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

#include <weingarten.h>

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

Collaboration diagram for Ponca::WeingartenCurvatureEstimatorDer< 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	ScalarArray = typename Base::ScalarArray
	Alias to scalar derivatives array.

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

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

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

Public Member Functions inherited from Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >
FIT_RESULT	finalize ()
	Finalize the procedure.

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

Protected Types inherited from Ponca::internal::WeingartenCurvatureEstimatorBase< DataPoint, _NFilter, T >
enum	{ Check }

using	Base = T
	Base class of the procedure.

Detailed Description

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

PROVIDES_TANGENT_PLANE_BASIS, PROVIDES_WEINGARTEN_MAP, PROVIDES_PRINCIPAL_CURVATURES

Definition at line 198 of file weingarten.h.