Hyperplane Class Template Reference
[Geometry module]

List of all members.

Detailed Description

template<typename _Scalar, int _AmbientDim>
class Eigen::Hyperplane< _Scalar, _AmbientDim >

A hyperplane.

This is defined in the Geometry module. 

 #include <Eigen/Geometry>

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.

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.

Public Types

enum  { AmbientDimAtCompileTime }
typedef Matrix< Scalar,
AmbientDimAtCompileTime==Dynamic?Dynamic:AmbientDimAtCompileTime+1, 1 > 		Coefficients
typedef Block< Coefficients,
AmbientDimAtCompileTime, 1 > 		NormalReturnType
typedef NumTraits< Scalar >::Real RealScalar
typedef _Scalar Scalar
typedef Matrix< Scalar,
AmbientDimAtCompileTime, 1 > 		VectorType

Public Member Functions

Scalar absDistance (const VectorType &p) const
template<typename NewScalarType>
ei_cast_return_type
< Hyperplane, Hyperplane
< NewScalarType,
AmbientDimAtCompileTime >
>::type 		cast () const
Coefficients & coeffs ()
const Coefficients & coeffs () const
int dim () const
template<typename OtherScalarType>
 Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime > &other)
 Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
 Hyperplane (const VectorType &n, Scalar d)
 Hyperplane (const VectorType &n, const VectorType &e)
 Hyperplane (int _dim)
 Hyperplane ()
VectorType intersection (const Hyperplane &other)
bool isApprox (const Hyperplane &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
NormalReturnType normal ()
const NormalReturnType normal () const
void normalize (void)
Scalar & offset ()
const Scalar & offset () const
VectorType projection (const VectorType &p) const
Scalar signedDistance (const VectorType &p) const
Hyperplane & transform (const Transform< Scalar, AmbientDimAtCompileTime > &t, TransformTraits traits=Affine)
template<typename XprType>
Hyperplane & transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)

Static Public Member Functions

static Hyperplane Through (const VectorType &p0, const VectorType &p1, const VectorType &p2)
static Hyperplane Through (const VectorType &p0, const VectorType &p1)

Protected Attributes

Coefficients m_coeffs

Constructor & Destructor Documentation

Hyperplane (  )  [inline, explicit]

Default constructor without initialization

Hyperplane ( int  _dim  )  [inline, explicit]

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

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.

Hyperplane ( const VectorType &  n,
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.

Hyperplane ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &  parametrized  )  [inline, explicit]

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.

Hyperplane ( const Hyperplane< OtherScalarType, AmbientDimAtCompileTime > &  other  )  [inline, explicit]

Copy constructor with scalar type conversion

Member Function Documentation

Scalar absDistance ( const VectorType &  p  )  const [inline]

Returns:
the absolute distance between the plane *this and a point p.
See also:
signedDistance()

ei_cast_return_type<Hyperplane, Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type 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.

Coefficients& 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 $

const Coefficients& 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 $

int dim (  )  const [inline]

Returns:
the dimension in which the plane holds

VectorType intersection ( const Hyperplane< _Scalar, _AmbientDim > &  other  )  [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.

bool isApprox ( const Hyperplane< _Scalar, _AmbientDim > &  other,
typename NumTraits< Scalar >::Real  prec = precision<Scalar>() 
) const [inline]

Returns:
true if *this is approximately equal to other, within the precision determined by prec.
See also:
MatrixBase::isApprox()

NormalReturnType 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.

const NormalReturnType 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.

void normalize ( void   )  [inline]

normalizes *this

Scalar& offset (  )  [inline]

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

const Scalar& 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.

VectorType projection ( const VectorType &  p  )  const [inline]

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

Scalar signedDistance ( const VectorType &  p  )  const [inline]

Returns:
the signed distance between the plane *this and a point p.
See also:
absDistance()

static Hyperplane Through ( const VectorType &  p0,
const VectorType &  p1,
const VectorType &  p2 
) [inline, static]

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

static Hyperplane Through ( const VectorType &  p0,
const VectorType &  p1 
) [inline, static]

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& transform ( const Transform< Scalar, AmbientDimAtCompileTime > &  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.

Hyperplane& 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.

The documentation for this class was generated from the following file:
Generated on Sat Apr 25 18:28:59 2009 for Eigen by  doxygen 1.5.5