Hyperplane< _Scalar, _AmbientDim > Class Template Reference
[Geometry module]
A hyperplane.
More...
List of all members.
Public Types |
enum | { AmbientDimAtCompileTime
} |
typedef Matrix< Scalar, int(AmbientDimAtCompileTime)==Dynamic?Dynamic:int(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 > ¶metrized) |
| 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 |
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
where
is a unit normal vector of the plane (linear part) and
is the distance (offset) to the origin.
Constructor & Destructor Documentation
Default constructor without initialization
Constructs a dynamic-size hyperplane with _dim the dimension of the ambient space
Construct a plane from its normal n and a point e onto the plane.
- Warning:
- the vector normal is assumed to be normalized.
Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is
.
- Warning:
- the vector normal is assumed to be normalized.
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
.
- Returns:
- a non-constant reference to the coefficients c_i of the plane equation:
- Returns:
- a constant reference to the coefficients c_i of the plane equation:
int dim |
( |
|
) |
const [inline] |
- Returns:
- the dimension in which the plane holds
- 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()
- Returns:
- a non-constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.
- 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] |
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.
- 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()
Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.
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: