This class contains some stand-alone CorrectedNormalCurrent formulas for triangles, using eigen as linear algebra backend. More...

#include <cncFormulaEigen.h>

Collaboration diagram for Ponca::internal::CNCEigen< DataPoint >:

Classes
struct	SphericalTriangle
	Represents a triangle on a sphere of radius one. More...

Public Types
using	MatrixType = typename DataPoint::MatrixType
using	Scalar = typename DataPoint::Scalar
using	VectorType = typename DataPoint::VectorType

Static Public Member Functions
Functions for computing measures
static Scalar	mu0InterpolatedU (const VectorType &a, const VectorType &b, const VectorType &c, const VectorType &ua, const VectorType &ub, const VectorType &uc, bool unit_u=false)
	Computes mu0 measure (area) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.
static Scalar	mu1InterpolatedU (const VectorType &a, const VectorType &b, const VectorType &c, const VectorType &ua, const VectorType &ub, const VectorType &uc, bool unit_u=false)
	Computes mu1 measure (mean curvature) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.
static Scalar	mu2InterpolatedU (const VectorType &a, const VectorType &b, const VectorType &c, const VectorType &ua, const VectorType &ub, const VectorType &uc, bool unit_u=false)
	Computes mu2 measure (Gaussian curvature) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.
static MatrixType	muXYInterpolatedU (const VectorType &a, const VectorType &b, const VectorType &c, const VectorType &ua, const VectorType &ub, const VectorType &uc, bool unit_u=false)
	Computes muXY measure (anisotropic curvature) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.
Helper functions
static std::pair< VectorType, VectorType >	curvDirFromTensor (const MatrixType &tensor, const Scalar area, const VectorType &N)
	Computing principal curvatures k1 and k2 from tensor.
static std::tuple< Scalar, Scalar, VectorType, VectorType >	curvaturesFromTensor (const MatrixType &tensor, const Scalar area, const VectorType &N)
	Computing principal curvatures k1 and k2 from tensor.

Static Public Attributes
static constexpr Scalar	epsilon = Eigen::NumTraits<Scalar>::epsilon()
	Small constant used to approximate zero.

Detailed Description

template<typename DataPoint>
struct Ponca::internal::CNCEigen< DataPoint >

This class contains some stand-alone CorrectedNormalCurrent formulas for triangles, using eigen as linear algebra backend.

Definition at line 75 of file cncFormulaEigen.h.

Member Typedef Documentation

◆ MatrixType

template<typename DataPoint>

using Ponca::internal::CNCEigen< DataPoint >::MatrixType = typename DataPoint::MatrixType

Definition at line 77 of file cncFormulaEigen.h.

◆ Scalar

template<typename DataPoint>

using Ponca::internal::CNCEigen< DataPoint >::Scalar = typename DataPoint::Scalar

Definition at line 78 of file cncFormulaEigen.h.

◆ VectorType

template<typename DataPoint>

using Ponca::internal::CNCEigen< DataPoint >::VectorType = typename DataPoint::VectorType

Definition at line 79 of file cncFormulaEigen.h.

Member Function Documentation

◆ curvaturesFromTensor()

template<typename DataPoint>

std::tuple< Scalar, Scalar, VectorType, VectorType > Ponca::internal::CNCEigen< DataPoint >::curvaturesFromTensor	(	const MatrixType &	tensor,
		const Scalar	area,
		const VectorType &	N )

inlinestatic

Computing principal curvatures k1 and k2 from tensor.

Parameters

tensor	The muXY integrated tensor
area	Area of the face
N	the normal vector

Returns: a pair of principal directions.

Definition at line 326 of file cncFormulaEigen.h.

◆ curvDirFromTensor()

template<typename DataPoint>

std::pair< VectorType, VectorType > Ponca::internal::CNCEigen< DataPoint >::curvDirFromTensor	(	const MatrixType &	tensor,
		const Scalar	area,
		const VectorType &	N )

inlinestatic

Computing principal curvatures k1 and k2 from tensor.

Parameters

tensor	The muXY integrated tensor
area	Area of the face
N	the normal vector

Returns: a pair of principal directions.

Definition at line 295 of file cncFormulaEigen.h.

◆ mu0InterpolatedU()

template<typename DataPoint>

Scalar Ponca::internal::CNCEigen< DataPoint >::mu0InterpolatedU	(	const VectorType &	a,
		const VectorType &	b,
		const VectorType &	c,
		const VectorType &	ua,
		const VectorType &	ub,
		const VectorType &	uc,
		bool	unit_u = false )

inlinestatic

Computes mu0 measure (area) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.

Parameters

a	any point
b	any point
c	any point
ua	the corrected normal vector at point a
ub	the corrected normal vector at point b
uc	the corrected normal vector at point c
unit_u	when 'true' considers that interpolated corrected normals should be made unitary, otherwise interpolated corrected normals may have smaller norms.

Returns: the mu0-measure of triangle abc, i.e. its area.

Definition at line 184 of file cncFormulaEigen.h.

◆ mu1InterpolatedU()

template<typename DataPoint>

Scalar Ponca::internal::CNCEigen< DataPoint >::mu1InterpolatedU	(	const VectorType &	a,
		const VectorType &	b,
		const VectorType &	c,
		const VectorType &	ua,
		const VectorType &	ub,
		const VectorType &	uc,
		bool	unit_u = false )

inlinestatic

Computes mu1 measure (mean curvature) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.

Parameters

a	any point
b	any point
c	any point
ua	the corrected normal vector at point a
ub	the corrected normal vector at point b
uc	the corrected normal vector at point c
unit_u	when 'true' considers that interpolated corrected normals should be made unitary, otherwise interpolated corrected normals may have smaller norms.

Returns: the mu1-measure of triangle abc, i.e. its mean curvature.

Definition at line 211 of file cncFormulaEigen.h.

◆ mu2InterpolatedU()

template<typename DataPoint>

Scalar Ponca::internal::CNCEigen< DataPoint >::mu2InterpolatedU	(	const VectorType &	a,
		const VectorType &	b,
		const VectorType &	c,
		const VectorType &	ua,
		const VectorType &	ub,
		const VectorType &	uc,
		bool	unit_u = false )

inlinestatic

Computes mu2 measure (Gaussian curvature) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.

Parameters

a	any point
b	any point
c	any point
ua	the corrected normal vector at point a
ub	the corrected normal vector at point b
uc	the corrected normal vector at point c
unit_u	when 'true' considers that interpolated corrected normals should be made unitary, otherwise interpolated corrected normals may have smaller norms.

Returns: the mu2-measure of triangle abc, i.e. its Gaussian curvature.

Definition at line 234 of file cncFormulaEigen.h.

◆ muXYInterpolatedU()

template<typename DataPoint>

MatrixType Ponca::internal::CNCEigen< DataPoint >::muXYInterpolatedU	(	const VectorType &	a,
		const VectorType &	b,
		const VectorType &	c,
		const VectorType &	ua,
		const VectorType &	ub,
		const VectorType &	uc,
		bool	unit_u = false )

inlinestatic

Computes muXY measure (anisotropic curvature) of triangle abc given an interpolated corrected normal vector ua, \ub , uc.

Parameters

a	any point
b	any point
c	any point
ua	the corrected normal vector at point a
ub	the corrected normal vector at point b
uc	the corrected normal vector at point c

Returns: the muXY-measure of triangle abc, i.e. its anisotropic curvature.

Definition at line 256 of file cncFormulaEigen.h.

Member Data Documentation

◆ epsilon

template<typename DataPoint>

Scalar Ponca::internal::CNCEigen< DataPoint >::epsilon = Eigen::NumTraits<Scalar>::epsilon()

staticconstexpr

Small constant used to approximate zero.

Definition at line 81 of file cncFormulaEigen.h.

Classes

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ MatrixType

◆ Scalar

◆ VectorType

Member Function Documentation

◆ curvaturesFromTensor()

◆ curvDirFromTensor()

◆ mu0InterpolatedU()

◆ mu1InterpolatedU()

◆ mu2InterpolatedU()

◆ muXYInterpolatedU()

Member Data Documentation

◆ epsilon