Compute a Weingarten map from the spatial derivatives of the normal field \( N \). More...

#include <weingarten.h>

Inheritance diagram for Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >:

Collaboration diagram for Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >:

Public Types
using	Scalar = typename DataPoint::Scalar
	Alias to scalar type.

using	VectorType = typename Base::VectorType
	Alias to vector type.

using	NeighborFilter = typename Base::NeighborFilter
	Alias to the filter applied on the neighbors.

using	MatrixType = typename DataPoint::MatrixType
	Alias to matrix type.

using	ScalarArray = typename Base::ScalarArray
	Alias to scalar derivatives array.

using	VectorArray = typename Base::VectorArray
	Alias to vector derivatives array.

using	Matrix2 = Eigen::Matrix< Scalar, 2, 2 >

Public Member Functions
NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T > &	normalDerivativeWeingartenEstimator ()
	Explicit conversion to NormalDerivativeWeingartenEstimator , to access methods potentially hidden by heritage.

const NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T > &	normalDerivativeWeingartenEstimator () const
	Explicit conversion to NormalDerivativeWeingartenEstimator , to access methods potentially hidden by heritage.

FIT_RESULT	finalize ()
	Finalize the procedure.

Matrix2	weingartenMap () const
	Returns the Weingarten Map.

template<typename Matrix2Derived >
void	weingartenMap (Matrix2Derived &w) const
	Returns the Weingarten Map.

VectorType	worldToTangentPlane (const VectorType &_q, bool _isPositionVector=true) const
	Express a point in ambient space relatively to the tangent plane.

VectorType	tangentPlaneToWorld (const VectorType &_q, bool _isPositionVector=true) const
	Transform a point from the tangent plane [h, u, v]^T to ambient space.

Protected Types
enum	{ Check = Base::PROVIDES_NORMAL_DERIVATIVE , PROVIDES_WEINGARTEN_MAP , PROVIDES_TANGENT_PLANE_BASIS }

using	Base = T
	Base class of the procedure.

Detailed Description

template<class DataPoint, class _NFilter, int DiffType, typename T>
class Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >

Compute a Weingarten map from the spatial derivatives of the normal field \( N \).

See also: WeingartenCurvatureEstimator and WeingartenCurvatureEstimatorDer to compute curvatures from the weingarten map

A tangent plane aligned with the map is also computed during the process.

Note: Computations are marked as UNSTABLE if the computed basis does not properly align with the gradient of the fitted primitive.

This primitive provides:

PROVIDES_WEINGARTEN_MAP, PROVIDES_TANGENT_PLANE_BASIS

This primitive requires:

PROVIDES_NORMAL_DERIVATIVE

Definition at line 107 of file weingarten.h.

Member Typedef Documentation

◆ Base

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::Base = T

protected

Base class of the procedure.

Definition at line 109 of file weingarten.h.

◆ Matrix2

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::Matrix2 = Eigen::Matrix<Scalar, 2, 2>

Definition at line 112 of file weingarten.h.

◆ MatrixType

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::MatrixType = typename DataPoint::MatrixType

Alias to matrix type.

Definition at line 110 of file weingarten.h.

◆ NeighborFilter

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::NeighborFilter = typename Base::NeighborFilter

Alias to the filter applied on the neighbors.

Definition at line 109 of file weingarten.h.

◆ Scalar

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::Scalar = typename DataPoint::Scalar

Alias to scalar type.

Definition at line 109 of file weingarten.h.

◆ ScalarArray

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::ScalarArray = typename Base::ScalarArray

Alias to scalar derivatives array.

Definition at line 111 of file weingarten.h.

◆ VectorArray

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::VectorArray = typename Base::VectorArray

Alias to vector derivatives array.

Definition at line 111 of file weingarten.h.

◆ VectorType

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::VectorType = typename Base::VectorType

Alias to vector type.

Definition at line 109 of file weingarten.h.

Member Enumeration Documentation

◆ anonymous enum

template<class DataPoint , class _NFilter , int DiffType, typename T >

anonymous enum

protected

Definition at line 117 of file weingarten.h.

Member Function Documentation

◆ finalize()

template<class DataPoint , class _NFilter , int DiffType, typename T >

FIT_RESULT Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::finalize ( )

inline

Finalize the procedure.

Returns: Fitting Status

Warning: Must be called be for any use of the fitting output

Definition at line 81 of file weingarten.hpp.

◆ normalDerivativeWeingartenEstimator() [1/2]

template<class DataPoint , class _NFilter , int DiffType, typename T >

NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T > & Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::normalDerivativeWeingartenEstimator ( )

inline

Explicit conversion to NormalDerivativeWeingartenEstimator , to access methods potentially hidden by heritage.

Definition at line 127 of file weingarten.h.

◆ normalDerivativeWeingartenEstimator() [2/2]

template<class DataPoint , class _NFilter , int DiffType, typename T >

const NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T > & Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::normalDerivativeWeingartenEstimator ( ) const

inline

Explicit conversion to NormalDerivativeWeingartenEstimator , to access methods potentially hidden by heritage.

Definition at line 127 of file weingarten.h.

◆ tangentPlaneToWorld()

template<class DataPoint , class _NFilter , int DiffType, typename T >

NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::VectorType Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::tangentPlaneToWorld	(	const VectorType &	_q,
		bool	_isPositionVector = `true`
	)		const

inline

Transform a point from the tangent plane [h, u, v]^T to ambient space.

Parameters

_q	Vector expressed in local tangent frame
_isPositionVector	Indicate if the input vector `_q` is a position that is influenced by translations (e.g., in contrast to displacement or normal vectors)

Returns: Vector expressed in ambient space

Definition at line 157 of file weingarten.hpp.

◆ weingartenMap() [1/2]

template<class DataPoint , class _NFilter , int DiffType, typename T >

NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::Matrix2 Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::weingartenMap ( ) const

inline

Returns the Weingarten Map.

Returns: Weingarten Map

See also: weingartenMap(Matrix2& w) for an in-place version

Definition at line 73 of file weingarten.hpp.

◆ weingartenMap() [2/2]

template<class DataPoint , class _NFilter , int DiffType, typename T >

template<typename Matrix2Derived >

void Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::weingartenMap ( Matrix2Derived & w ) const

inline

Returns the Weingarten Map.

Template Parameters

Matrix2Derived Input matrix type that must have same interface than Matrix2

Definition at line 115 of file weingarten.hpp.

◆ worldToTangentPlane()

template<class DataPoint , class _NFilter , int DiffType, typename T >

NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::VectorType Ponca::NormalDerivativeWeingartenEstimator< DataPoint, _NFilter, DiffType, T >::worldToTangentPlane	(	const VectorType &	_q,
		bool	_isPositionVector = `true`
	)		const

inline

Express a point in ambient space relatively to the tangent plane.

Output vector is: [h, u, v]^T, where u, v are 2d coordinates on the plane, and h the height of the sample.

Parameters

_q	Vector expressed in ambient space
_isPositionVector	Indicate if the input vector `_q` is a position that is influenced by translations (e.g., in contrast to displacement or normal vectors)

Returns: Vector expressed in local tangent frame

Definition at line 149 of file weingarten.hpp.

Public Types

Public Member Functions

Protected Types

Detailed Description

Member Typedef Documentation

◆ Base

◆ Matrix2

◆ MatrixType

◆ NeighborFilter

◆ Scalar

◆ ScalarArray

◆ VectorArray

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Member Function Documentation

◆ finalize()

◆ normalDerivativeWeingartenEstimator() [1/2]

◆ normalDerivativeWeingartenEstimator() [2/2]

◆ tangentPlaneToWorld()

◆ weingartenMap() [1/2]

◆ weingartenMap() [2/2]

◆ worldToTangentPlane()