Algebraic Sphere fitting procedure on point sets with non-oriented normals. More...

#include <unorientedSphereFit.h>

Inheritance diagram for Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >:

Collaboration diagram for Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >:

Public Types
using	Scalar = typename DataPoint::Scalar
	Alias to scalar type.

using	VectorType = typename Base::VectorType
	Alias to vector type.

using	WFunctor = typename Base::WFunctor
	Alias to weight function.

using	Solver = Eigen::EigenSolver< MatrixBB >

Public Member Functions
UnorientedSphereFitImpl< DataPoint, _WFunctor, T > &	unorientedSphereFit ()
	Explicit conversion to UnorientedSphereFitImpl , to access methods potentially hidden by heritage.

const UnorientedSphereFitImpl< DataPoint, _WFunctor, T > &	unorientedSphereFit () const
	Explicit conversion to UnorientedSphereFitImpl , to access methods potentially hidden by heritage.

void	init (const VectorType &_evalPos)
	Set the evaluation position and reset the internal states.

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

FIT_RESULT	finalize ()
	Finalize the procedure.

constexpr bool	isSigned ()
	Is scalar field signed.

Public Attributes
MatrixBB	m_matA {MatrixBB::Zero()}
	The accumulated covariance matrix.

MatrixBB	m_matQ {MatrixBB::Zero()}
	The constraint matrix.

Scalar	m_sumDotPP {0}
	Sum of the squared relative positions.

Solver	m_solver

Protected Types
enum	{ Check = Base::PROVIDES_ALGEBRAIC_SPHERE && Base::PROVIDES_MEAN_POSITION }

using	Base = T
	Base class of the procedure.

typedef Eigen::Matrix< Scalar, DataPoint::Dim+1, 1 >	VectorB

typedef Eigen::Matrix< Scalar, DataPoint::Dim+1, DataPoint::Dim+1 >	MatrixBB

Detailed Description

template<class DataPoint, class _WFunctor, typename T>
class Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >

Algebraic Sphere fitting procedure on point sets with non-oriented normals.

This method published in [4] maximizes the sum of squared dot product between the input normal vectors and the gradient of the algebraic sphere. The maximization is done under the constraint that the norm of the gradient is unitary on average. In practice, it amounts to solve the generalized eigenvalue problem

\[ A \mathbf{u} = \lambda Q \mathbf{u} \]

where

\[ \mathbf{u} = \begin{bmatrix} u_l \\ u_q \end{bmatrix} \]

\[ A = \sum_i w_i \begin{bmatrix} \mathbf{n}_i \\ \mathbf{n}_i^T\mathbf{p}_i \end{bmatrix}\begin{bmatrix} \mathbf{n}_i^T & \mathbf{n}_i^T\mathbf{p}_i \end{bmatrix} \]

\[ Q = \frac{1}{\sum_i w_i} \begin{bmatrix} I & \sum_i w_i \mathbf{p}_i \\ \sum_i w_i \mathbf{p}_i^T & \sum_i w_i \mathbf{p}_i^T\mathbf{p}_i \end{bmatrix} \]

The constant coefficient \(u_c\) is computed as in OrientedSphereFitImpl by minimizing the sum of squared potential evaluated at the points \(\mathbf{p}_i\). This fitting method corresponds to the case where the scalar field is \( f^* \) in the Section 3.3 of [4].

See also: class AlgebraicSphere, class OrientedSphereFit

Definition at line 45 of file unorientedSphereFit.h.

Member Typedef Documentation

◆ Base

template<class DataPoint , class _WFunctor , typename T >

using Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::Base = T

protected

Base class of the procedure.

Definition at line 47 of file unorientedSphereFit.h.

◆ MatrixBB

template<class DataPoint , class _WFunctor , typename T >

typedef Eigen::Matrix<Scalar, DataPoint::Dim+1, DataPoint::Dim+1> Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::MatrixBB

protected

Definition at line 53 of file unorientedSphereFit.h.

◆ Scalar

template<class DataPoint , class _WFunctor , typename T >

using Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::Scalar = typename DataPoint::Scalar

Alias to scalar type.

Definition at line 47 of file unorientedSphereFit.h.

◆ Solver

template<class DataPoint , class _WFunctor , typename T >

using Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::Solver = Eigen::EigenSolver<MatrixBB>

Definition at line 56 of file unorientedSphereFit.h.

◆ VectorB

template<class DataPoint , class _WFunctor , typename T >

typedef Eigen::Matrix<Scalar, DataPoint::Dim+1, 1> Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::VectorB

protected

Definition at line 52 of file unorientedSphereFit.h.

◆ VectorType

template<class DataPoint , class _WFunctor , typename T >

using Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::VectorType = typename Base::VectorType

Alias to vector type.

Definition at line 47 of file unorientedSphereFit.h.

◆ WFunctor

template<class DataPoint , class _WFunctor , typename T >

using Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::WFunctor = typename Base::WFunctor

Alias to weight function.

Definition at line 47 of file unorientedSphereFit.h.

Member Enumeration Documentation

◆ anonymous enum

template<class DataPoint , class _WFunctor , typename T >

anonymous enum

protected

Definition at line 50 of file unorientedSphereFit.h.

Member Function Documentation

◆ addLocalNeighbor()

template<class DataPoint , class _WFunctor , typename T >

bool Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::addLocalNeighbor	(	Scalar	w,
		const VectorType &	localQ,
		const DataPoint &	attributes
	)

inline

Add a neighbor to perform the fit.

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

Definition at line 22 of file unorientedSphereFit.hpp.

◆ finalize()

template<class DataPoint , class _WFunctor , typename T >

FIT_RESULT Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::finalize

inline

Finalize the procedure.

Returns: Fitting Status

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

Definition at line 41 of file unorientedSphereFit.hpp.

◆ init()

template<class DataPoint , class _WFunctor , typename T >

void Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::init ( const VectorType & _evalPos )

inline

Set the evaluation position and reset the internal states.

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

Definition at line 12 of file unorientedSphereFit.hpp.

◆ isSigned()

template<class DataPoint , class _WFunctor , typename T >

constexpr bool Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::isSigned ( )

inlineconstexpr

Is scalar field signed.

If not, the method the sign of potential() must be ignored

Definition at line 67 of file unorientedSphereFit.h.

◆ unorientedSphereFit() [1/2]

template<class DataPoint , class _WFunctor , typename T >

UnorientedSphereFitImpl< DataPoint, _WFunctor, T > & Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::unorientedSphereFit ( )

inline

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

Definition at line 65 of file unorientedSphereFit.h.

◆ unorientedSphereFit() [2/2]

template<class DataPoint , class _WFunctor , typename T >

const UnorientedSphereFitImpl< DataPoint, _WFunctor, T > & Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::unorientedSphereFit ( ) const

inline

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

Definition at line 65 of file unorientedSphereFit.h.

Member Data Documentation

◆ m_matA

template<class DataPoint , class _WFunctor , typename T >

MatrixBB Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::m_matA {MatrixBB::Zero()}

The accumulated covariance matrix.

Definition at line 58 of file unorientedSphereFit.h.

◆ m_matQ

template<class DataPoint , class _WFunctor , typename T >

MatrixBB Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::m_matQ {MatrixBB::Zero()}

The constraint matrix.

Definition at line 59 of file unorientedSphereFit.h.

◆ m_solver

template<class DataPoint , class _WFunctor , typename T >

Solver Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::m_solver

Definition at line 62 of file unorientedSphereFit.h.

◆ m_sumDotPP

template<class DataPoint , class _WFunctor , typename T >

Scalar Ponca::UnorientedSphereFitImpl< DataPoint, _WFunctor, T >::m_sumDotPP {0}

Sum of the squared relative positions.

Definition at line 60 of file unorientedSphereFit.h.

Public Types

Public Member Functions

Public Attributes

Protected Types

Detailed Description

Member Typedef Documentation

◆ Base

◆ MatrixBB

◆ Scalar

◆ Solver

◆ VectorB

◆ VectorType

◆ WFunctor

Member Enumeration Documentation

◆ anonymous enum

Member Function Documentation

◆ addLocalNeighbor()

◆ finalize()

◆ init()

◆ isSigned()

◆ unorientedSphereFit() [1/2]

◆ unorientedSphereFit() [2/2]

Member Data Documentation

◆ m_matA

◆ m_matQ

◆ m_solver

◆ m_sumDotPP