Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T > Class Template Reference

Compute principal curvatures from a base class providing fundamental forms. More...

#include <weingarten.h>

Inheritance diagram for Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >:

Collaboration diagram for Ponca::internal::WeingartenCurvatureEstimatorBase< 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
FIT_RESULT	finalize ()
Scalar	kmin () const
	Returns an estimate of the minimal principal curvature value.
Scalar	kmax () const
	Returns an estimate of the maximal principal curvature value.
VectorType	kminDirection () const
	Returns an estimate of the minimal principal curvature direction.
VectorType	kmaxDirection () const
	Returns an estimate of the maximal principal curvature direction.
Scalar	kMean () const
	Returns an estimate of the mean curvature.
Scalar	GaussianCurvature () const
	Returns an estimate of the Gaussian curvature.

Protected Types
using	Base = T
	Base class of the procedure.

Detailed Description

template<class DataPoint, class _NFilter, typename T>
requires ProvidesTangentPlaneBasis<T>&& ProvidesWeingartenMap<T>&& Is3D<DataPoint>
class Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >

Compute principal curvatures from a base class providing fundamental forms.

Since the weingarten map is self-adjoint, a basis exists consisting of the eigenvectors of W. The eigenvectors, combined with their eigenvalues, define the principal curvature directions and values. The Gaussian and mean curvatures can be retrieved as \(\text{K} = \text{det}(\text{W})\) and \(\text{H} = \frac{1}{2}\text{trace}(\text{W})\), respectively.

Warning

To map from the tangent plane to ambiant space, we assume that the patch is represented as (h(u,v), u, v) because CovariancePlaneFitImpl::worldToTangentPlane() wraps up coordinates in this order (height, u and v).

This primitive requires:

ProvidesTangentPlaneBasis, PROVIDES_WEINGARTEN_MAP, ProvidesPrincipalCurvatures 

Definition at line 167 of file weingarten.h.

Member Typedef Documentation

Base

template<class DataPoint , class _NFilter , typename T >

using Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >::Base = T

protected

Base class of the procedure.

Definition at line 169 of file weingarten.h.

Matrix2

template<class DataPoint , class _NFilter , typename T >

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

Definition at line 170 of file weingarten.h.

NeighborFilter

template<class DataPoint , class _NFilter , typename T >

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

Alias to the filter applied on the neighbors.

Definition at line 169 of file weingarten.h.

Scalar

template<class DataPoint , class _NFilter , typename T >

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

Alias to scalar type.

Definition at line 169 of file weingarten.h.

VectorType

template<class DataPoint , class _NFilter , typename T >

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

Alias to vector type.

Definition at line 169 of file weingarten.h.

Member Function Documentation

finalize()

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

FIT_RESULT Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >::finalize ( )

inline

Definition at line 194 of file weingarten.hpp.

GaussianCurvature()

template<class DataPoint , class _NFilter , typename T >

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

inline

Returns an estimate of the Gaussian curvature.

Definition at line 208 of file weingarten.h.

kmax()

template<class DataPoint , class _NFilter , typename T >

Scalar Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >::kmax ( ) const

inline

Returns an estimate of the maximal principal curvature value.

Definition at line 182 of file weingarten.h.

kmaxDirection()

template<class DataPoint , class _NFilter , typename T >

VectorType Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >::kmaxDirection ( ) const

inline

Returns an estimate of the maximal principal curvature direction.

Definition at line 195 of file weingarten.h.

kMean()

template<class DataPoint , class _NFilter , typename T >

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

inline

Returns an estimate of the mean curvature.

Definition at line 205 of file weingarten.h.

kmin()

template<class DataPoint , class _NFilter , typename T >

Scalar Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >::kmin ( ) const

inline

Returns an estimate of the minimal principal curvature value.

Definition at line 179 of file weingarten.h.

kminDirection()

template<class DataPoint , class _NFilter , typename T >

VectorType Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >::kminDirection ( ) const

inline

Returns an estimate of the minimal principal curvature direction.

Definition at line 185 of file weingarten.h.