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ParametrizedLine< _Scalar, _AmbientDim > Class Template Reference
[Geometry_Module]

Detailed Description

template<typename _Scalar, int _AmbientDim>
class 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:
_Scalarthe scalar type, i.e., the type of the coefficients
_AmbientDimthe dimension of the ambient space, can be a compile time value or Dynamic.

Definition at line 43 of file ParametrizedLine.h.

#include <src/Geometry/ParametrizedLine.h>

List of all members.

Public Types

enum  { AmbientDimAtCompileTime = _AmbientDim }
typedef _Scalar Scalar
typedef NumTraits< Scalar >::Real RealScalar
typedef DenseIndex Index
typedef Matrix< Scalar,
AmbientDimAtCompileTime, 1 > 		VectorType

Public Member Functions

 ParametrizedLine ()
 Default constructor without initialization.
 ParametrizedLine (Index _dim)
 Constructs a dynamic-size line with _dim the dimension of the ambient space.
 ParametrizedLine (const VectorType &origin, const VectorType &direction)
 Initializes a parametrized line of direction direction and origin origin.
 ParametrizedLine (const Hyperplane< _Scalar, _AmbientDim > &hyperplane)
 Constructs a parametrized line from a 2D hyperplane.
 ~ParametrizedLine ()
Index dim () const
const VectorType & origin () const
VectorType & origin ()
const VectorType & direction () const
VectorType & direction ()
RealScalar squaredDistance (const VectorType &p) const
RealScalar distance (const VectorType &p) const
VectorType projection (const VectorType &p) const
Scalar intersection (const Hyperplane< _Scalar, _AmbientDim > &hyperplane)
template<typename NewScalarType >
internal::cast_return_type
< ParametrizedLine,
ParametrizedLine
< NewScalarType,
AmbientDimAtCompileTime >
>::type 		cast () const
template<typename OtherScalarType >
 ParametrizedLine (const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime > &other)
 Copy constructor with scalar type conversion.
bool isApprox (const ParametrizedLine &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const

Static Public Member Functions

static ParametrizedLine Through (const VectorType &p0, const VectorType &p1)
 Constructs a parametrized line going from p0 to p1.

Protected Attributes

VectorType m_origin
VectorType m_direction

Member Typedef Documentation

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

Definition at line 50 of file ParametrizedLine.h.

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

Definition at line 49 of file ParametrizedLine.h.

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

Definition at line 48 of file ParametrizedLine.h.

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

Definition at line 51 of file ParametrizedLine.h.

Member Enumeration Documentation

template<typename _Scalar, int _AmbientDim>
anonymous enum
Enumerator:
AmbientDimAtCompileTime 

Definition at line 47 of file ParametrizedLine.h.

Constructor & Destructor Documentation

template<typename _Scalar, int _AmbientDim>
ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine (  ) [inline, explicit]

Default constructor without initialization.

Definition at line 54 of file ParametrizedLine.h.

Referenced by ParametrizedLine< _Scalar, _AmbientDim >::cast(), and ParametrizedLine< _Scalar, _AmbientDim >::Through().

template<typename _Scalar, int _AmbientDim>
ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine ( Index  _dim ) [inline, explicit]

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

Definition at line 58 of file ParametrizedLine.h.

template<typename _Scalar, int _AmbientDim>
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 63 of file ParametrizedLine.h.

template<typename _Scalar , int _AmbientDim>
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 140 of file ParametrizedLine.h.

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

template<typename _Scalar, int _AmbientDim>
ParametrizedLine< _Scalar, _AmbientDim >::~ParametrizedLine (  ) [inline]

Definition at line 72 of file ParametrizedLine.h.

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

Copy constructor with scalar type conversion.

Definition at line 117 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::direction(), ParametrizedLine< _Scalar, _AmbientDim >::m_direction, ParametrizedLine< _Scalar, _AmbientDim >::m_origin, and ParametrizedLine< _Scalar, _AmbientDim >::origin().

Member Function Documentation

template<typename _Scalar, int _AmbientDim>
template<typename NewScalarType >
internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type 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 109 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine().

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

Definition at line 75 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::m_direction.

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

Definition at line 80 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::m_direction.

Referenced by Hyperplane< _Scalar, _AmbientDim >::Hyperplane(), ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine(), ParametrizedLine< _Scalar, _AmbientDim >::projection(), and ParametrizedLine< _Scalar, _AmbientDim >::squaredDistance().

template<typename _Scalar, int _AmbientDim>
VectorType& ParametrizedLine< _Scalar, _AmbientDim >::direction (  ) [inline]

Definition at line 81 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::m_direction.

template<typename _Scalar, int _AmbientDim>
RealScalar 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 94 of file ParametrizedLine.h.

References sqrt(), and ParametrizedLine< _Scalar, _AmbientDim >::squaredDistance().

template<typename _Scalar , int _AmbientDim>
_Scalar 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 150 of file ParametrizedLine.h.

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

template<typename _Scalar, int _AmbientDim>
bool 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 127 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::m_direction, and ParametrizedLine< _Scalar, _AmbientDim >::m_origin.

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

Definition at line 77 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::m_origin.

Referenced by Hyperplane< _Scalar, _AmbientDim >::Hyperplane(), ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine(), ParametrizedLine< _Scalar, _AmbientDim >::projection(), and ParametrizedLine< _Scalar, _AmbientDim >::squaredDistance().

template<typename _Scalar, int _AmbientDim>
VectorType& ParametrizedLine< _Scalar, _AmbientDim >::origin (  ) [inline]

Definition at line 78 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::m_origin.

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

Definition at line 97 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::direction(), and ParametrizedLine< _Scalar, _AmbientDim >::origin().

template<typename _Scalar, int _AmbientDim>
RealScalar 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 86 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::direction(), and ParametrizedLine< _Scalar, _AmbientDim >::origin().

Referenced by ParametrizedLine< _Scalar, _AmbientDim >::distance().

template<typename _Scalar, int _AmbientDim>
static ParametrizedLine ParametrizedLine< _Scalar, _AmbientDim >::Through ( const VectorType &  p0,
const VectorType &  p1 
) [inline, static]

Constructs a parametrized line going from p0 to p1.

Definition at line 69 of file ParametrizedLine.h.

References ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine().

Member Data Documentation

template<typename _Scalar, int _AmbientDim>
VectorType ParametrizedLine< _Scalar, _AmbientDim >::m_direction [protected]

Definition at line 132 of file ParametrizedLine.h.

Referenced by ParametrizedLine< _Scalar, _AmbientDim >::dim(), ParametrizedLine< _Scalar, _AmbientDim >::direction(), ParametrizedLine< _Scalar, _AmbientDim >::isApprox(), and ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine().

template<typename _Scalar, int _AmbientDim>
VectorType ParametrizedLine< _Scalar, _AmbientDim >::m_origin [protected]

Definition at line 132 of file ParametrizedLine.h.

Referenced by ParametrizedLine< _Scalar, _AmbientDim >::isApprox(), ParametrizedLine< _Scalar, _AmbientDim >::origin(), and ParametrizedLine< _Scalar, _AmbientDim >::ParametrizedLine().



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