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Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options > Class Template Reference
Geometry_Module

A parametrized line. More...

#include <ParametrizedLine.h>

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List of all members.

Public Types

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

Public Member Functions

 ParametrizedLine ()
template<int OtherOptions>
 ParametrizedLine (const ParametrizedLine< Scalar, AmbientDimAtCompileTime, OtherOptions > &other)
 ParametrizedLine (Index _dim)
 ParametrizedLine (const VectorType &origin, const VectorType &direction)
template<int OtherOptions>
 ParametrizedLine (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &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
VectorType pointAt (const Scalar &t) const
template<int OtherOptions>
Scalar intersectionParameter (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const
template<int OtherOptions>
Scalar intersection (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const
template<int OtherOptions>
VectorType intersectionPoint (const Hyperplane< _Scalar, _AmbientDim, OtherOptions > &hyperplane) const
template<typename NewScalarType >
internal::cast_return_type
< ParametrizedLine,
ParametrizedLine
< NewScalarType,
AmbientDimAtCompileTime,
Options > >::type 		cast () const
template<typename OtherScalarType , int OtherOptions>
 ParametrizedLine (const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
bool isApprox (const ParametrizedLine &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

Static Public Member Functions

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

Protected Attributes

VectorType m_origin
VectorType m_direction

Detailed Description

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

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} $, $ t \in \mathbf{R} $.

Template 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 30 of file ParametrizedLine.h.

Member Typedef Documentation

template<typename _Scalar, int _AmbientDim, int _Options>
typedef Eigen::Index Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::Index
Deprecated:
since Eigen 3.3

Definition at line 40 of file ParametrizedLine.h.

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

Definition at line 39 of file ParametrizedLine.h.

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

Definition at line 38 of file ParametrizedLine.h.

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

Definition at line 41 of file ParametrizedLine.h.

Member Enumeration Documentation

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

Definition at line 34 of file ParametrizedLine.h.

       {
    AmbientDimAtCompileTime = _AmbientDim,
    Options = _Options
  };

Constructor & Destructor Documentation

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

Default constructor without initialization

Definition at line 44 of file ParametrizedLine.h.

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

Definition at line 47 of file ParametrizedLine.h.

   : m_origin(other.origin()), m_direction(other.direction())
  {}
template<typename _Scalar, int _AmbientDim, int _Options>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::ParametrizedLine ( Index  _dim) [inline, explicit]

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

Definition at line 53 of file ParametrizedLine.h.

: m_origin(_dim), m_direction(_dim) {}
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.

Definition at line 58 of file ParametrizedLine.h.

    : m_origin(origin), m_direction(direction) {}
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 ParametrizedLine.h.

{
  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
  direction() = hyperplane.normal().unitOrthogonal();
  origin() = -hyperplane.normal()*hyperplane.offset();
}
template<typename _Scalar, int _AmbientDim, int _Options>
Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::~ParametrizedLine ( ) [inline]

Definition at line 68 of file ParametrizedLine.h.

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

Copy constructor with scalar type conversion

Definition at line 122 of file ParametrizedLine.h.

  {
    m_origin = other.origin().template cast<Scalar>();
    m_direction = other.direction().template cast<Scalar>();
  }

Member Function Documentation

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.

Definition at line 114 of file ParametrizedLine.h.

  {
    return typename internal::cast_return_type<ParametrizedLine,
                    ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
  }
template<typename _Scalar, int _AmbientDim, int _Options>
Index Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::dim ( ) const [inline]
Returns:
the dimension in which the line holds

Definition at line 71 of file ParametrizedLine.h.

{ return m_direction.size(); }
template<typename _Scalar, int _AmbientDim, int _Options>
const VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::direction ( ) const [inline]

Definition at line 76 of file ParametrizedLine.h.

{ return m_direction; }
template<typename _Scalar, int _AmbientDim, int _Options>
VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::direction ( ) [inline]

Definition at line 77 of file ParametrizedLine.h.

{ return m_direction; }
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()

Definition at line 90 of file ParametrizedLine.h.

{ using std::sqrt; return sqrt(squaredDistance(p)); }
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 ParametrizedLine.h.

{
  return intersectionParameter(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 [inline]
Returns:
the parameter value of the intersection between *this and the given hyperplane

Definition at line 166 of file ParametrizedLine.h.

{
  return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
          / hyperplane.normal().dot(direction());
}
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 ParametrizedLine.h.

{
  return pointAt(intersectionParameter(hyperplane));
}
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()

Definition at line 132 of file ParametrizedLine.h.

  { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
template<typename _Scalar, int _AmbientDim, int _Options>
const VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::origin ( ) const [inline]

Definition at line 73 of file ParametrizedLine.h.

{ return m_origin; }
template<typename _Scalar, int _AmbientDim, int _Options>
VectorType& Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::origin ( ) [inline]

Definition at line 74 of file ParametrizedLine.h.

{ return m_origin; }
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

Definition at line 157 of file ParametrizedLine.h.

{
  return origin() + (direction()*t); 
}
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.

Definition at line 93 of file ParametrizedLine.h.

  { return origin() + direction().dot(p-origin()) * direction(); }
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()

Definition at line 82 of file ParametrizedLine.h.

  {
    VectorType diff = p - origin();
    return (diff - direction().dot(diff) * direction()).squaredNorm();
  }
template<typename _Scalar, int _AmbientDim, int _Options>
static ParametrizedLine Eigen::ParametrizedLine< _Scalar, _AmbientDim, _Options >::Through ( const VectorType &  p0,
const VectorType &  p1 
) [inline, static]

Constructs a parametrized line going from p0 to p1.

Definition at line 65 of file ParametrizedLine.h.

  { return ParametrizedLine(p0, (p1-p0).normalized()); }

Member Data Documentation

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

Definition at line 137 of file ParametrizedLine.h.

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

Definition at line 137 of file ParametrizedLine.h.

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