Ponca::FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > Class Template Reference

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.
FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > &	firstFondamentalFormComponent ()
	Explicit conversion to FundamentalFormWeingartenEstimator , to access methods potentially hidden by heritage.
const FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > &	firstFondamentalFormComponent () const
	Explicit conversion to FundamentalFormWeingartenEstimator , to access methods potentially hidden by heritage.
FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > &	secondFondamentalFormComponent ()
	Explicit conversion to FundamentalFormWeingartenEstimator , to access methods potentially hidden by heritage.
const FundamentalFormWeingartenEstimator< DataPoint, _NFilter, T > &	secondFondamentalFormComponent () 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 > requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS
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 > requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS
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 > requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS
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
using	Base = T
	Base class of the procedure.

Detailed Description

template<class DataPoint, class _NFilter, typename T>
requires ProvidesFirstFondamentalFormComponents<T>&& ProvidesSecondFondamentalFormComponents<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:

ProvidesFirstFondamentalFormComponents, ProvidesSecondFondamentalFormComponents 

Definition at line 39 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 41 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 42 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 41 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 41 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 41 of file weingarten.h.

Member Function Documentation

firstFondamentalFormComponent() [1/2]

template<class DataPoint , class _NFilter , typename T >

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

inline

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

Definition at line 47 of file weingarten.h.

firstFondamentalFormComponent() [2/2]

template<class DataPoint , class _NFilter , typename T >

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

inline

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

Definition at line 47 of file weingarten.h.

firstFundamentalForm() [1/2]

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 10 of file weingarten.hpp.

firstFundamentalForm() [2/2]

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

template<typename Matrix2Derived >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 20 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 >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 77 of file weingarten.hpp.

kMean()

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 66 of file weingarten.hpp.

secondFondamentalFormComponent() [1/2]

template<class DataPoint , class _NFilter , typename T >

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

inline

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

Definition at line 48 of file weingarten.h.

secondFondamentalFormComponent() [2/2]

template<class DataPoint , class _NFilter , typename T >

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

inline

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

Definition at line 48 of file weingarten.h.

secondFundamentalForm() [1/2]

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 29 of file weingarten.hpp.

secondFundamentalForm() [2/2]

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

template<typename Matrix2Derived >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 39 of file weingarten.hpp.

weingartenMap() [1/2]

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 48 of file weingarten.hpp.

weingartenMap() [2/2]

template<class DataPoint , class _NFilter , typename T >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

template<typename Matrix2Derived >
requires FUNDAMENTAL_FORM_WEINGARTEN_ESTIMATOR_REQUIREMENTS

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 58 of file weingarten.hpp.