Ponca::SphereFitImpl< DataPoint, _WFunctor, T > Class Template Reference

Algebraic Sphere fitting procedure on point set without normals. More...

#include <sphereFit.h>

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

Collaboration diagram for Ponca::SphereFitImpl< 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< MatrixA >

Public Member Functions
SphereFitImpl< DataPoint, _WFunctor, T > &	sphereFit ()
	Explicit conversion to SphereFitImpl , to access methods potentially hidden by heritage.
const SphereFitImpl< DataPoint, _WFunctor, T > &	sphereFit () const
	Explicit conversion to SphereFitImpl , 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.
const Solver &	solver () const

Protected Types
enum	{ Check = Base::PROVIDES_ALGEBRAIC_SPHERE }
using	Base = T
	Base class of the procedure.
typedef Eigen::Matrix< Scalar, DataPoint::Dim+2, 1 >	VectorA
typedef Eigen::Matrix< Scalar, DataPoint::Dim+2, DataPoint::Dim+2 >	MatrixA

Protected Attributes
MatrixA	m_matA {MatrixA::Zero()}
	Covariance matrix of [1, p, p^2].
Solver	m_solver

Detailed Description

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

Algebraic Sphere fitting procedure on point set without normals.

This method published in [6] minimizes

\[ \mathcal{L}(\mathbf{u}) = \frac{1}{2} \sum_i w_i f_{\mathbf{u}}(\mathbf{x}_i)^2 = \frac{1}{2} \mathbf{u}^T A \mathbf{u} \]

with \( A = \sum_i w_i \tilde{\mathbf{x}_i} \tilde{\mathbf{x}_i}^T\) and \( f_{\mathbf{u}} \) the algebraic sphere defined by

\[ f_{\mathbf{u}}(\mathbf{x}) = u_c + \mathbf{u}_l.\mathbf{x} + u_q \mathbf{x}.\mathbf{x} = \begin{bmatrix} 1 & \mathbf{x}^T & \mathbf{x}.\mathbf{x} \end{bmatrix} \begin{bmatrix} u_c \\ u_l \\ u_q \end{bmatrix} = \tilde{\mathbf{x}}^T \mathbf{u}, \]

under the constraint (unitary gradient onto the surface)

\[ \|\mathbf{u}_l\|^2 - 4 u_c u_q = \mathbf{u}^T C \mathbf{u} = 1 \]

where

\[ C = \begin{bmatrix} 0 & & & & -2 \\ & 1 & & & \\ & & \ddots & & \\ & & & 1 & \\ -2 & & & & 0 \end{bmatrix} \]

which amounts to solve the generalized eigenvalue problem \( A\mathbf{u} = \lambda C \mathbf{u} \).

See also

AlgebraicSphere

Definition at line 56 of file sphereFit.h.

Member Typedef Documentation

Base

template<class DataPoint , class _WFunctor , typename T >

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

protected

Base class of the procedure.

Definition at line 58 of file sphereFit.h.

MatrixA

template<class DataPoint , class _WFunctor , typename T >

typedef Eigen::Matrix<Scalar, DataPoint::Dim+2, DataPoint::Dim+2> Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::MatrixA

protected

Definition at line 67 of file sphereFit.h.

Scalar

template<class DataPoint , class _WFunctor , typename T >

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

Alias to scalar type.

Definition at line 58 of file sphereFit.h.

Solver

template<class DataPoint , class _WFunctor , typename T >

using Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::Solver = Eigen::EigenSolver<MatrixA>

Definition at line 70 of file sphereFit.h.

VectorA

template<class DataPoint , class _WFunctor , typename T >

typedef Eigen::Matrix<Scalar, DataPoint::Dim+2, 1> Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::VectorA

protected

Definition at line 66 of file sphereFit.h.

VectorType

template<class DataPoint , class _WFunctor , typename T >

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

Alias to vector type.

Definition at line 58 of file sphereFit.h.

WFunctor

template<class DataPoint , class _WFunctor , typename T >

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

Alias to weight function.

Definition at line 58 of file sphereFit.h.

Member Enumeration Documentation

anonymous enum

template<class DataPoint , class _WFunctor , typename T >

anonymous enum

protected

Definition at line 61 of file sphereFit.h.

Member Function Documentation

addLocalNeighbor()

template<class DataPoint , class _WFunctor , typename T >

bool SphereFitImpl::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 18 of file sphereFit.hpp.

finalize()

template<class DataPoint , class _WFunctor , typename T >

FIT_RESULT SphereFitImpl::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 sphereFit.hpp.

init()

template<class DataPoint , class _WFunctor , typename T >

void SphereFitImpl::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 10 of file sphereFit.hpp.

isSigned()

template<class DataPoint , class _WFunctor , typename T >

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

inlineconstexpr

Is scalar field signed.

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

Definition at line 81 of file sphereFit.h.

solver()

template<class DataPoint , class _WFunctor , typename T >

const Solver & Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::solver ( ) const

inline

Definition at line 83 of file sphereFit.h.

sphereFit() [1/2]

template<class DataPoint , class _WFunctor , typename T >

SphereFitImpl< DataPoint, _WFunctor, T > & Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::sphereFit ( )

inline

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

Definition at line 79 of file sphereFit.h.

sphereFit() [2/2]

template<class DataPoint , class _WFunctor , typename T >

const SphereFitImpl< DataPoint, _WFunctor, T > & Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::sphereFit ( ) const

inline

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

Definition at line 79 of file sphereFit.h.

Member Data Documentation

m_matA

template<class DataPoint , class _WFunctor , typename T >

MatrixA Ponca::SphereFitImpl< DataPoint, _WFunctor, T >::m_matA {MatrixA::Zero()}

protected

Covariance matrix of [1, p, p^2].

Definition at line 74 of file sphereFit.h.

m_solver

template<class DataPoint , class _WFunctor , typename T >

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

protected

Definition at line 76 of file sphereFit.h.