A parametrized line. More...

#include <ParametrizedLine.h>

Public Types
enum	{ AmbientDimAtCompileTime = _AmbientDim }
enum	{ AmbientDimAtCompileTime = _AmbientDim, Options = _Options }
typedef DenseIndex	Index
typedef NumTraits< Scalar >::Real	RealScalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef _Scalar	Scalar
typedef _Scalar	Scalar
typedef Matrix< Scalar, AmbientDimAtCompileTime, 1 >	VectorType
typedef Matrix< Scalar, AmbientDimAtCompileTime, 1, Options >	VectorType
Public Member Functions
template<typename NewScalarType >
internal::cast_return_type < ParametrizedLine, ParametrizedLine < NewScalarType, AmbientDimAtCompileTime > >::type	cast () const
template<typename NewScalarType >
internal::cast_return_type < ParametrizedLine, ParametrizedLine < NewScalarType, AmbientDimAtCompileTime, Options > >::type	cast () const
int	dim () const
Index	dim () const
const VectorType &	direction () const
VectorType &	direction ()
const VectorType &	direction () const
VectorType &	direction ()
RealScalar	distance (const VectorType &p) const
RealScalar	distance (const VectorType &p) const
Scalar	intersection (const Hyperplane< _Scalar, _AmbientDim > &hyperplane)
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, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
bool	isApprox (const ParametrizedLine &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
const VectorType &	origin () const
VectorType &	origin ()
const VectorType &	origin () const
VectorType &	origin ()
	ParametrizedLine ()
	ParametrizedLine (int _dim)
	ParametrizedLine ()
	ParametrizedLine (const VectorType &origin, const VectorType &direction)
template<int OtherOptions>
	ParametrizedLine (const ParametrizedLine< Scalar, AmbientDimAtCompileTime, OtherOptions > &other)
	ParametrizedLine (const Hyperplane< _Scalar, _AmbientDim > &hyperplane)
	ParametrizedLine (Index _dim)
	ParametrizedLine (const VectorType &origin, const VectorType &direction)
template<int OtherOptions>
	ParametrizedLine (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane)
template<typename OtherScalarType >
	ParametrizedLine (const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime > &other)
template<typename OtherScalarType , int OtherOptions>
	ParametrizedLine (const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
VectorType	pointAt (Scalar t) const
VectorType	projection (const VectorType &p) const
VectorType	projection (const VectorType &p) const
RealScalar	squaredDistance (const VectorType &p) const
RealScalar	squaredDistance (const VectorType &p) const
	~ParametrizedLine ()
	~ParametrizedLine ()
Static Public Member Functions
static ParametrizedLine	Through (const VectorType &p0, const VectorType &p1)
static ParametrizedLine	Through (const VectorType &p0, const VectorType &p1)
Protected Attributes
VectorType	m_direction
VectorType	m_origin

Detailed Description

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

A parametrized line.

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 $l(t) = \mathbf{o} + t \mathbf{d}$ , $l \in \mathbf{R}$ .

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.

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 $l(t) = \mathbf{o} + t \mathbf{d}$ , $t \in \mathbf{R}$ .

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.

Definition at line 29 of file Eigen2Support/Geometry/ParametrizedLine.h.

Member Typedef Documentation

template<typename _Scalar, int _AmbientDim>

typedef DenseIndex Eigen::ParametrizedLine< _Scalar, _AmbientDim >::Index

Definition at line 40 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

typedef NumTraits<Scalar>::Real Eigen::ParametrizedLine< _Scalar, _AmbientDim >::RealScalar

Definition at line 35 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

typedef NumTraits<Scalar>::Real Eigen::ParametrizedLine< _Scalar, _AmbientDim >::RealScalar

Definition at line 39 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

typedef _Scalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::Scalar

Definition at line 34 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

typedef _Scalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::Scalar

Definition at line 38 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

typedef Matrix<Scalar,AmbientDimAtCompileTime,1> Eigen::ParametrizedLine< _Scalar, _AmbientDim >::VectorType

Definition at line 36 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> Eigen::ParametrizedLine< _Scalar, _AmbientDim >::VectorType

Definition at line 41 of file Geometry/ParametrizedLine.h.

Member Enumeration Documentation

template<typename _Scalar, int _AmbientDim>

anonymous enum

Enumerator:

AmbientDimAtCompileTime

Definition at line 33 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

anonymous enum

Enumerator:

AmbientDimAtCompileTime
Options

Definition at line 34 of file Geometry/ParametrizedLine.h.

Constructor & Destructor Documentation

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( ) [inline, explicit]

Default constructor without initialization

Definition at line 39 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( int _dim ) [inline, explicit]

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

Definition at line 43 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::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.

Definition at line 48 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar , int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( const Hyperplane< _Scalar, _AmbientDim > & hyperplane ) [inline, explicit]

Constructs a parametrized line from a 2D hyperplane

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

Definition at line 125 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::~ParametrizedLine ( ) [inline]

Definition at line 57 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

template<typename OtherScalarType >

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime > & other ) [inline, explicit]

Copy constructor with scalar type conversion

Definition at line 102 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( ) [inline, explicit]

Default constructor without initialization

Definition at line 44 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

template<int OtherOptions>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime, OtherOptions > & other ) [inline]

Definition at line 47 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( Index _dim ) [inline, explicit]

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

Definition at line 53 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::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.

Definition at line 58 of file Geometry/ParametrizedLine.h.

template<typename _Scalar , int _AmbientDim, int _Options>

template<int OtherOptions>

Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( const Hyperplane< _Scalar, _AmbientDim, OtherOptions > & hyperplane ) [inline, explicit]

Constructs a parametrized line from a 2D hyperplane

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

Definition at line 146 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::~ParametrizedLine ( ) [inline]

Definition at line 68 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

template<typename OtherScalarType , int OtherOptions>

Eigen::ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > & other ) [inline, explicit]

Copy constructor with scalar type conversion

Definition at line 122 of file Geometry/ParametrizedLine.h.

Member Function Documentation

template<typename _Scalar, int _AmbientDim>

template<typename NewScalarType >

internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type Eigen::ParametrizedLine< _Scalar, _AmbientDim >::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.

Definition at line 94 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

template<typename NewScalarType >

internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type Eigen::ParametrizedLine< _Scalar, _AmbientDim >::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.

Definition at line 114 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

int Eigen::ParametrizedLine< _Scalar, _AmbientDim >::dim ( ) const [inline]

Returns:: the dimension in which the line holds

Definition at line 60 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

Index Eigen::ParametrizedLine< _Scalar, _AmbientDim >::dim ( ) const [inline]

Returns:: the dimension in which the line holds

Definition at line 71 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

const VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::direction ( ) const [inline]

Definition at line 65 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::direction ( ) [inline]

Definition at line 66 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

const VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::direction ( ) const [inline]

Definition at line 76 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::direction ( ) [inline]

Definition at line 77 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

RealScalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::distance ( const VectorType & p ) const [inline]

Returns:: the distance of a point p to its projection onto the line *this.

See also:: squaredDistance()

Definition at line 79 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

RealScalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::distance ( const VectorType & p ) const [inline]

Returns:: the distance of a point p to its projection onto the line *this.

See also:: squaredDistance()

Definition at line 90 of file Geometry/ParametrizedLine.h.

template<typename _Scalar , int _AmbientDim>

_Scalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::intersection ( const Hyperplane< _Scalar, _AmbientDim > & hyperplane ) [inline]

Returns:: the parameter value of the intersection between *this and the given hyperplane

Definition at line 135 of file Eigen2Support/Geometry/ParametrizedLine.h.

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

Definition at line 178 of file Geometry/ParametrizedLine.h.

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

Definition at line 166 of file Geometry/ParametrizedLine.h.

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

Definition at line 188 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

bool Eigen::ParametrizedLine< _Scalar, _AmbientDim >::isApprox	(	const ParametrizedLine< _Scalar, _AmbientDim > &	other,
		typename NumTraits< Scalar >::Real	prec = `precision<Scalar>()`
	)		const `[inline]`

Returns:: true if *this is approximately equal to other, within the precision determined by prec.

See also:: MatrixBase::isApprox()

Definition at line 112 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

bool Eigen::ParametrizedLine< _Scalar, _AmbientDim >::isApprox	(	const ParametrizedLine< _Scalar, _AmbientDim > &	other,
		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()

Definition at line 132 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

const VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::origin ( ) const [inline]

Definition at line 62 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::origin ( ) [inline]

Definition at line 63 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

const VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::origin ( ) const [inline]

Definition at line 73 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim >::origin ( ) [inline]

Definition at line 74 of file Geometry/ParametrizedLine.h.

template<typename _Scalar , int _AmbientDim, int _Options>

ParametrizedLine< _Scalar, _AmbientDim, _Options >::VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::pointAt ( Scalar t ) const [inline]

Returns:: the point at t along this line

Definition at line 157 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim >::projection ( const VectorType & p ) const [inline]

Returns:: the projection of a point p onto the line *this.

Definition at line 82 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim >::projection ( const VectorType & p ) const [inline]

Returns:: the projection of a point p onto the line *this.

Definition at line 93 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

RealScalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::squaredDistance ( const VectorType & p ) const [inline]

Returns:: the squared distance of a point p to its projection onto the line *this.

See also:: distance()

Definition at line 71 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

RealScalar Eigen::ParametrizedLine< _Scalar, _AmbientDim >::squaredDistance ( const VectorType & p ) const [inline]

Returns:: the squared distance of a point p to its projection onto the line *this.

See also:: distance()

Definition at line 82 of file Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

static ParametrizedLine Eigen::ParametrizedLine< _Scalar, _AmbientDim >::Through	(	const VectorType &	p0,
		const VectorType &	p1
	)		`[inline, static]`

Constructs a parametrized line going from p0 to p1.

Definition at line 54 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

static ParametrizedLine Eigen::ParametrizedLine< _Scalar, _AmbientDim >::Through	(	const VectorType &	p0,
		const VectorType &	p1
	)		`[inline, static]`

Constructs a parametrized line going from p0 to p1.

Definition at line 65 of file Geometry/ParametrizedLine.h.

Member Data Documentation

template<typename _Scalar, int _AmbientDim>

VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim >::m_direction [protected]

Definition at line 117 of file Eigen2Support/Geometry/ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>

VectorType Eigen::ParametrizedLine< _Scalar, _AmbientDim >::m_origin [protected]

Definition at line 117 of file Eigen2Support/Geometry/ParametrizedLine.h.

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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