Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ > Class Template Reference

A parametrized line. More...

Public Types
enum	{   AmbientDimAtCompileTime ,   Options }
typedef Eigen::Index	Index
typedef NumTraits< Scalar >::Real	RealScalar
typedef Scalar_	Scalar
typedef Matrix< Scalar, AmbientDimAtCompileTime, 1, Options >	VectorType

Public Member Functions
template<typename NewScalarType >
internal::cast_return_type< ParametrizedLine, ParametrizedLine< NewScalarType, AmbientDimAtCompileTime, Options > >::type	cast () const
Index	dim () const
VectorType &	direction ()
const VectorType &	direction () const
RealScalar	distance (const VectorType &p) const
template<int OtherOptions>
Scalar	intersection (const Hyperplane< Scalar_, AmbientDim_, OtherOptions > &hyperplane) 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>
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, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
VectorType &	origin ()
const VectorType &	origin () const
	ParametrizedLine ()
template<int OtherOptions>
	ParametrizedLine (const Hyperplane< Scalar_, AmbientDim_, OtherOptions > &hyperplane)
template<typename OtherScalarType , int OtherOptions>
	ParametrizedLine (const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
template<int OtherOptions>
	ParametrizedLine (const ParametrizedLine< Scalar, AmbientDimAtCompileTime, OtherOptions > &other)
	ParametrizedLine (const VectorType &origin, const VectorType &direction)
	ParametrizedLine (Index _dim)
VectorType	pointAt (const Scalar &t) const
VectorType	projection (const VectorType &p) const
RealScalar	squaredDistance (const VectorType &p) const
template<typename XprType >
ParametrizedLine &	transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
template<int TrOptions>
ParametrizedLine &	transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)
	~ParametrizedLine ()

Static Public Member Functions
static ParametrizedLine	Through (const VectorType &p0, const VectorType &p1)

Protected Attributes
VectorType	m_direction
VectorType	m_origin

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

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.

Definition at line 32 of file ParametrizedLine.h.

Member Typedef Documentation

Index

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef Eigen::Index Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::Index

Deprecated:

since Eigen 3.3

Definition at line 42 of file ParametrizedLine.h.

RealScalar

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef NumTraits<Scalar>::Real Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::RealScalar

Definition at line 41 of file ParametrizedLine.h.

Scalar

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef Scalar_ Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::Scalar

Definition at line 40 of file ParametrizedLine.h.

VectorType

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::VectorType

Definition at line 43 of file ParametrizedLine.h.

Member Enumeration Documentation

anonymous enum

template<typename Scalar_ , int AmbientDim_, int Options_>

anonymous enum

Enumerator
AmbientDimAtCompileTime
Options

Definition at line 36 of file ParametrizedLine.h.

       {
    AmbientDimAtCompileTime = AmbientDim_,
    Options = Options_
  };

Constructor & Destructor Documentation

ParametrizedLine() [1/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine ( )

inline

Default constructor without initialization

Definition at line 46 of file ParametrizedLine.h.

{}

ParametrizedLine() [2/6]

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 49 of file ParametrizedLine.h.

   : m_origin(other.origin()), m_direction(other.direction())
  {}

ParametrizedLine() [3/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine ( Index  _dim )

inlineexplicit

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

Definition at line 55 of file ParametrizedLine.h.

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

ParametrizedLine() [4/6]

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 60 of file ParametrizedLine.h.

    : m_origin(origin), m_direction(direction) {}

ParametrizedLine() [5/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::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

Definition at line 185 of file ParametrizedLine.h.

{
  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
  direction() = hyperplane.normal().unitOrthogonal();
  origin() = -hyperplane.normal()*hyperplane.offset();
}

~ParametrizedLine()

template<typename Scalar_ , int AmbientDim_, int Options_>

Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::~ParametrizedLine ( )

inline

Definition at line 70 of file ParametrizedLine.h.

{}

ParametrizedLine() [6/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename OtherScalarType , int OtherOptions>

Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine ( const ParametrizedLine< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &  other )

inlineexplicit

Copy constructor with scalar type conversion

Definition at line 161 of file ParametrizedLine.h.

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

Member Function Documentation

cast()

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 153 of file ParametrizedLine.h.

  {
    return typename internal::cast_return_type<ParametrizedLine,
                    ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
  }

dim()

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 73 of file ParametrizedLine.h.

{ return m_direction.size(); }

direction() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

VectorType& Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction ( )

inline

Definition at line 79 of file ParametrizedLine.h.

{ return m_direction; }

direction() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

const VectorType& Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction ( ) const

inline

Definition at line 78 of file ParametrizedLine.h.

{ return m_direction; }

distance()

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 92 of file ParametrizedLine.h.

{ EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p)); }

intersection() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

Scalar Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::intersection

(

const Hyperplane< Scalar_, AmbientDim_, OtherOptions > &

hyperplane

)

const

intersection() [2/2]

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 217 of file ParametrizedLine.h.

{
  return intersectionParameter(hyperplane);
}

intersectionParameter() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

Scalar Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::intersectionParameter

(

const Hyperplane< Scalar_, AmbientDim_, OtherOptions > &

hyperplane

)

const

intersectionParameter() [2/2]

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 205 of file ParametrizedLine.h.

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

intersectionPoint()

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 227 of file ParametrizedLine.h.

{
  return pointAt(intersectionParameter(hyperplane));
}

isApprox()

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 171 of file ParametrizedLine.h.

  { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }

origin() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

VectorType& Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin ( )

inline

Definition at line 76 of file ParametrizedLine.h.

{ return m_origin; }

origin() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

const VectorType& Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin ( ) const

inline

Definition at line 75 of file ParametrizedLine.h.

{ return m_origin; }

pointAt()

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 196 of file ParametrizedLine.h.

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

projection()

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 95 of file ParametrizedLine.h.

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

squaredDistance()

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 84 of file ParametrizedLine.h.

  {
    VectorType diff = p - origin();
    return (diff - direction().dot(diff) * direction()).squaredNorm();
  }

Through()

template<typename Scalar_ , int AmbientDim_, int Options_>

static ParametrizedLine Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::Through ( const VectorType &  p0, const VectorType &  p1  )

inlinestatic

Constructs a parametrized line going from p0 to p1.

Definition at line 67 of file ParametrizedLine.h.

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

transform() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename XprType >

ParametrizedLine& Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::transform ( const MatrixBase< XprType > &  mat, TransformTraits  traits = Affine  )

inline

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

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.

Definition at line 116 of file ParametrizedLine.h.

  {
    if (traits==Affine)
      direction() = (mat * direction()).normalized();
    else if (traits==Isometry)
      direction() = mat * direction();
    else
    {
      eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
    }
    origin() = mat * origin();
    return *this;
  }

transform() [2/2]

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  )

inline

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

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.

Definition at line 138 of file ParametrizedLine.h.

  {
    transform(t.linear(), traits);
    origin() += t.translation();
    return *this;
  }

Member Data Documentation

m_direction

template<typename Scalar_ , int AmbientDim_, int Options_>

VectorType Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_direction

protected

Definition at line 176 of file ParametrizedLine.h.

m_origin

template<typename Scalar_ , int AmbientDim_, int Options_>

VectorType Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_origin

protected

Definition at line 176 of file ParametrizedLine.h.

---

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

• ForwardDeclarations.h
• ParametrizedLine.h