const Scalar &t) const </td></tr>
<tr class="separator:a0dfdd3abc1d123cfd6da5deba6ac51ac"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac93039c47cde2b60b29d99f3e1a7dc71"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Matrix.html">VectorType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#ac93039c47cde2b60b29d99f3e1a7dc71">projection</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p) const </td></tr>
<tr class="separator:ac93039c47cde2b60b29d99f3e1a7dc71"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac1a8c756c2619371a35f80e062a16deb"><td class="memItemLeft" align="right" valign="top">RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#ac1a8c756c2619371a35f80e062a16deb">squaredDistance</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p) const </td></tr>
<tr class="separator:ac1a8c756c2619371a35f80e062a16deb"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr class="memitem:af9509e5253a2b64d8be3a2c3a59395b4"><td class="memItemLeft" align="right" valign="top">static <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1ParametrizedLine.html#af9509e5253a2b64d8be3a2c3a59395b4">Through</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p0, const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p1)</td></tr>
<tr class="separator:af9509e5253a2b64d8be3a2c3a59395b4"><td class="memSeparator" colspan="2"> </td></tr>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<p>Default constructor without initialization </p>
<p>Referenced by <a class="el" href="classEigen_1_1ParametrizedLine.html#a1c65a5e9e83b2ba93c71739cad4a6c94">ParametrizedLine< _Scalar, _AmbientDim, Options >::cast()</a>, and <a class="el" href="classEigen_1_1ParametrizedLine.html#af9509e5253a2b64d8be3a2c3a59395b4">ParametrizedLine< _Scalar, _AmbientDim, Options >::Through()</a>.</p>
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<td class="paramname"><em>_dim</em></td><td>)</td>
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<p>Constructs a dynamic-size line with <em>_dim</em> the dimension of the ambient space </p>
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<p>Initializes a parametrized line of direction <em>direction</em> and origin <em>origin</em>. </p>
<dl class="section warning"><dt>Warning</dt><dd>the vector direction is assumed to be normalized. </dd></dl>
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<p>Constructs a parametrized line from a 2D hyperplane</p>
<dl class="section warning"><dt>Warning</dt><dd>the ambient space must have dimension 2 such that the hyperplane actually describes a line </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>, and <a class="el" href="classEigen_1_1Hyperplane.html#a32ddf277ab2a650e7d520bcbbc09fb99">Hyperplane< _Scalar, _AmbientDim, Options >::offset()</a>.</p>
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<p>Copy constructor with scalar type conversion </p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">internal::cast_return_type<<a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>, <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a><NewScalarType,AmbientDimAtCompileTime,Options> >::type cast </td>
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<dl class="section return"><dt>Returns</dt><dd><code>*this</code> with scalar type casted to <em>NewScalarType</em> </dd></dl>
<p>Note that if <em>NewScalarType</em> is equal to the current scalar type of <code>*this</code> then this function smartly returns a const reference to <code>*this</code>. </p>
<p>References <a class="el" href="classEigen_1_1ParametrizedLine.html#ac5c2ec38035eb882c02df80d7e94c2a9">ParametrizedLine< _Scalar, _AmbientDim, Options >::ParametrizedLine()</a>.</p>
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<td class="memname">Index dim </td>
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<dl class="section return"><dt>Returns</dt><dd>the dimension in which the line holds </dd></dl>
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<td class="memname">RealScalar distance </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> & </td>
<td class="paramname"><em>p</em></td><td>)</td>
<td> const</td>
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<dl class="section return"><dt>Returns</dt><dd>the distance of a point <em>p</em> to its projection onto the line <code>*this</code>. </dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1ParametrizedLine.html#ac1a8c756c2619371a35f80e062a16deb">squaredDistance()</a> </dd></dl>
<p>References <a class="el" href="classEigen_1_1ParametrizedLine.html#ac1a8c756c2619371a35f80e062a16deb">ParametrizedLine< _Scalar, _AmbientDim, Options >::squaredDistance()</a>.</p>
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<td class="memname">_Scalar intersection </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > & </td>
<td class="paramname"><em>hyperplane</em></td><td>)</td>
<td> const</td>
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<dl class="section return"><dt>Returns</dt><dd>the parameter value of the intersection between <code>*this</code> and the given <em>hyperplane</em> </dd></dl>
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<td class="memname">_Scalar intersectionParameter </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > & </td>
<td class="paramname"><em>hyperplane</em></td><td>)</td>
<td> const</td>
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<dl class="section return"><dt>Returns</dt><dd>the parameter value of the intersection between <code>*this</code> and the given <em>hyperplane</em> </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>, and <a class="el" href="classEigen_1_1Hyperplane.html#a32ddf277ab2a650e7d520bcbbc09fb99">Hyperplane< _Scalar, _AmbientDim, Options >::offset()</a>.</p>
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<td class="memname"><a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a><_Scalar, _AmbientDim,_Options>::<a class="el" href="classEigen_1_1Matrix.html">VectorType</a> intersectionPoint </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< _Scalar, _AmbientDim, OtherOptions > & </td>
<td class="paramname"><em>hyperplane</em></td><td>)</td>
<td> const</td>
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<dl class="section return"><dt>Returns</dt><dd>the point of the intersection between <code>*this</code> and the given hyperplane </dd></dl>
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<td class="memname">bool isApprox </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>< _Scalar, _AmbientDim, Options > & </td>
<td class="paramname"><em>other</em>, </td>
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<td class="paramtype">typename <a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>< Scalar >::Real </td>
<td class="paramname"><em>prec</em> = <code><a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a><Scalar>::dummy_precision()</code> </td>
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<dl class="section return"><dt>Returns</dt><dd><code>true</code> if <code>*this</code> is approximately equal to <em>other</em>, within the precision determined by <em>prec</em>.</dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1DenseBase.html#a158c2184951e6e415c2e9b98db8e8966">MatrixBase::isApprox()</a> </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>< _Scalar, _AmbientDim, _Options >::<a class="el" href="classEigen_1_1Matrix.html">VectorType</a> pointAt </td>
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<dl class="section return"><dt>Returns</dt><dd>the point at <em>t</em> along this line </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1Matrix.html">VectorType</a> projection </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> & </td>
<td class="paramname"><em>p</em></td><td>)</td>
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<dl class="section return"><dt>Returns</dt><dd>the projection of a point <em>p</em> onto the line <code>*this</code>. </dd></dl>
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<td class="memname">RealScalar squaredDistance </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> & </td>
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<dl class="section return"><dt>Returns</dt><dd>the squared distance of a point <em>p</em> to its projection onto the line <code>*this</code>. </dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1ParametrizedLine.html#a07e68c35a13ec165902e8f5e670acd26">distance()</a> </dd></dl>
<p>Referenced by <a class="el" href="classEigen_1_1ParametrizedLine.html#a07e68c35a13ec165902e8f5e670acd26">ParametrizedLine< _Scalar, _AmbientDim, Options >::distance()</a>.</p>
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<td class="memname">static <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a> Through </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> & </td>
<td class="paramname"><em>p0</em>, </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> & </td>
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<p>Constructs a parametrized line going from <em>p0</em> to <em>p1</em>. </p>
<p>References <a class="el" href="classEigen_1_1ParametrizedLine.html#ac5c2ec38035eb882c02df80d7e94c2a9">ParametrizedLine< _Scalar, _AmbientDim, Options >::ParametrizedLine()</a>.</p>
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<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="ForwardDeclarations_8h_source.html">ForwardDeclarations.h</a></li>
<li><a class="el" href="ParametrizedLine_8h_source.html">ParametrizedLine.h</a></li>
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