Eigen  3.4.90 (git rev 9589cc4e7fd8e4538bedef80dd36c7738977a8be)
 
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Public Types | Public Member Functions | Static Public Member Functions | List of all members
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ > Class Template Reference
Geometry » Reference » Geometry module

#include <Eigen/src/Geometry/Hyperplane.h>

Detailed Description

template<typename Scalar_, int AmbientDim_, int Options_>
class Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >

A hyperplane.

This is defined in the Geometry module.

#include <Eigen/Geometry>

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.

Template Parameters
Scalar_the scalar type, i.e., the type of the coefficients
AmbientDim_the dimension of the ambient space, can be a compile time value or Dynamic. Notice that the dimension of the hyperplane is AmbientDim_-1.

This class represents an hyperplane as the zero set of the implicit equation $ n \cdot x + d = 0 $ where $ n $ is a unit normal vector of the plane (linear part) and $ d $ is the distance (offset) to the origin.

Public Types

typedef Eigen::Index Index
 

Public Member Functions

Scalar absDistance (const VectorType &p) const
 
template<typename NewScalarType>
internal::cast_return_type< Hyperplane, Hyperplane< NewScalarType, AmbientDimAtCompileTime, Options > >::type cast () const
 
Coefficients & coeffs ()
 
const Coefficients & coeffs () const
 
Index dim () const
 
 Hyperplane ()
 
template<typename OtherScalarType, int OtherOptions>
 Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
 
 Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
 
 Hyperplane (const VectorType &n, const Scalar &d)
 
 Hyperplane (const VectorType &n, const VectorType &e)
 
 Hyperplane (Index _dim)
 
VectorType intersection (const Hyperplane &other) const
 
template<int OtherOptions>
bool isApprox (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
 
NormalReturnType normal ()
 
ConstNormalReturnType normal () const
 
void normalize (void)
 
Scalar & offset ()
 
const Scalar & offset () const
 
VectorType projection (const VectorType &p) const
 
Scalar signedDistance (const VectorType &p) const
 
template<typename XprType>
Hyperplane & transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
 
template<int TrOptions>
Hyperplane & transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)
 

Static Public Member Functions

static Hyperplane Through (const VectorType &p0, const VectorType &p1)
 
static Hyperplane Through (const VectorType &p0, const VectorType &p1, const VectorType &p2)
 

Member Typedef Documentation

◆ Index

template<typename Scalar_, int AmbientDim_, int Options_>
typedef Eigen::Index Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Index

Constructor & Destructor Documentation

◆ Hyperplane() [1/6]

template<typename Scalar_, int AmbientDim_, int Options_>
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( )
inline

Default constructor without initialization

◆ Hyperplane() [2/6]

template<typename Scalar_, int AmbientDim_, int Options_>
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( Index _dim)
inlineexplicit

Constructs a dynamic-size hyperplane with _dim the dimension of the ambient space

◆ Hyperplane() [3/6]

template<typename Scalar_, int AmbientDim_, int Options_>
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( const VectorType & n,
const VectorType & e )
inline

Construct a plane from its normal n and a point e onto the plane.

Warning
the vector normal is assumed to be normalized.

◆ Hyperplane() [4/6]

template<typename Scalar_, int AmbientDim_, int Options_>
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( const VectorType & n,
const Scalar & d )
inline

Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is $ n \cdot x + d = 0 $.

Warning
the vector normal is assumed to be normalized.

◆ Hyperplane() [5/6]

template<typename Scalar_, int AmbientDim_, int Options_>
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime > & parametrized)
inlineexplicit

Constructs a hyperplane passing through the parametrized line parametrized. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.

◆ Hyperplane() [6/6]

template<typename Scalar_, int AmbientDim_, int Options_>
template<typename OtherScalarType, int OtherOptions>
Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > & other)
inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

◆ absDistance()

template<typename Scalar_, int AmbientDim_, int Options_>
Scalar Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::absDistance ( const VectorType & p) const
inline
Returns
the absolute distance between the plane *this and a point p.
See also
signedDistance()

◆ cast()

template<typename Scalar_, int AmbientDim_, int Options_>
template<typename NewScalarType>
internal::cast_return_type< Hyperplane, Hyperplane< NewScalarType, AmbientDimAtCompileTime, Options > >::type Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::cast ( ) const
inline
Returns
*this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

◆ coeffs() [1/2]

template<typename Scalar_, int AmbientDim_, int Options_>
Coefficients & Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs ( )
inline
Returns
a non-constant reference to the coefficients c_i of the plane equation: $ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 $

◆ coeffs() [2/2]

template<typename Scalar_, int AmbientDim_, int Options_>
const Coefficients & Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs ( ) const
inline
Returns
a constant reference to the coefficients c_i of the plane equation: $ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 $

◆ dim()

template<typename Scalar_, int AmbientDim_, int Options_>
Index Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::dim ( ) const
inline
Returns
the dimension in which the plane holds

◆ intersection()

template<typename Scalar_, int AmbientDim_, int Options_>
VectorType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::intersection ( const Hyperplane< Scalar_, AmbientDim_, Options_ > & other) const
inline
Returns
the intersection of *this with other.
Warning
The ambient space must be a plane, i.e. have dimension 2, so that *this and other are lines.
Note
If other is approximately parallel to *this, this method will return any point on *this.

◆ isApprox()

template<typename Scalar_, int AmbientDim_, int Options_>
template<int OtherOptions>
bool Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::isApprox ( const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > & other,
const typename NumTraits< Scalar >::Real & prec = NumTraits<Scalar>::dummy_precision() ) const
inline
Returns
true if *this is approximately equal to other, within the precision determined by prec.
See also
MatrixBase::isApprox()

◆ normal() [1/2]

template<typename Scalar_, int AmbientDim_, int Options_>
NormalReturnType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal ( )
inline
Returns
a non-constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.

◆ normal() [2/2]

template<typename Scalar_, int AmbientDim_, int Options_>
ConstNormalReturnType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal ( ) const
inline
Returns
a constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.

◆ normalize()

template<typename Scalar_, int AmbientDim_, int Options_>
void Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normalize ( void )
inline

normalizes *this

◆ offset() [1/2]

template<typename Scalar_, int AmbientDim_, int Options_>
Scalar & Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset ( )
inline
Returns
a non-constant reference to the distance to the origin, which is also the constant part of the implicit equation

◆ offset() [2/2]

template<typename Scalar_, int AmbientDim_, int Options_>
const Scalar & Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset ( ) const
inline
Returns
the distance to the origin, which is also the "constant term" of the implicit equation
Warning
the vector normal is assumed to be normalized.

◆ projection()

template<typename Scalar_, int AmbientDim_, int Options_>
VectorType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::projection ( const VectorType & p) const
inline
Returns
the projection of a point p onto the plane *this.

◆ signedDistance()

template<typename Scalar_, int AmbientDim_, int Options_>
Scalar Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::signedDistance ( const VectorType & p) const
inline
Returns
the signed distance between the plane *this and a point p.
See also
absDistance()

◆ Through() [1/2]

template<typename Scalar_, int AmbientDim_, int Options_>
static Hyperplane Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Through ( const VectorType & p0,
const VectorType & p1 )
inlinestatic

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.

◆ Through() [2/2]

template<typename Scalar_, int AmbientDim_, int Options_>
static Hyperplane Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Through ( const VectorType & p0,
const VectorType & p1,
const VectorType & p2 )
inlinestatic

Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.

◆ transform() [1/2]

template<typename Scalar_, int AmbientDim_, int Options_>
template<typename XprType>
Hyperplane & Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::transform ( const MatrixBase< XprType > & mat,
TransformTraits traits = Affine )
inline

Applies the transformation matrix mat to *this and returns a reference to *this.

Parameters
matthe Dim x Dim transformation matrix
traitsspecifies whether the matrix mat represents an Isometry or a more generic Affine transformation. The default is Affine.

◆ transform() [2/2]

template<typename Scalar_, int AmbientDim_, int Options_>
template<int TrOptions>
Hyperplane & Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::transform ( const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > & t,
TransformTraits traits = Affine )
inline

Applies the transformation t to *this and returns a reference to *this.

Parameters
tthe transformation of dimension Dim
traitsspecifies whether the transformation t represents an Isometry or a more generic Affine transformation. The default is Affine. Other kind of transformations are not supported.
The documentation for this class was generated from the following files: