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Eigen::ParametrizedLine

template<typename _Scalar, int _AmbientDim, int _Options>
class Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >

A parametrized line.

This is defined in the Geometry module.

#include <Eigen/Geometry>

A parametrized line is defined by an origin point \( \mathbf{o} \) and a unit direction vector \( \mathbf{d} \) such that the line corresponds to the set \( l(t) = \mathbf{o} + t \mathbf{d} \), \( t \in \mathbf{R} \).

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.
typedef Eigen::Index Index
template<typename NewScalarType >
internal::cast_return_type< ParametrizedLine, ParametrizedLine< NewScalarType, AmbientDimAtCompileTime, Options > >::type cast () const
Index dim () const
RealScalar distance (const VectorType &p) const
template<int OtherOptions>
_Scalar intersection (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const
template<int OtherOptions>
_Scalar intersectionParameter (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const
template<int OtherOptions>
VectorType intersectionPoint (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const
bool isApprox (const ParametrizedLine &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
ParametrizedLine ()
template<int OtherOptions>
ParametrizedLine (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane)
template<typename OtherScalarType , int OtherOptions>
ParametrizedLine (const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
ParametrizedLine (const VectorType &origin, const VectorType &direction)
ParametrizedLine (Index _dim)
VectorType pointAt (const Scalar &t) const
VectorType projection (const VectorType &p) const
RealScalar squaredDistance (const VectorType &p) const
template<typename XprType >
ParametrizedLine & transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
template<int TrOptions>
ParametrizedLine & transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)
static ParametrizedLine Through (const VectorType &p0, const VectorType &p1)

Index

template<typename _Scalar , int _AmbientDim, int _Options>
typedef Eigen::Index Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::Index
Deprecated:
since Eigen 3.3

ParametrizedLine() [1/5]

template<typename _Scalar , int _AmbientDim, int _Options>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( )
inline

Default constructor without initialization

ParametrizedLine() [2/5]

template<typename _Scalar , int _AmbientDim, int _Options>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( Index _dim )
inlineexplicit

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

ParametrizedLine() [3/5]

template<typename _Scalar , int _AmbientDim, int _Options>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( const VectorType & origin,
const VectorType & direction
)
inline

Initializes a parametrized line of direction direction and origin origin.

Warning
the vector direction is assumed to be normalized.

ParametrizedLine() [4/5]

template<typename _Scalar , int _AmbientDim, int _Options>
template<int OtherOptions>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( const Hyperplane< _Scalar, _AmbientDim, OtherOptions > & hyperplane )
inlineexplicit

Constructs a parametrized line from a 2D hyperplane

Warning
the ambient space must have dimension 2 such that the hyperplane actually describes a line

ParametrizedLine() [5/5]

template<typename _Scalar , int _AmbientDim, int _Options>
template<typename OtherScalarType , int OtherOptions>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > & other )
inlineexplicit

Copy constructor with scalar type conversion

cast()

template<typename _Scalar , int _AmbientDim, int _Options>
template<typename NewScalarType >
internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type Eigen::ParametrizedLine< _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.

dim()

template<typename _Scalar , int _AmbientDim, int _Options>
Index Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::dim ( ) const
inline
Returns
the dimension in which the line holds

distance()

template<typename _Scalar , int _AmbientDim, int _Options>
RealScalar Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::distance ( const VectorType & p ) const
inline
Returns
the distance of a point p to its projection onto the line *this.
See also
squaredDistance()

intersection()

template<typename _Scalar , int _AmbientDim, int _Options>
template<int OtherOptions>
_Scalar Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::intersection ( const Hyperplane< _Scalar, _AmbientDim, OtherOptions > & hyperplane ) const
inline
Deprecated:
use intersectionParameter()
Returns
the parameter value of the intersection between *this and the given hyperplane

intersectionParameter()

template<typename _Scalar , int _AmbientDim, int _Options>
template<int OtherOptions>
_Scalar Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::intersectionParameter ( const Hyperplane< _Scalar, _AmbientDim, OtherOptions > & hyperplane ) const
inline
Returns
the parameter value of the intersection between *this and the given hyperplane

intersectionPoint()

template<typename _Scalar , int _AmbientDim, int _Options>
template<int OtherOptions>
ParametrizedLine< _Scalar, _AmbientDim, _Options >::VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::intersectionPoint ( const Hyperplane< _Scalar, _AmbientDim, OtherOptions > & hyperplane ) const
inline
Returns
the point of the intersection between *this and the given hyperplane

isApprox()

template<typename _Scalar , int _AmbientDim, int _Options>
bool Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::isApprox ( const ParametrizedLine< _Scalar, _AmbientDim, _Options > & 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()

pointAt()

template<typename _Scalar , int _AmbientDim, int _Options>
ParametrizedLine< _Scalar, _AmbientDim, _Options >::VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::pointAt ( const Scalar & t ) const
inline
Returns
the point at t along this line

projection()

template<typename _Scalar , int _AmbientDim, int _Options>
VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::projection ( const VectorType & p ) const
inline
Returns
the projection of a point p onto the line *this.

squaredDistance()

template<typename _Scalar , int _AmbientDim, int _Options>
RealScalar Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::squaredDistance ( const VectorType & p ) const
inline
Returns
the squared distance of a point p to its projection onto the line *this.
See also
distance()

Through()

template<typename _Scalar , int _AmbientDim, int _Options>
static ParametrizedLine Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::Through ( const VectorType & p0,
const VectorType & p1
)
inlinestatic

Constructs a parametrized line going from p0 to p1.

transform() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>
template<typename XprType >
ParametrizedLine& Eigen::ParametrizedLine< _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
mat the Dim x Dim transformation matrix
traits specifies 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>
ParametrizedLine& Eigen::ParametrizedLine< _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
t the transformation of dimension Dim
traits specifies 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 file:

© Eigen.
Licensed under the MPL2 License.
https://eigen.tuxfamily.org/dox/classEigen_1_1ParametrizedLine.html