Public Member Functions | Static Public Member Functions | List of all members
ParametrizedLine< _Scalar, _AmbientDim, _Options > Class Template Reference
Geometry_Module

A parametrized line. More...

#include <ParametrizedLine.h>

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, 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 (Scalar t) const
 
VectorType projection (const VectorType &p) const
 
RealScalar squaredDistance (const VectorType &p) const
 

Static Public Member Functions

static ParametrizedLine Through (const VectorType &p0, const VectorType &p1)
 

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} $.

Parameters
_Scalarthe scalar type, i.e., the type of the coefficients
_AmbientDimthe dimension of the ambient space, can be a compile time value or Dynamic.

Constructor & Destructor Documentation

◆ ParametrizedLine() [1/5]

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

Default constructor without initialization

Referenced by cast(), isApprox(), ParametrizedLine(), and Through().

◆ ParametrizedLine() [2/5]

template<typename _Scalar, int _AmbientDim, int _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>
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>
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

References Hyperplane< _Scalar, _AmbientDim, _Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, _Options >::offset().

◆ ParametrizedLine() [5/5]

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

Copy constructor with scalar type conversion

References cast(), and ParametrizedLine().

Member Function Documentation

◆ cast()

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

References ParametrizedLine().

Referenced by ParametrizedLine().

◆ dim()

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

◆ distance()

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

References squaredDistance().

◆ intersection()

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

References Hyperplane< _Scalar, _AmbientDim, _Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, _Options >::offset().

◆ intersectionPoint()

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

References pointAt().

◆ isApprox()

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

References ParametrizedLine().

◆ pointAt()

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

Referenced by intersectionPoint().

◆ projection()

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

References MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::dot().

◆ squaredDistance()

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

Referenced by distance().

◆ Through()

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

Constructs a parametrized line going from p0 to p1.

References ParametrizedLine().

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