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/***************************************************************************
* Copyright (c) 2020 Graeme van der Vlugt *
* *
* This file is part of the FreeCAD CAx development system. *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Library General Public *
* License as published by the Free Software Foundation; either *
* version 2 of the License, or (at your option) any later version. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; see the file COPYING.LIB. If not, *
* write to the Free Software Foundation, Inc., 59 Temple Place, *
* Suite 330, Boston, MA 02111-1307, USA *
* *
***************************************************************************/
#ifndef MESH_SPHERE_FIT_H
#define MESH_SPHERE_FIT_H
#include "Approximation.h"
#include <Eigen/Eigenvalues>
// -------------------------------------------------------------------------------
namespace MeshCoreFit
{
using Matrix4x4 = Eigen::Matrix<double, 4, 4, Eigen::RowMajor>;
/**
* Best-fit sphere for a given set of points.
*/
class MeshExport SphereFit: public MeshCore::Approximation
{
public:
/**
* Construction
*/
SphereFit();
/**
* Set approximations before calling Fit()
*/
void SetApproximations(double radius, const Base::Vector3d& center);
/**
* Set iteration convergence criteria for the fit if special values are needed.
* The default values set in the constructor are suitable for most uses
*/
void SetConvergenceCriteria(double posConvLimit, double vConvLimit, int maxIter);
/**
* Returns the radius of the fitted sphere. If Fit() has not been called then zero is returned.
*/
double GetRadius() const;
/**
* Returns the center of the fitted sphere. If Fit() has not been called the null vector is
* returned.
*/
Base::Vector3d GetCenter() const;
/**
* Returns the number of iterations that Fit() needed to converge. If Fit() has not been called
* then zero is returned.
*/
int GetNumIterations() const;
/**
* Compute approximations for the parameters using all points
*/
void ComputeApproximations();
/**
* Fit a sphere onto the given points. If the fit fails FLOAT_MAX is returned.
*/
float Fit() override;
/**
* Returns the distance from the point \a rcPoint to the fitted sphere. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetDistanceToSphere(const Base::Vector3f& rcPoint) const;
/**
* Returns the standard deviation from the points to the fitted sphere. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetStdDeviation() const;
/**
* Projects the points onto the fitted sphere.
*/
void ProjectToSphere();
protected:
/**
* Set up the normal equations
*/
void setupNormalEquationMatrices(
const std::vector<Base::Vector3d>& residuals,
Matrix4x4& atpa,
Eigen::VectorXd& atpl
) const;
/**
* Sets up contributions of given observation to the normal equation matrices.
*/
void setupObservation(
const Base::Vector3f& point,
const Base::Vector3d& residual,
double a[4],
double& f0,
double& qw,
double b[3]
) const;
/**
* Computes contribution of the given observation equation on the normal equation matrices
*/
void addObservationU(double a[4], double li, double pi, Matrix4x4& atpa, Eigen::VectorXd& atpl) const;
/**
* Set the lower part of the normal matrix equal to the upper part
*/
void setLowerPart(Matrix4x4& atpa) const;
/**
* Compute the residuals and sigma0 and check the residual convergence
*/
bool computeResiduals(
const Eigen::VectorXd& x,
std::vector<Base::Vector3d>& residuals,
double& sigma0,
double vConvLimit,
bool& vConverged
) const;
private:
Base::Vector3d _vCenter; /**< Center of sphere. */
double _dRadius {0}; /**< Radius of the sphere. */
int _numIter {0}; /**< Number of iterations for solution to converge. */
double _posConvLimit {0.0001}; /**< Position and radius parameter convergence threshold. */
double _vConvLimit {0.001}; /**< Residual convergence threshold. */
int _maxIter {50}; /**< Maximum number of iterations. */
};
} // namespace MeshCoreFit
#endif // MESH_SPHERE_FIT_H
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