Detailed Description

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.

Public Types
typedef Eigen::Index	Index

Public Member Functions
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 Public Member Functions
static ParametrizedLine	Through (const VectorType &p0, const VectorType &p1)

Member Typedef Documentation

◆ Index

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef Eigen::Index Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::Index

Deprecated:: since Eigen 3.3

Constructor & Destructor Documentation

◆ 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

Member Function Documentation

◆ 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:

ParametrizedLine.h

Detailed Description

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

Public Types

Public Member Functions

Static Public Member Functions

Member Typedef Documentation

◆ Index

Constructor & Destructor Documentation

◆ ParametrizedLine() [1/5]

◆ ParametrizedLine() [2/5]

◆ ParametrizedLine() [3/5]

◆ ParametrizedLine() [4/5]

◆ ParametrizedLine() [5/5]

Member Function Documentation

◆ cast()

◆ dim()

◆ distance()

◆ intersection()

◆ intersectionParameter()

◆ intersectionPoint()

◆ isApprox()

◆ pointAt()

◆ projection()

◆ squaredDistance()

◆ Through()

◆ transform() [1/2]

◆ transform() [2/2]

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