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<a href="classEigen_1_1Hyperplane-members.html">List of all members</a> |
<a href="#pub-methods">Public Member Functions</a> |
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<div class="title">Hyperplane< _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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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<typename _Scalar, int _AmbientDim, int Options = AutoAlign><br/>
class Eigen::Hyperplane< _Scalar, _AmbientDim, Options ></h3>
<p>A hyperplane. </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 hyperplane is an affine subspace of dimension n-1 in a space of dimension n. For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.</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. Notice that the dimension of the hyperplane is _AmbientDim-1.</td></tr>
</table>
</dd>
</dl>
<p>This class represents an hyperplane as the zero set of the implicit equation <img class="formulaInl" alt="$ n \cdot x + d = 0 $" src="form_101.png"/> where <img class="formulaInl" alt="$ n $" src="form_45.png"/> is a unit normal vector of the plane (linear part) and <img class="formulaInl" alt="$ d $" src="form_102.png"/> is the distance (offset) to the origin. </p>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a8383bb22fa5f6024856f2c781f6ec0db"><td class="memItemLeft" align="right" valign="top">Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a8383bb22fa5f6024856f2c781f6ec0db">absDistance</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p) const </td></tr>
<tr class="separator:a8383bb22fa5f6024856f2c781f6ec0db"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad8e93f5ebbfdfeaafbdce587c389c26b"><td class="memTemplParams" colspan="2">template<typename NewScalarType > </td></tr>
<tr class="memitem:ad8e93f5ebbfdfeaafbdce587c389c26b"><td class="memTemplItemLeft" align="right" valign="top">internal::cast_return_type<br class="typebreak"/>
< <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>, <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</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_1Hyperplane.html#ad8e93f5ebbfdfeaafbdce587c389c26b">cast</a> () const </td></tr>
<tr class="separator:ad8e93f5ebbfdfeaafbdce587c389c26b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a67d7e844f940f6ca2673eadacaf08b3b"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Matrix.html">Coefficients</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a67d7e844f940f6ca2673eadacaf08b3b">coeffs</a> () const </td></tr>
<tr class="separator:a67d7e844f940f6ca2673eadacaf08b3b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1617ce16af4ff4c65d2155848f2ea161"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Matrix.html">Coefficients</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a1617ce16af4ff4c65d2155848f2ea161">coeffs</a> ()</td></tr>
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<tr class="memitem:a8809dd8f7c45e11b3f62c3fcf0175e68"><td class="memItemLeft" align="right" valign="top">Index </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a8809dd8f7c45e11b3f62c3fcf0175e68">dim</a> () const </td></tr>
<tr class="separator:a8809dd8f7c45e11b3f62c3fcf0175e68"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af5da8814bd3fb91f730302692c736069"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#af5da8814bd3fb91f730302692c736069">Hyperplane</a> ()</td></tr>
<tr class="separator:af5da8814bd3fb91f730302692c736069"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acd150a51ba003162b7a3d919b6b11341"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#acd150a51ba003162b7a3d919b6b11341">Hyperplane</a> (Index _dim)</td></tr>
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<tr class="memitem:ad3ab0f5ce565bb0561e5dd3d82358c0e"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#ad3ab0f5ce565bb0561e5dd3d82358c0e">Hyperplane</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &n, const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &e)</td></tr>
<tr class="separator:ad3ab0f5ce565bb0561e5dd3d82358c0e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a16de15865999fc85f912727fdaaa16f2"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a16de15865999fc85f912727fdaaa16f2">Hyperplane</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &n, const Scalar &d)</td></tr>
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<tr class="memitem:a7e93264afdcb9e5e762413df10bad3dd"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a7e93264afdcb9e5e762413df10bad3dd">Hyperplane</a> (const <a class="el" href="classEigen_1_1ParametrizedLine.html">ParametrizedLine</a>< Scalar, AmbientDimAtCompileTime > &parametrized)</td></tr>
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<tr class="memitem:a079adfa5d26ae1f00de7f756a0d2c00b"><td class="memTemplParams" colspan="2">template<typename OtherScalarType , int OtherOptions> </td></tr>
<tr class="memitem:a079adfa5d26ae1f00de7f756a0d2c00b"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a079adfa5d26ae1f00de7f756a0d2c00b">Hyperplane</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)</td></tr>
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<tr class="memitem:ad10ca15c93ee4d825f92a2c4563ed678"><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_1Hyperplane.html#ad10ca15c93ee4d825f92a2c4563ed678">intersection</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> &other) const </td></tr>
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<tr class="memitem:ae3f0cc3141ee484c2e1a8a391a47c624"><td class="memTemplParams" colspan="2">template<int OtherOptions> </td></tr>
<tr class="memitem:ae3f0cc3141ee484c2e1a8a391a47c624"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#ae3f0cc3141ee484c2e1a8a391a47c624">isApprox</a> (const <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, const 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:ace24c10a33475a675f45cfbf085378ad"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Block.html">ConstNormalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">normal</a> () const </td></tr>
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<tr class="memitem:a115e276ad412ed6378e3291095132591"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Block.html">NormalReturnType</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a115e276ad412ed6378e3291095132591">normal</a> ()</td></tr>
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<tr class="memitem:a7494eb6e7ee0d104f3a01dcceed8607a"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a7494eb6e7ee0d104f3a01dcceed8607a">normalize</a> (void)</td></tr>
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<tr class="memitem:a32ddf277ab2a650e7d520bcbbc09fb99"><td class="memItemLeft" align="right" valign="top">const Scalar & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a32ddf277ab2a650e7d520bcbbc09fb99">offset</a> () const </td></tr>
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<tr class="memitem:a12c3df61f19531230e282a879b605842"><td class="memItemLeft" align="right" valign="top">Scalar & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a12c3df61f19531230e282a879b605842">offset</a> ()</td></tr>
<tr class="separator:a12c3df61f19531230e282a879b605842"><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_1Hyperplane.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:aacd139793b951a521e0e5147a4793d9c"><td class="memItemLeft" align="right" valign="top">Scalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#aacd139793b951a521e0e5147a4793d9c">signedDistance</a> (const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p) const </td></tr>
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<tr class="memitem:a35877b483d288e5c4569163b41e79ecc"><td class="memTemplParams" colspan="2">template<typename XprType > </td></tr>
<tr class="memitem:a35877b483d288e5c4569163b41e79ecc"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a35877b483d288e5c4569163b41e79ecc">transform</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< XprType > &mat, <a class="el" href="group__enums.html#ga302a826315506a7217d4b477ea78425f">TransformTraits</a> traits=<a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a>)</td></tr>
<tr class="separator:a35877b483d288e5c4569163b41e79ecc"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae5243c6aa230fcd95572c3a99cdd014d"><td class="memTemplParams" colspan="2">template<int TrOptions> </td></tr>
<tr class="memitem:ae5243c6aa230fcd95572c3a99cdd014d"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#ae5243c6aa230fcd95572c3a99cdd014d">transform</a> (const <a class="el" href="classEigen_1_1Transform.html">Transform</a>< Scalar, AmbientDimAtCompileTime, <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a>, TrOptions > &t, <a class="el" href="group__enums.html#ga302a826315506a7217d4b477ea78425f">TransformTraits</a> traits=<a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a>)</td></tr>
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</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:a10fad5ae000f23b20ebc9e54ed7202dd"><td class="memItemLeft" align="right" valign="top">static <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#a10fad5ae000f23b20ebc9e54ed7202dd">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>
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<tr class="memitem:aabfcda23a80edfd62387bb3d930f4b96"><td class="memItemLeft" align="right" valign="top">static <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Hyperplane.html#aabfcda23a80edfd62387bb3d930f4b96">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, const <a class="el" href="classEigen_1_1Matrix.html">VectorType</a> &p2)</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_1Hyperplane.html#ad8e93f5ebbfdfeaafbdce587c389c26b">Hyperplane< _Scalar, _AmbientDim, Options >::cast()</a>.</p>
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<p>Constructs a dynamic-size hyperplane with <em>_dim</em> the dimension of the ambient space </p>
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<p>Construct a plane from its normal <em>n</em> and a point <em>e</em> onto the plane. </p>
<dl class="section warning"><dt>Warning</dt><dd>the vector normal is assumed to be normalized. </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>Constructs a plane from its normal <em>n</em> and distance to the origin <em>d</em> such that the algebraic equation of the plane is <img class="formulaInl" alt="$ n \cdot x + d = 0 $" src="form_101.png"/>. </p>
<dl class="section warning"><dt>Warning</dt><dd>the vector normal is assumed to be normalized. </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>Constructs a hyperplane passing through the parametrized line <em>parametrized</em>. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made. </p>
<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">Scalar absDistance </td>
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<dl class="section return"><dt>Returns</dt><dd>the absolute distance between the plane <code>*this</code> and a point <em>p</em>. </dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1Hyperplane.html#aacd139793b951a521e0e5147a4793d9c">signedDistance()</a> </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#aacd139793b951a521e0e5147a4793d9c">Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance()</a>.</p>
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<td class="memname">internal::cast_return_type<<a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>, <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</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_1Hyperplane.html#af5da8814bd3fb91f730302692c736069">Hyperplane< _Scalar, _AmbientDim, Options >::Hyperplane()</a>.</p>
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<td class="memname">const <a class="el" href="classEigen_1_1Matrix.html">Coefficients</a>& coeffs </td>
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<dl class="section return"><dt>Returns</dt><dd>a constant reference to the coefficients c_i of the plane equation: <img class="formulaInl" alt="$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 $" src="form_103.png"/> </dd></dl>
<p>Referenced by <a class="el" href="classEigen_1_1Hyperplane.html#ad10ca15c93ee4d825f92a2c4563ed678">Hyperplane< _Scalar, _AmbientDim, Options >::intersection()</a>.</p>
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<td class="memname"><a class="el" href="classEigen_1_1Matrix.html">Coefficients</a>& coeffs </td>
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<dl class="section return"><dt>Returns</dt><dd>a non-constant reference to the coefficients c_i of the plane equation: <img class="formulaInl" alt="$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 $" src="form_103.png"/> </dd></dl>
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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 plane holds </dd></dl>
<p>References <a class="el" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a>.</p>
<p>Referenced by <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_1Matrix.html">VectorType</a> intersection </td>
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<dl class="section return"><dt>Returns</dt><dd>the intersection of *this with <em>other</em>.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>The ambient space must be a plane, i.e. have dimension 2, so that <code>*this</code> and <em>other</em> are lines.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>If <em>other</em> is approximately parallel to *this, this method will return any point on *this. </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#a67d7e844f940f6ca2673eadacaf08b3b">Hyperplane< _Scalar, _AmbientDim, Options >::coeffs()</a>.</p>
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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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<dl class="section return"><dt>Returns</dt><dd>a constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation. </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#a8809dd8f7c45e11b3f62c3fcf0175e68">Hyperplane< _Scalar, _AmbientDim, Options >::dim()</a>.</p>
<p>Referenced by <a class="el" href="classEigen_1_1Hyperplane.html#ad3ab0f5ce565bb0561e5dd3d82358c0e">Hyperplane< _Scalar, _AmbientDim, Options >::Hyperplane()</a>, <a class="el" href="classEigen_1_1ParametrizedLine.html#a122c56306b853cf5128f5cc8c480afb1">ParametrizedLine< _Scalar, _AmbientDim, Options >::intersectionParameter()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#a7494eb6e7ee0d104f3a01dcceed8607a">Hyperplane< _Scalar, _AmbientDim, Options >::normalize()</a>, <a class="el" href="classEigen_1_1ParametrizedLine.html#a585e0885f09c39b72d99791e8de387b6">ParametrizedLine< _Scalar, _AmbientDim, Options >::ParametrizedLine()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#ac93039c47cde2b60b29d99f3e1a7dc71">Hyperplane< _Scalar, _AmbientDim, Options >::projection()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#aacd139793b951a521e0e5147a4793d9c">Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#a10fad5ae000f23b20ebc9e54ed7202dd">Hyperplane< _Scalar, _AmbientDim, Options >::Through()</a>, and <a class="el" href="classEigen_1_1Hyperplane.html#a35877b483d288e5c4569163b41e79ecc">Hyperplane< _Scalar, _AmbientDim, Options >::transform()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>a non-constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation. </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#a8809dd8f7c45e11b3f62c3fcf0175e68">Hyperplane< _Scalar, _AmbientDim, Options >::dim()</a>.</p>
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<p>normalizes <code>*this</code> </p>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>the distance to the origin, which is also the "constant term" of the implicit equation </dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>the vector normal is assumed to be normalized. </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#a8809dd8f7c45e11b3f62c3fcf0175e68">Hyperplane< _Scalar, _AmbientDim, Options >::dim()</a>.</p>
<p>Referenced by <a class="el" href="classEigen_1_1Hyperplane.html#ad3ab0f5ce565bb0561e5dd3d82358c0e">Hyperplane< _Scalar, _AmbientDim, Options >::Hyperplane()</a>, <a class="el" href="classEigen_1_1ParametrizedLine.html#a122c56306b853cf5128f5cc8c480afb1">ParametrizedLine< _Scalar, _AmbientDim, Options >::intersectionParameter()</a>, <a class="el" href="classEigen_1_1ParametrizedLine.html#a585e0885f09c39b72d99791e8de387b6">ParametrizedLine< _Scalar, _AmbientDim, Options >::ParametrizedLine()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#aacd139793b951a521e0e5147a4793d9c">Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance()</a>, and <a class="el" href="classEigen_1_1Hyperplane.html#ae5243c6aa230fcd95572c3a99cdd014d">Hyperplane< _Scalar, _AmbientDim, Options >::transform()</a>.</p>
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<dl class="section return"><dt>Returns</dt><dd>a non-constant reference to the distance to the origin, which is also the constant part of the implicit equation </dd></dl>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#a8809dd8f7c45e11b3f62c3fcf0175e68">Hyperplane< _Scalar, _AmbientDim, Options >::dim()</a>.</p>
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<td class="memname"><a class="el" href="classEigen_1_1Matrix.html">VectorType</a> projection </td>
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<dl class="section return"><dt>Returns</dt><dd>the projection of a point <em>p</em> onto the plane <code>*this</code>. </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#aacd139793b951a521e0e5147a4793d9c">Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance()</a>.</p>
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<td class="memname">Scalar signedDistance </td>
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<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 signed distance between the plane <code>*this</code> and a point <em>p</em>. </dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1Hyperplane.html#a8383bb22fa5f6024856f2c781f6ec0db">absDistance()</a> </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>
<p>Referenced by <a class="el" href="classEigen_1_1Hyperplane.html#a8383bb22fa5f6024856f2c781f6ec0db">Hyperplane< _Scalar, _AmbientDim, Options >::absDistance()</a>, and <a class="el" href="classEigen_1_1Hyperplane.html#ac93039c47cde2b60b29d99f3e1a7dc71">Hyperplane< _Scalar, _AmbientDim, Options >::projection()</a>.</p>
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<td class="memname">static <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> Through </td>
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<p>Constructs a hyperplane passing through the two points. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made. </p>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>.</p>
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<td class="memname">static <a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a> Through </td>
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<p>Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3. </p>
<p>References <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>.</p>
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<td class="memname"><a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>& transform </td>
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<td class="paramtype"><a class="el" href="group__enums.html#ga302a826315506a7217d4b477ea78425f">TransformTraits</a> </td>
<td class="paramname"><em>traits</em> = <code><a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a></code> </td>
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<p>Applies the transformation matrix <em>mat</em> to <code>*this</code> and returns a reference to <code>*this</code>.</p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">mat</td><td>the Dim x Dim transformation matrix </td></tr>
<tr><td class="paramname">traits</td><td>specifies whether the matrix <em>mat</em> represents an <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac6ccc3814bb6d2a8bf7f75d7131c6b17">Isometry</a> or a more generic <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a> transformation. The default is <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a>. </td></tr>
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<p>References <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Eigen::Affine</a>, <a class="el" href="classEigen_1_1MatrixBase.html#aa2834da4c855fa35fed8c4030f79f9da">MatrixBase< Derived >::inverse()</a>, <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac6ccc3814bb6d2a8bf7f75d7131c6b17">Eigen::Isometry</a>, and <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>.</p>
<p>Referenced by <a class="el" href="classEigen_1_1Hyperplane.html#ae5243c6aa230fcd95572c3a99cdd014d">Hyperplane< _Scalar, _AmbientDim, Options >::transform()</a>.</p>
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<td class="memname"><a class="el" href="classEigen_1_1Hyperplane.html">Hyperplane</a>& transform </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1Transform.html">Transform</a>< Scalar, AmbientDimAtCompileTime, <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a>, TrOptions > & </td>
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<td class="paramtype"><a class="el" href="group__enums.html#ga302a826315506a7217d4b477ea78425f">TransformTraits</a> </td>
<td class="paramname"><em>traits</em> = <code><a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a></code> </td>
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<p>Applies the transformation <em>t</em> to <code>*this</code> and returns a reference to <code>*this</code>.</p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">t</td><td>the transformation of dimension Dim </td></tr>
<tr><td class="paramname">traits</td><td>specifies whether the transformation <em>t</em> represents an <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac6ccc3814bb6d2a8bf7f75d7131c6b17">Isometry</a> or a more generic <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a> transformation. The default is <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac0984f0c0fc7cdcea1c0bde170f9c925">Affine</a>. Other kind of transformations are not supported. </td></tr>
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<p>References <a class="el" href="classEigen_1_1Transform.html#abbee559820c5cdfe7653a646396b0a8f">Transform< Scalar, Dim, Mode, _Options >::linear()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#ace24c10a33475a675f45cfbf085378ad">Hyperplane< _Scalar, _AmbientDim, Options >::normal()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#a32ddf277ab2a650e7d520bcbbc09fb99">Hyperplane< _Scalar, _AmbientDim, Options >::offset()</a>, <a class="el" href="classEigen_1_1Hyperplane.html#a35877b483d288e5c4569163b41e79ecc">Hyperplane< _Scalar, _AmbientDim, Options >::transform()</a>, and <a class="el" href="classEigen_1_1Transform.html#a4619e6e4e0659443ad2bdb24c80af281">Transform< Scalar, Dim, Mode, _Options >::translation()</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="Hyperplane_8h_source.html">Hyperplane.h</a></li>
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