Extension performing derivation of the mls surface. More...

#include <mlsSphereFitDer.h>

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

Collaboration diagram for Ponca::MlsSphereFitDer< 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.

typedef Eigen::Matrix< Scalar, DerDim, DerDim >	Matrix
	Static squared matrix of scalars with a size adapted to the differentiation type.

typedef Eigen::Matrix< Scalar, DerDim, Dim *DerDim >	MatrixArray
	Static matrix of scalars with a size adapted to the differentiation type and the dimension of the ambient space.

Public Member Functions
MlsSphereFitDer< DataPoint, _NFilter, DiffType, T > &	mlsSphereFitDer ()
	Explicit conversion to MlsSphereFitDer , to access methods potentially hidden by heritage.

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

void	init ()
	Set the evaluation position and reset the internal states.

bool	addLocalNeighbor (Scalar w, const VectorType &localQ, const DataPoint &attributes, ScalarArray &dw)
	Add a neighbor to perform the fit.

FIT_RESULT	finalize ()
	Finalize the procedure.

ScalarArray	dPotential () const
	Returns the derivatives of the scalar field at the evaluation point.

VectorType	primitiveGradient () const
	Value of the normal of the primitive at the evaluation point.

VectorArray	dNormal () const
	Returns the second derivatives of the scalar field at the evaluation point.

Public Attributes
Matrix	m_d2Uc
	Second derivative of the hyper-sphere constant term

Matrix	m_d2Uq
	Second derivative of the hyper-sphere quadratic term.

MatrixArray	m_d2Ul
	Second derivative of the hyper-sphere linear term

Protected Types
enum	{ Check = Base::PROVIDES_PRIMITIVE_DERIVATIVE & Base::PROVIDES_ALGEBRAIC_SPHERE_DERIVATIVE , PROVIDES_NORMAL_DERIVATIVE }

enum	{ Dim = DataPoint::Dim , DerDim = Base::NbDerivatives }

using	Base = T
	Base class of the procedure.

Protected Attributes
Matrix	m_d2SumDotPN
	Sum of the dot product between relative positions and normals with second-order weight derivatives.

Matrix	m_d2SumDotPP
	Sum of the squared relative positions with second-order weight derivatives.

Matrix	m_d2SumW
	Sum of queries weight with second-order weight derivatives.

MatrixArray	m_d2SumP
	Sum of relative positions with second-order weight derivatives.

MatrixArray	m_d2SumN
	Sum of normal vectors with second-order weight derivatives.

Detailed Description

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

Extension performing derivation of the mls surface.

The differentiation is determined by a previous basket elements that must provides first order derivatives of the algebraic sphere parameters.

Definition at line 24 of file mlsSphereFitDer.h.

Member Typedef Documentation

◆ Base

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::Base = T

protected

Base class of the procedure.

Definition at line 26 of file mlsSphereFitDer.h.

◆ Matrix

template<class DataPoint , class _NFilter , int DiffType, typename T >

typedef Eigen::Matrix< Scalar, DerDim, DerDim > Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::Matrix

Static squared matrix of scalars with a size adapted to the differentiation type.

The size is adapted to the differentiation type (scale and/or space) only. Such Matrix is typically used to represent Hessian matrix of multivariate single-valued functions such as \( u_c \) and \( u_q \) of an AlgebraicSphere obtained from a fitting procedure.

Definition at line 54 of file mlsSphereFitDer.h.

◆ MatrixArray

template<class DataPoint , class _NFilter , int DiffType, typename T >

typedef Eigen::Matrix< Scalar, DerDim, Dim*DerDim > Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::MatrixArray

Static matrix of scalars with a size adapted to the differentiation type and the dimension of the ambient space.

The size is adapted to the differentiation type (scale and/or space) and the dimension of the ambient space. Such Matrix is typically used to represent Hessian matrices of multivariate multi-valued functions such as \( u_l \) of an AlgebraicSphere obtained from a fitting procedure.

A MatrixArray is an array of Matrix (that mimics a 3D matrix) where the number of Matrix is equal to the dimension of the ambient space. The i-th Matrix can be accessed by the following block operation:

MatrixArray a;
int i;
//...
Matrix m_i = a.template block<DerDim, DerDim>(0, i*DerDim);

Definition at line 75 of file mlsSphereFitDer.h.

◆ NeighborFilter

template<class DataPoint , class _NFilter , int DiffType, typename T >

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

Alias to the filter applied on the neighbors.

Definition at line 26 of file mlsSphereFitDer.h.

◆ Scalar

template<class DataPoint , class _NFilter , int DiffType, typename T >

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

Alias to scalar type.

Definition at line 26 of file mlsSphereFitDer.h.

◆ ScalarArray

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::ScalarArray = typename Base::ScalarArray

Alias to scalar derivatives array.

Definition at line 27 of file mlsSphereFitDer.h.

◆ VectorArray

template<class DataPoint , class _NFilter , int DiffType, typename T >

using Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::VectorArray = typename Base::VectorArray

Alias to vector derivatives array.

Definition at line 27 of file mlsSphereFitDer.h.

◆ VectorType

template<class DataPoint , class _NFilter , int DiffType, typename T >

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

Alias to vector type.

Definition at line 26 of file mlsSphereFitDer.h.

Member Enumeration Documentation

◆ anonymous enum

template<class DataPoint , class _NFilter , int DiffType, typename T >

anonymous enum

protected

Definition at line 30 of file mlsSphereFitDer.h.

◆ anonymous enum

template<class DataPoint , class _NFilter , int DiffType, typename T >

anonymous enum

protected

Enumerator
Dim	Dimension of the ambient space.
DerDim	Number of dimensions used for the differentiation.

Definition at line 36 of file mlsSphereFitDer.h.

Member Function Documentation

◆ addLocalNeighbor()

template<class DataPoint , class _NFilter , int DiffType, typename T >

bool MlsSphereFitDer::addLocalNeighbor	(	Scalar	w,
		const VectorType &	localQ,
		const DataPoint &	attributes,
		ScalarArray &	dw
	)

inline

Add a neighbor to perform the fit.

Returns: false if param nei is not a valid neighbour (weight = 0)

Definition at line 28 of file mlsSphereFitDer.hpp.

◆ dNormal()

template<class DataPoint , class _NFilter , int DiffType, typename T >

MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::VectorArray MlsSphereFitDer::dNormal ( ) const

inline

Returns the second derivatives of the scalar field at the evaluation point.

Definition at line 185 of file mlsSphereFitDer.hpp.

◆ dPotential()

template<class DataPoint , class _NFilter , int DiffType, typename T >

MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::ScalarArray MlsSphereFitDer::dPotential ( ) const

inline

Returns the derivatives of the scalar field at the evaluation point.

See also: method #isSigned of the fit to check if the sign is reliable

Definition at line 160 of file mlsSphereFitDer.hpp.

◆ finalize()

template<class DataPoint , class _NFilter , int DiffType, typename T >

FIT_RESULT MlsSphereFitDer::finalize ( )

inline

Finalize the procedure.

Returns: Fitting Status

Warning: Must be called be for any use of the fitting output

Definition at line 66 of file mlsSphereFitDer.hpp.

◆ init()

template<class DataPoint , class _NFilter , int DiffType, typename T >

void MlsSphereFitDer::init ( )

inline

Set the evaluation position and reset the internal states.

Warning: Must be called be for any computation (but after #setNeighborFilter)

Definition at line 10 of file mlsSphereFitDer.hpp.

◆ mlsSphereFitDer() [1/2]

template<class DataPoint , class _NFilter , int DiffType, typename T >

MlsSphereFitDer< DataPoint, _NFilter, DiffType, T > & Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::mlsSphereFitDer ( )

inline

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

Definition at line 93 of file mlsSphereFitDer.h.

◆ mlsSphereFitDer() [2/2]

template<class DataPoint , class _NFilter , int DiffType, typename T >

const MlsSphereFitDer< DataPoint, _NFilter, DiffType, T > & Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::mlsSphereFitDer ( ) const

inline

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

Definition at line 93 of file mlsSphereFitDer.h.

◆ primitiveGradient()

template<class DataPoint , class _NFilter , int DiffType, typename T >

MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::VectorType MlsSphereFitDer::primitiveGradient ( ) const

inline

Value of the normal of the primitive at the evaluation point.

Definition at line 176 of file mlsSphereFitDer.hpp.

Member Data Documentation

◆ m_d2SumDotPN

template<class DataPoint , class _NFilter , int DiffType, typename T >

Matrix Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2SumDotPN

protected

Sum of the dot product between relative positions and normals with second-order weight derivatives.

Definition at line 79 of file mlsSphereFitDer.h.

◆ m_d2SumDotPP

template<class DataPoint , class _NFilter , int DiffType, typename T >

Matrix Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2SumDotPP

protected

Sum of the squared relative positions with second-order weight derivatives.

Definition at line 80 of file mlsSphereFitDer.h.

◆ m_d2SumN

template<class DataPoint , class _NFilter , int DiffType, typename T >

MatrixArray Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2SumN

protected

Sum of normal vectors with second-order weight derivatives.

Definition at line 84 of file mlsSphereFitDer.h.

◆ m_d2SumP

template<class DataPoint , class _NFilter , int DiffType, typename T >

MatrixArray Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2SumP

protected

Sum of relative positions with second-order weight derivatives.

Definition at line 83 of file mlsSphereFitDer.h.

◆ m_d2SumW

template<class DataPoint , class _NFilter , int DiffType, typename T >

Matrix Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2SumW

protected

Sum of queries weight with second-order weight derivatives.

Definition at line 81 of file mlsSphereFitDer.h.

◆ m_d2Uc

template<class DataPoint , class _NFilter , int DiffType, typename T >

Matrix Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2Uc

Second derivative of the hyper-sphere constant term

Definition at line 88 of file mlsSphereFitDer.h.

◆ m_d2Ul

template<class DataPoint , class _NFilter , int DiffType, typename T >

MatrixArray Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2Ul

Second derivative of the hyper-sphere linear term

Definition at line 90 of file mlsSphereFitDer.h.

◆ m_d2Uq

template<class DataPoint , class _NFilter , int DiffType, typename T >

Matrix Ponca::MlsSphereFitDer< DataPoint, _NFilter, DiffType, T >::m_d2Uq

Second derivative of the hyper-sphere quadratic term.

Definition at line 89 of file mlsSphereFitDer.h.

Public Types

Public Member Functions

Public Attributes

Protected Types

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ Matrix

◆ MatrixArray

◆ NeighborFilter

◆ Scalar

◆ ScalarArray

◆ VectorArray

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Member Function Documentation

◆ addLocalNeighbor()

◆ dNormal()

◆ dPotential()

◆ finalize()

◆ init()

◆ mlsSphereFitDer() [1/2]

◆ mlsSphereFitDer() [2/2]

◆ primitiveGradient()

Member Data Documentation

◆ m_d2SumDotPN

◆ m_d2SumDotPP

◆ m_d2SumN

◆ m_d2SumP

◆ m_d2SumW

◆ m_d2Uc

◆ m_d2Ul

◆ m_d2Uq