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

A hyperplane. More...

#include <Hyperplane.h>

Public Types
typedef Scalar_	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef Eigen::Index	Index
typedef Matrix< Scalar, AmbientDimAtCompileTime, 1 >	VectorType
typedef Matrix< Scalar, Index(AmbientDimAtCompileTime)==Dynamic ? Dynamic :Index(AmbientDimAtCompileTime)+1, 1, Options >	Coefficients
typedef Block< Coefficients, AmbientDimAtCompileTime, 1 >	NormalReturnType
typedef const Block< const Coefficients, AmbientDimAtCompileTime, 1 >	ConstNormalReturnType

Public Member Functions
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE (Scalar_, AmbientDim_==Dynamic ? Dynamic :AmbientDim_+1) enum
EIGEN_DEVICE_FUNC	Hyperplane ()
template<int OtherOptions>
EIGEN_DEVICE_FUNC	Hyperplane (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other)
EIGEN_DEVICE_FUNC	Hyperplane (Index _dim)
EIGEN_DEVICE_FUNC	Hyperplane (const VectorType &n, const VectorType &e)
EIGEN_DEVICE_FUNC	Hyperplane (const VectorType &n, const Scalar &d)
EIGEN_DEVICE_FUNC	Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
EIGEN_DEVICE_FUNC	~Hyperplane ()
EIGEN_DEVICE_FUNC Index	dim () const
EIGEN_DEVICE_FUNC void	normalize (void)
EIGEN_DEVICE_FUNC Scalar	signedDistance (const VectorType &p) const
EIGEN_DEVICE_FUNC Scalar	absDistance (const VectorType &p) const
EIGEN_DEVICE_FUNC VectorType	projection (const VectorType &p) const
EIGEN_DEVICE_FUNC ConstNormalReturnType	normal () const
EIGEN_DEVICE_FUNC NormalReturnType	normal ()
EIGEN_DEVICE_FUNC const Scalar &	offset () const
EIGEN_DEVICE_FUNC Scalar &	offset ()
EIGEN_DEVICE_FUNC const Coefficients &	coeffs () const
EIGEN_DEVICE_FUNC Coefficients &	coeffs ()
EIGEN_DEVICE_FUNC VectorType	intersection (const Hyperplane &other) const
template<typename XprType >
EIGEN_DEVICE_FUNC Hyperplane &	transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
template<int TrOptions>
EIGEN_DEVICE_FUNC Hyperplane &	transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)
template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::cast_return_type< Hyperplane, Hyperplane< NewScalarType, AmbientDimAtCompileTime, Options > >::type	cast () const
template<typename OtherScalarType , int OtherOptions>
EIGEN_DEVICE_FUNC	Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
template<int OtherOptions>
EIGEN_DEVICE_FUNC bool	isApprox (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

Static Public Member Functions
static EIGEN_DEVICE_FUNC Hyperplane	Through (const VectorType &p0, const VectorType &p1)
static EIGEN_DEVICE_FUNC Hyperplane	Through (const VectorType &p0, const VectorType &p1, const VectorType &p2)

Protected Attributes
Coefficients	m_coeffs

Detailed Description

template<typename Scalar_, int AmbientDim_, int Options_>
class Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >

A hyperplane.

\geometry_module

A hyperplane is an affine subspace of dimension n-1 in a space of dimension n. For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.

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. Notice that the dimension of the hyperplane is AmbientDim_-1.

This class represents an hyperplane as the zero set of the implicit equation \( n \cdot x + d = 0 \) where \( n \) is a unit normal vector of the plane (linear part) and \( d \) is the distance (offset) to the origin.

Member Typedef Documentation

Coefficients

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef Matrix<Scalar, Index(AmbientDimAtCompileTime) == Dynamic ? Dynamic : Index(AmbientDimAtCompileTime) + 1, 1, Options> Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Coefficients

ConstNormalReturnType

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef const Block<const Coefficients, AmbientDimAtCompileTime, 1> Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::ConstNormalReturnType

Index

template<typename Scalar_ , int AmbientDim_, int Options_>

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

Deprecated:

since Eigen 3.3

NormalReturnType

template<typename Scalar_ , int AmbientDim_, int Options_>

typedef Block<Coefficients, AmbientDimAtCompileTime, 1> Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::NormalReturnType

RealScalar

template<typename Scalar_ , int AmbientDim_, int Options_>

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

Scalar

template<typename Scalar_ , int AmbientDim_, int Options_>

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

VectorType

template<typename Scalar_ , int AmbientDim_, int Options_>

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

Constructor & Destructor Documentation

Hyperplane() [1/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

Default constructor without initialization

{}

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::cast().

Hyperplane() [2/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

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

inline

      : m_coeffs(other.coeffs()) {}

Hyperplane() [3/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inlineexplicit

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

: m_coeffs(_dim + 1) {}

Hyperplane() [4/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( const VectorType &  n, const VectorType &  e  )

inline

Construct a plane from its normal n and a point e onto the plane.

Warning

the vector normal is assumed to be normalized.

                                                                                : m_coeffs(n.size() + 1) {
    normal() = n;
    offset() = -n.dot(e);
  }

References e(), n, Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset().

Hyperplane() [5/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane ( const VectorType &  n, const Scalar &  d  )

inline

Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is \( n \cdot x + d = 0 \).

Warning

the vector normal is assumed to be normalized.

                                                                            : m_coeffs(n.size() + 1) {
    normal() = n;
    offset() = d;
  }

References n, Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset().

Hyperplane() [6/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inlineexplicit

Constructs a hyperplane passing through the parametrized line parametrized. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.

                                                                                                               {
    normal() = parametrized.direction().unitOrthogonal();
    offset() = -parametrized.origin().dot(normal());
  }

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

~Hyperplane()

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

{}

Hyperplane() [7/7]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename OtherScalarType , int OtherOptions>

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

inlineexplicit

Copy constructor with scalar type conversion

                                                                                       {
    m_coeffs = other.coeffs().template cast<Scalar>();
  }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

Member Function Documentation

absDistance()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Scalar Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::absDistance ( const VectorType &  p ) const

inline

Returns

the absolute distance between the plane *this and a point p.

See also

signedDistance()

{ return numext::abs(signedDistance(p)); }

References Eigen::numext::abs(), p, and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::signedDistance().

cast()

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename NewScalarType >

EIGEN_DEVICE_FUNC internal::cast_return_type<Hyperplane, Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options> >::type Eigen::Hyperplane< 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<Hyperplane,
                                            Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options> >::type(*this);
  }

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

coeffs() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Coefficients& Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs ( )

inline

Returns

a non-constant reference to the coefficients c_i of the plane equation: \( c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \)

{ return m_coeffs; }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

coeffs() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC const Coefficients& Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs ( ) const

inline

Returns

a constant reference to the coefficients c_i of the plane equation: \( c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \)

{ return m_coeffs; }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::intersection().

dim()

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

Returns

the dimension in which the plane holds

                                             {
    return AmbientDimAtCompileTime == Dynamic ? m_coeffs.size() - 1 : Index(AmbientDimAtCompileTime);
  }

References Eigen::Dynamic, and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset().

EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE()

template<typename Scalar_ , int AmbientDim_, int Options_>

Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE ( Scalar_  , AmbientDim_  = = Dynamic ? Dynamic : AmbientDim_ + 1  )

inline

                                                                                              : AmbientDim_ + 1)
  enum { AmbientDimAtCompileTime = AmbientDim_, Options = Options_ };

intersection()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC VectorType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::intersection ( const Hyperplane< Scalar_, AmbientDim_, Options_ > &  other ) const

inline

Returns

the intersection of *this with other.

Warning

The ambient space must be a plane, i.e. have dimension 2, so that *this and other are lines.

Note

If other is approximately parallel to *this, this method will return any point on *this.

                                                                           {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
    Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
    // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
    // whether the two lines are approximately parallel.
    if (internal::isMuchSmallerThan(det, Scalar(1))) {  // special case where the two lines are approximately parallel.
                                                        // Pick any point on the first line.
      if (numext::abs(coeffs().coeff(1)) > numext::abs(coeffs().coeff(0)))
        return VectorType(coeffs().coeff(1), -coeffs().coeff(2) / coeffs().coeff(1) - coeffs().coeff(0));
      else
        return VectorType(-coeffs().coeff(2) / coeffs().coeff(0) - coeffs().coeff(1), coeffs().coeff(0));
    } else {  // general case
      Scalar invdet = Scalar(1) / det;
      return VectorType(
          invdet * (coeffs().coeff(1) * other.coeffs().coeff(2) - other.coeffs().coeff(1) * coeffs().coeff(2)),
          invdet * (other.coeffs().coeff(0) * coeffs().coeff(2) - coeffs().coeff(0) * other.coeffs().coeff(2)));
    }
  }

References Eigen::numext::abs(), Eigen::PlainObjectBase< Derived >::coeff(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs(), EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE, and Eigen::internal::isMuchSmallerThan().

isApprox()

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int OtherOptions>

EIGEN_DEVICE_FUNC bool Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::isApprox ( const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &  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_coeffs.isApprox(other.m_coeffs, prec);
  }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

normal() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC NormalReturnType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal ( )

inline

Returns

a non-constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.

{ return NormalReturnType(m_coeffs, 0, 0, dim(), 1); }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::dim(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

normal() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC ConstNormalReturnType Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal ( ) const

inline

Returns

a constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.

                                                                {
    return ConstNormalReturnType(m_coeffs, 0, 0, dim(), 1);
  }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::dim(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normalize(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::projection(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::signedDistance(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Through(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::transform().

normalize()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC void Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normalize ( void  )

inline

normalizes *this

{ m_coeffs /= normal().norm(); }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs, and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal().

offset() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Scalar& Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset ( )

inline

Returns

a non-constant reference to the distance to the origin, which is also the constant part of the implicit equation

{ return m_coeffs(dim()); }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::dim(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

offset() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC const Scalar& Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset ( ) const

inline

Returns

the distance to the origin, which is also the "constant term" of the implicit equation

Warning

the vector normal is assumed to be normalized.

{ return m_coeffs.coeff(dim()); }

References Eigen::PlainObjectBase< Derived >::coeff(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::dim(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs.

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::signedDistance(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Through(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::transform().

projection()

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inline

Returns

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

{ return p - signedDistance(p) * normal(); }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), p, and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::signedDistance().

signedDistance()

template<typename Scalar_ , int AmbientDim_, int Options_>

EIGEN_DEVICE_FUNC Scalar Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::signedDistance ( const VectorType &  p ) const

inline

Returns

the signed distance between the plane *this and a point p.

See also

absDistance()

{ return normal().dot(p) + offset(); }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset(), and p.

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

Through() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

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

inlinestatic

Constructs a hyperplane passing through the two points. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.

                                                                                                 {
    Hyperplane result(p0.size());
    result.normal() = (p1 - p0).unitOrthogonal();
    result.offset() = -p0.dot(result.normal());
    return result;
  }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset(), p0, and p1.

Through() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

static EIGEN_DEVICE_FUNC Hyperplane Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Through ( const VectorType &  p0, const VectorType &  p1, const VectorType &  p2  )

inlinestatic

Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.

                                                                                                                       {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
    Hyperplane result(p0.size());
    VectorType v0(p2 - p0), v1(p1 - p0);
    result.normal() = v0.cross(v1);
    RealScalar norm = result.normal().norm();
    if (norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon()) {
      Matrix<Scalar, 2, 3> m;
      m << v0.transpose(), v1.transpose();
      JacobiSVD<Matrix<Scalar, 2, 3>, ComputeFullV> svd(m);
      result.normal() = svd.matrixV().col(2);
    } else
      result.normal() /= norm;
    result.offset() = -p0.dot(result.normal());
    return result;
  }

References Eigen::ComputeFullV, EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE, m, Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset(), p0, p1, svd(), and v1().

transform() [1/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<typename XprType >

EIGEN_DEVICE_FUNC Hyperplane& Eigen::Hyperplane< 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) {
      normal() = mat.inverse().transpose() * normal();
      m_coeffs /= normal().norm();
    } else if (traits == Isometry)
      normal() = mat * normal();
    else {
      eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
    }
    return *this;
  }

References Eigen::Affine, eigen_assert, Eigen::Isometry, Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs, Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), and Eigen::SparseMatrixBase< Derived >::transpose().

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

transform() [2/2]

template<typename Scalar_ , int AmbientDim_, int Options_>

template<int TrOptions>

EIGEN_DEVICE_FUNC Hyperplane& Eigen::Hyperplane< 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);
    offset() -= normal().dot(t.translation());
    return *this;
  }

References Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset(), plotPSD::t, and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::transform().

Member Data Documentation

m_coeffs

template<typename Scalar_ , int AmbientDim_, int Options_>

Coefficients Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::m_coeffs

protected

Referenced by Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::coeffs(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::dim(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Hyperplane(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::isApprox(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normal(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::normalize(), Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::offset(), and Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::transform().

---

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

• ForwardDeclarations.h
• Hyperplane.h