Ponca::WeingartenCurvatureEstimator< DataPoint, _NFilter, T > Struct Template Reference

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

#include <weingarten.h>

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

Collaboration diagram for Ponca::WeingartenCurvatureEstimator< 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.
Public Types inherited from Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >
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
WeingartenCurvatureEstimator< DataPoint, _NFilter, T > &	meanCurvature ()
	Explicit conversion to WeingartenCurvatureEstimator , to access methods potentially hidden by heritage.
const WeingartenCurvatureEstimator< DataPoint, _NFilter, T > &	meanCurvature () const
	Explicit conversion to WeingartenCurvatureEstimator , to access methods potentially hidden by heritage.
WeingartenCurvatureEstimator< DataPoint, _NFilter, T > &	curvatureTensor ()
	Explicit conversion to WeingartenCurvatureEstimator , to access methods potentially hidden by heritage.
const WeingartenCurvatureEstimator< DataPoint, _NFilter, T > &	curvatureTensor () const
	Explicit conversion to WeingartenCurvatureEstimator , to access methods potentially hidden by heritage.
Public Member Functions inherited from Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >
FIT_RESULT	finalize ()
	Finalize the procedure.
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.
Protected Types inherited from Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >
using	Base = T
	Base class of the procedure.

Detailed Description

template<class DataPoint, class _NFilter, typename T>
struct Ponca::WeingartenCurvatureEstimator< 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 214 of file weingarten.h.

Member Typedef Documentation

Base

template<class DataPoint , class _NFilter , typename T >

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

protected

Base class of the procedure.

Definition at line 216 of file weingarten.h.

NeighborFilter

template<class DataPoint , class _NFilter , typename T >

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

Alias to the filter applied on the neighbors.

Definition at line 216 of file weingarten.h.

Scalar

template<class DataPoint , class _NFilter , typename T >

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

Alias to scalar type.

Definition at line 216 of file weingarten.h.

VectorType

template<class DataPoint , class _NFilter , typename T >

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

Alias to vector type.

Definition at line 216 of file weingarten.h.

Member Function Documentation

curvatureTensor() [1/2]

template<class DataPoint , class _NFilter , typename T >

WeingartenCurvatureEstimator< DataPoint, _NFilter, T > & Ponca::WeingartenCurvatureEstimator< DataPoint, _NFilter, T >::curvatureTensor ( )

inline

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

Definition at line 218 of file weingarten.h.

curvatureTensor() [2/2]

template<class DataPoint , class _NFilter , typename T >

const WeingartenCurvatureEstimator< DataPoint, _NFilter, T > & Ponca::WeingartenCurvatureEstimator< DataPoint, _NFilter, T >::curvatureTensor ( ) const

inline

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

Definition at line 218 of file weingarten.h.

meanCurvature() [1/2]

template<class DataPoint , class _NFilter , typename T >

WeingartenCurvatureEstimator< DataPoint, _NFilter, T > & Ponca::WeingartenCurvatureEstimator< DataPoint, _NFilter, T >::meanCurvature ( )

inline

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

Definition at line 217 of file weingarten.h.

meanCurvature() [2/2]

template<class DataPoint , class _NFilter , typename T >

const WeingartenCurvatureEstimator< DataPoint, _NFilter, T > & Ponca::WeingartenCurvatureEstimator< DataPoint, _NFilter, T >::meanCurvature ( ) const

inline

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

Definition at line 217 of file weingarten.h.