Compute a Weingarten map from fundamental forms. More...

#include <weingarten.h>

Inheritance diagram for Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >:

Collaboration diagram for Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, 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	Matrix2 = Eigen::Matrix< Scalar, 2, 2 >

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

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

Matrix2	firstFundamentalForm () const
	Assembles and returns the first fundamental form from the base class.

template<typename Matrix2Derived >
void	firstFundamentalForm (Matrix2Derived &first) const
	Assembles and returns the first fundamental form from the base class.

Matrix2	secondFundamentalForm () const
	Assembles and returns the second fundamental form from the base class.

template<typename Matrix2Derived >
void	secondFundamentalForm (Matrix2Derived &second) const
	Assembles and returns the second fundamental form from the base class.

Matrix2	weingartenMap () const
	Returns the Weingarten Map.

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

Scalar	kMean () const
	Returns an estimate of the mean curvature directly from the fundamental forms.

Scalar	GaussianCurvature () const
	Returns an estimate of the Gaussian curvature directly from the fundamental forms.

Protected Types
enum	{ Check , PROVIDES_WEINGARTEN_MAP }

using	Base = T
	Base class of the procedure.

Detailed Description

template<class DataPoint, class _NFilter, typename T>
class Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >

Compute a Weingarten map from fundamental forms.

The Weingarten map, also called Shape Operator, is defined in its matrix form as

\[ \text{W} = \text{F}_\text{I}^{-1}\text{F}_\text{II}, \]

with \(\text{F}_\text{I}, \text{F}_\text{II}\) the first and second fundamental forms, respectively.

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

This class also provides mean and Gaussian curvature directly from the fundamental forms.

This primitive provides:

PROVIDES_WEINGARTEN_MAP

This primitive requires:

PROVIDES_FIRST_FUNDAMENTAL_FORM_COMPONENTS, PROVIDES_SECOND_FUNDAMENTAL_FORM_COMPONENTS

Definition at line 33 of file weingarten.h.

Member Typedef Documentation

◆ Base

template<class DataPoint , class _NFilter , typename T >

using Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::Base = T

protected

Base class of the procedure.

Definition at line 35 of file weingarten.h.

◆ Matrix2

template<class DataPoint , class _NFilter , typename T >

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

Definition at line 36 of file weingarten.h.

◆ NeighborFilter

template<class DataPoint , class _NFilter , typename T >

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

Alias to the filter applied on the neighbors.

Definition at line 35 of file weingarten.h.

◆ Scalar

template<class DataPoint , class _NFilter , typename T >

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

Alias to scalar type.

Definition at line 35 of file weingarten.h.

◆ VectorType

template<class DataPoint , class _NFilter , typename T >

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

Alias to vector type.

Definition at line 35 of file weingarten.h.

Member Enumeration Documentation

◆ anonymous enum

template<class DataPoint , class _NFilter , typename T >

anonymous enum

protected

Definition at line 40 of file weingarten.h.

Member Function Documentation

◆ firstFundamentalForm() [1/2]

template<class DataPoint , class _NFilter , typename T >

FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::Matrix2 Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::firstFundamentalForm ( ) const

inline

Assembles and returns the first fundamental form from the base class.

Returns: first fundamental form

See also: firstFundamentalForm(Matrix2& first) for an in-place version

Definition at line 9 of file weingarten.hpp.

◆ firstFundamentalForm() [2/2]

template<class DataPoint , class _NFilter , typename T >

template<typename Matrix2Derived >

void Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::firstFundamentalForm ( Matrix2Derived & first ) const

inline

Assembles and returns the first fundamental form from the base class.

Template Parameters

Matrix2Derived Input matrix type that must have same interface than Matrix2

Definition at line 17 of file weingarten.hpp.

◆ fundamentalFormWeingartenEstimator() [1/2]

template<class DataPoint , class _NFilter , typename T >

FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > & Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::fundamentalFormWeingartenEstimator ( )

inline

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

Definition at line 46 of file weingarten.h.

◆ fundamentalFormWeingartenEstimator() [2/2]

template<class DataPoint , class _NFilter , typename T >

const FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > & Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::fundamentalFormWeingartenEstimator ( ) const

inline

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

Definition at line 46 of file weingarten.h.

◆ GaussianCurvature()

template<class DataPoint , class _NFilter , typename T >

FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::Scalar Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::GaussianCurvature ( ) const

inline

Returns an estimate of the Gaussian curvature directly from the fundamental forms.

Definition at line 63 of file weingarten.hpp.

◆ kMean()

template<class DataPoint , class _NFilter , typename T >

FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::Scalar Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::kMean ( ) const

inline

Returns an estimate of the mean curvature directly from the fundamental forms.

Definition at line 54 of file weingarten.hpp.

◆ secondFundamentalForm() [1/2]

template<class DataPoint , class _NFilter , typename T >

FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::Matrix2 Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::secondFundamentalForm ( ) const

inline

Assembles and returns the second fundamental form from the base class.

Returns: second fundamental form

See also: secondFundamentalForm(Matrix2& second) for an in-place version

Definition at line 24 of file weingarten.hpp.

◆ secondFundamentalForm() [2/2]

template<class DataPoint , class _NFilter , typename T >

template<typename Matrix2Derived >

void Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T >::secondFundamentalForm ( Matrix2Derived & second ) const

inline

Assembles and returns the second fundamental form from the base class.

Template Parameters

Matrix2Derived Input matrix type that must have same interface than Matrix2

Definition at line 32 of file weingarten.hpp.

◆ weingartenMap() [1/2]

template<class DataPoint , class _NFilter , typename T >

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

inline

Returns the Weingarten Map.

Returns: Weingarten Map

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

Definition at line 40 of file weingarten.hpp.

◆ weingartenMap() [2/2]

template<class DataPoint , class _NFilter , typename T >

template<typename Matrix2Derived >

void Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, 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 48 of file weingarten.hpp.

Public Types

Public Member Functions

Protected Types

Detailed Description

Member Typedef Documentation

◆ Base

◆ Matrix2

◆ NeighborFilter

◆ Scalar

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Member Function Documentation

◆ firstFundamentalForm() [1/2]

◆ firstFundamentalForm() [2/2]

◆ fundamentalFormWeingartenEstimator() [1/2]

◆ fundamentalFormWeingartenEstimator() [2/2]

◆ GaussianCurvature()

◆ kMean()

◆ secondFundamentalForm() [1/2]

◆ secondFundamentalForm() [2/2]

◆ weingartenMap() [1/2]

◆ weingartenMap() [2/2]