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

A parametrized line.

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.
_Options

Contents

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} $ .

Public types

enum (anonymous) { AmbientDimAtCompileTime = _AmbientDim, Options = _Options }
using Index = Eigen::Index deprecated
using RealScalar = NumTraits<Scalar>::Real
using Scalar = _Scalar
using VectorType = Matrix<Scalar, AmbientDimAtCompileTime, 1, Options>

Public static functions

static auto Through(const VectorType& p0, const VectorType& p1) -> ParametrizedLine

Constructors, destructors, conversion operators

ParametrizedLine()
template<int OtherOptions>
ParametrizedLine(const ParametrizedLine<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
ParametrizedLine(Index _dim) explicit
ParametrizedLine(const VectorType& origin, const VectorType& direction)
template<int OtherOptions>
ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) explicit
template<typename OtherScalarType, int OtherOptions>
ParametrizedLine(const ParametrizedLine<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other) explicit
~ParametrizedLine()

Public functions

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

Protected variables

VectorType m_direction
VectorType m_origin

Enum documentation

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

Enumerators
AmbientDimAtCompileTime
Options

Typedef documentation

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

template<typename _Scalar, int _AmbientDim, int _Options>
typedef NumTraits<Scalar>::Real Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::RealScalar

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

template<typename _Scalar, int _AmbientDim, int _Options>
typedef Matrix<Scalar, AmbientDimAtCompileTime, 1, Options> Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::VectorType

Function documentation

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

Constructs a parametrized line going from p0 to p1.

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

Default constructor without initialization

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

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

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

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

Initializes a parametrized line of direction direction and origin origin.

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

Constructs a parametrized line from a 2D hyperplane

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

Copy constructor with scalar type conversion

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

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

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.

template<typename _Scalar, int _AmbientDim, int _Options>
Index Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::dim() const

Returns the dimension in which the line holds

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

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

template<typename _Scalar, int _AmbientDim, int _Options>
RealScalar Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::distance(const VectorType& p) const

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

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

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

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

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

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

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

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

Returns the point of the intersection between *this and the given hyperplane

template<typename _Scalar, int _AmbientDim, int _Options>
bool Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const

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

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

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

template<typename _Scalar, int _AmbientDim, int _Options>
VectorType Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::pointAt(const Scalar& t) const

Returns the point at t along this line

template<typename _Scalar, int _AmbientDim, int _Options>
VectorType Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::projection(const VectorType& p) const

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

template<typename _Scalar, int _AmbientDim, int _Options>
RealScalar Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::squaredDistance(const VectorType& p) const

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

template<typename _Scalar, int _AmbientDim, int _Options> template<typename XprType>
ParametrizedLine& Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)

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.

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

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)

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.

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

Variable documentation

template<typename _Scalar, int _AmbientDim, int _Options>
VectorType Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::m_direction protected

template<typename _Scalar, int _AmbientDim, int _Options>
VectorType Eigen::ParametrizedLine<_Scalar, _AmbientDim, _Options>::m_origin protected