A hyperplane
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.
Public Types |
| enum | { AmbientDimAtCompileTime = _AmbientDim,
Options = _Options
} |
| typedef _Scalar | Scalar |
| typedef NumTraits< Scalar >::Real | RealScalar |
| typedef DenseIndex | 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 |
| | Hyperplane () |
| | Default constructor without initialization.
|
| template<int OtherOptions> |
| | Hyperplane (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other) |
| | Hyperplane (Index _dim) |
| | Constructs a dynamic-size hyperplane with _dim the dimension of the ambient space.
|
| | Hyperplane (const VectorType &n, const VectorType &e) |
| | Construct a plane from its normal n and a point e onto the plane.
|
| | Hyperplane (const VectorType &n, Scalar d) |
| | Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is .
|
| | Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > ¶metrized) |
| | Constructs a hyperplane passing through the parametrized line parametrized.
|
| | ~Hyperplane () |
| Index | dim () const |
| void | normalize (void) |
| | normalizes *this
|
| Scalar | signedDistance (const VectorType &p) const |
| Scalar | absDistance (const VectorType &p) const |
| VectorType | projection (const VectorType &p) const |
| ConstNormalReturnType | normal () const |
| NormalReturnType | normal () |
| const Scalar & | offset () const |
| Scalar & | offset () |
| const Coefficients & | coeffs () const |
| Coefficients & | coeffs () |
| VectorType | intersection (const Hyperplane &other) const |
| template<typename XprType > |
| Hyperplane & | transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine) |
| | Applies the transformation matrix mat to *this and returns a reference to *this.
|
| template<int TrOptions> |
| Hyperplane & | transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine) |
| | Applies the transformation t to *this and returns a reference to *this.
|
| template<typename NewScalarType > |
internal::cast_return_type
< Hyperplane, Hyperplane
< NewScalarType,
AmbientDimAtCompileTime,
Options > >::type | cast () const |
| template<typename OtherScalarType , int OtherOptions> |
| | Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other) |
| | Copy constructor with scalar type conversion.
|
| template<int OtherOptions> |
| bool | isApprox (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const |
Static Public Member Functions |
| static Hyperplane | Through (const VectorType &p0, const VectorType &p1) |
| | Constructs a hyperplane passing through the two points.
|
| static Hyperplane | Through (const VectorType &p0, const VectorType &p1, const VectorType &p2) |
| | Constructs a hyperplane passing through the three points.
|
Protected Attributes |
| Coefficients | m_coeffs |
