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

A parametrized line. More...

#include <ParametrizedLine.h>

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

Static Public Member Functions
static EIGEN_DEVICE_FUNC 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.

\geometry_module

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.

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

RealScalar

template<typename Scalar_ , int AmbientDim_, int Options_>

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

Scalar

template<typename Scalar_ , int AmbientDim_, int Options_>

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

VectorType

template<typename Scalar_ , int AmbientDim_, int Options_>

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

Member Enumeration Documentation

anonymous enum

template<typename Scalar_ , int AmbientDim_, int Options_>

anonymous enum

Enumerator
AmbientDimAtCompileTime
Options

{ AmbientDimAtCompileTime = AmbientDim_, Options = Options_ };

Constructor & Destructor Documentation

ParametrizedLine() [1/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

Default constructor without initialization

{}

Referenced by Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::cast(), and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::Through().

ParametrizedLine() [2/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

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

inline

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

ParametrizedLine() [3/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inlineexplicit

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

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

ParametrizedLine() [4/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC 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.

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

ParametrizedLine() [5/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

EIGEN_DEVICE_FUNC 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

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

References EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE, and hyperplane().

~ParametrizedLine()

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

{}

ParametrizedLine() [6/6]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename OtherScalarType , int OtherOptions>

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

inlineexplicit

Copy constructor with scalar type conversion

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

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_direction, Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_origin, and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin().

Member Function Documentation

cast()

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename NewScalarType >

EIGEN_DEVICE_FUNC 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.

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

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine(), and compute_granudrum_aor::type.

dim()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Index Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::dim ( ) const

inline

Returns

the dimension in which the line holds

{ return m_direction.size(); }

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_direction.

direction() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

{ return m_direction; }

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_direction.

direction() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

{ return m_direction; }

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_direction.

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::projection(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::squaredDistance(), and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::transform().

distance()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC 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()

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

References EIGEN_USING_STD, p, sqrt(), and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::squaredDistance().

intersection() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC 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

                                                                            {
  return intersectionParameter(hyperplane);
}

References hyperplane().

intersectionParameter() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC 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

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

References hyperplane().

intersectionPoint()

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

EIGEN_DEVICE_FUNC 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

                                                                            {
  return pointAt(intersectionParameter(hyperplane));
}

References hyperplane().

isApprox()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC 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()

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

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_direction, and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_origin.

origin() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

{ return m_origin; }

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_origin.

origin() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

{ return m_origin; }

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::m_origin.

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::projection(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::squaredDistance(), and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::transform().

pointAt()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC ParametrizedLine< Scalar_, AmbientDim_, Options_ >::VectorType Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::pointAt ( const Scalar &  t ) const

inline

Returns

the point at t along this line

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

References plotPSD::t.

projection()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC VectorType Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::projection ( const VectorType &  p ) const

inline

Returns

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

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

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin(), and p.

squaredDistance()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC 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()

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

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction(), dot(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin(), and p.

Referenced by Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::distance().

Through()

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inlinestatic

Constructs a parametrized line going from p0 to p1.

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

References p0, p1, and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine().

transform() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename XprType >

EIGEN_DEVICE_FUNC 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.

                                                                                        {
    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;
  }

References Eigen::Affine, Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction(), eigen_assert, Eigen::Isometry, and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin().

Referenced by Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::transform().

transform() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int TrOptions>

EIGEN_DEVICE_FUNC 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.

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

References Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin(), plotPSD::t, and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::transform().

Member Data Documentation

m_direction

template<typename Scalar_ , int AmbientDim_, int Options_>

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

protected

Referenced by Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::dim(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::direction(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::isApprox(), and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine().

m_origin

template<typename Scalar_ , int AmbientDim_, int Options_>

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

protected

Referenced by Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::isApprox(), Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::origin(), and Eigen::ParametrizedLine< Scalar_, AmbientDim_, Options_ >::ParametrizedLine().

---

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

• ForwardDeclarations.h
• ParametrizedLine.h