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/***************************************************************************
* Copyright (c) 2008 Werner Mayer <wmayer[at]users.sourceforge.net> *
* *
* 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 REEN_APPROXSURFACE_H
#define REEN_APPROXSURFACE_H
#include <Geom_BSplineSurface.hxx>
#include <TColStd_Array1OfInteger.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <TColgp_Array2OfPnt.hxx>
#include <math_Matrix.hxx>
#include <Base/Vector3D.h>
#include <Mod/ReverseEngineering/ReverseEngineeringGlobal.h>
namespace Base
{
class SequencerLauncher;
}
// TODO: Replace OCC stuff with ublas & co
namespace Reen
{
class ReenExport SplineBasisfunction
{
public:
enum ValueT
{
Zero = 0,
Full,
Other
};
/**
* Constructor
* @param iSize Length of Knots vector
*/
explicit SplineBasisfunction(int iSize);
/**
* Constructor
* @param vKnots Knot vector
* @param iOrder Order (degree + 1) of the basic polynomial
*/
explicit SplineBasisfunction(TColStd_Array1OfReal& vKnots, int iOrder = 1);
/**
* Constructor
* @param vKnots Knot vector of shape (value)
* @param vMults Knot vector of shape (multiplicity)
* @param iSize Length of the knot vector
* The arrays @a vKnots and @a vMults have to be of the same size
* and the sum of the values in @a vMults has to be identical to @a iSize.
* @param iOrder Order (degree + 1) of the basic polynomial
*/
SplineBasisfunction(
TColStd_Array1OfReal& vKnots,
TColStd_Array1OfInteger& vMults,
int iSize,
int iOrder = 1
);
virtual ~SplineBasisfunction();
/**
* Indicates whether the function value Nik(t) at the point fParam
* results in 0, 1 or a value in between.
* This serves to speed up the calculation under certain circumstances.
*
* @param iIndex Index
* @param fParam Parameter value
* @return ValueT
*/
virtual ValueT LocalSupport(int iIndex, double fParam) = 0;
/**
* Calculates the function value Nik(t) at the point fParam
* (from: Piegl/Tiller 96 The NURBS-Book)
*
* @param iIndex Index
* @param fParam Parameter value
* @return Function value Nik(t)
*/
virtual double BasisFunction(int iIndex, double fParam) = 0;
/**
* Calculates the function values of the first iMaxDer derivatives on the
* fParam position (from: Piegl/Tiller 96 The NURBS-Book)
*
* @param iIndex Index
* @param iMaxDer max. derivative
* @param fParam Parameter value.
* @return Derivative list of function values
*
* The list must be sufficiently long for iMaxDer+1 elements.
*/
virtual void DerivativesOfBasisFunction(
int iIndex,
int iMaxDer,
double fParam,
TColStd_Array1OfReal& Derivat
) = 0;
/**
* Calculates the kth derivative at the point fParam
*/
virtual double DerivativeOfBasisFunction(int iIndex, int k, double fParam) = 0;
/**
* Sets the knot vector and the order. The size of the knot vector has to be exactly as
* large as defined in the constructor.
*/
virtual void SetKnots(TColStd_Array1OfReal& vKnots, int iOrder = 1);
/**
* Sets the knot vector and the order. The knot vector in the form of (Value, Multiplicity)
* is passed on. Internally, this is converted into a knot vector in the form of (value, 1).
* The size of this new vector has to be exactly as big as specified in the constructor.
*/
virtual void SetKnots(TColStd_Array1OfReal& vKnots, TColStd_Array1OfInteger& vMults, int iOrder = 1);
protected: // Member
// Knot vector
TColStd_Array1OfReal _vKnotVector;
// Order (=Degree+1)
int _iOrder;
};
class ReenExport BSplineBasis: public SplineBasisfunction
{
public:
/**
* Constructor
* @param iSize Length of the knot vector
*/
explicit BSplineBasis(int iSize);
/**
* Constructor
* @param vKnots Knot vector
* @param iOrder Order (degree + 1) of the basic polynomial
*/
explicit BSplineBasis(TColStd_Array1OfReal& vKnots, int iOrder = 1);
/**
* Constructor
* @param vKnots Knot vector of shape (value)
* @param vMults Knot vector of shape (multiplicity)
* @param iSize Length of the knot vector
* The arrays @a vKnots and @a vMults have to be of the same size and the
* sum of the values in @a vMults has to be identical to @a iSize.
* @param iOrder Order (degree + 1) of the basic polynomial
*/
BSplineBasis(TColStd_Array1OfReal& vKnots, TColStd_Array1OfInteger& vMults, int iSize, int iOrder = 1);
/**
* Specifies the knot index for the parameter value (from: Piegl/Tiller 96 The NURBS-Book)
* @param fParam Parameter value
* @return Knot index
*/
virtual int FindSpan(double fParam);
/**
* Calculates the function values of the basic functions that do not vanish at fParam.
* It must be ensured that the list for d (= degree of the B-spline)
* elements (0, ..., d-1) is sufficient (from: Piegl/Tiller 96 The NURBS-Book)
* @param fParam Parameter
* @param vFuncVals List of function values
* Index, Parameter value
*/
virtual void AllBasisFunctions(double fParam, TColStd_Array1OfReal& vFuncVals);
/**
* Specifies whether the function value Nik(t) at the position fParam
* results in 0, 1 or a value in between.
* This serves to speed up the calculation under certain circumstances.
*
* @param iIndex Index
* @param fParam Parameter value
* @return ValueT
*/
ValueT LocalSupport(int iIndex, double fParam) override;
/**
* Calculates the function value Nik(t) at the point fParam
* (from: Piegl/Tiller 96 The NURBS-Book)
* @param iIndex Index
* @param fParam Parameter value
* @return Function value Nik(t)
*/
double BasisFunction(int iIndex, double fParam) override;
/**
* Calculates the function values of the first iMaxDer derivatives at the point fParam
* (from: Piegl/Tiller 96 The NURBS-Book)
* @param iIndex Index
* @param iMaxDer max. derivative
* @param fParam Parameter value
* @param Derivat
* The list must be sufficiently long for iMaxDer+1 elements.
* @return List of function values
*/
void DerivativesOfBasisFunction(
int iIndex,
int iMaxDer,
double fParam,
TColStd_Array1OfReal& Derivat
) override;
/**
* Calculates the kth derivative at the point fParam
*/
double DerivativeOfBasisFunction(int iIndex, int k, double fParam) override;
/**
* Calculates the integral of the product of two B-splines or their derivatives.
* The integration area extends over the entire domain of definition.
* The integral is calculated by means of the Gaussian quadrature formulas.
*/
virtual double GetIntegralOfProductOfBSplines(int i, int j, int r, int s);
/**
* Destructor
*/
~BSplineBasis() override;
protected:
/**
* Calculates the roots of the Legendre-Polynomials and the corresponding weights
*/
virtual void GenerateRootsAndWeights(
TColStd_Array1OfReal& vAbscissas,
TColStd_Array1OfReal& vWeights
);
/**
* Calculates the limits of integration (Indexes of the knots)
*/
virtual void FindIntegrationArea(int iIdx1, int iIdx2, int& iBegin, int& iEnd);
/**
* Calculates the number of roots/weights of the Legendre-Polynomials to be used as a function
* of the degree
*/
int CalcSize(int r, int s);
};
class ReenExport ParameterCorrection
{
public:
// Constructor
explicit ParameterCorrection(
unsigned usUOrder = 4, // Order in u-direction (order = degree + 1)
unsigned usVOrder = 4, // Order in v-direction
unsigned usUCtrlpoints = 6, // Qty. of the control points in the u-direction
unsigned usVCtrlpoints = 6
); // Qty. of the control points in the v-direction
virtual ~ParameterCorrection()
{
delete _pvcPoints;
delete _pvcUVParam;
}
protected:
/**
* Calculates the eigenvectors of the covariance matrix
*/
virtual void CalcEigenvectors();
/**
* Projects the control points onto the fit plane
*/
void ProjectControlPointsOnPlane();
/**
* Calculates an initial area at the beginning of the algorithm.
* For this purpose, the best-fit plane for the point cloud is calculated.
* The points are calculated with respect to the base consisting of the
* eigenvectors of the covariance matrix and projected onto the best-fit plane.
* The bounding box is calculated from these points, then the u/v parameters for
* the points are calculated.
*/
virtual bool DoInitialParameterCorrection(double fSizeFactor = 0.0f);
/**
* Calculates the (u, v) values of the points
*/
virtual bool GetUVParameters(double fSizeFactor);
/**
* Carries out a parameter correction.
*/
virtual void DoParameterCorrection(int iIter) = 0;
/**
* Solves system of equations
*/
virtual bool SolveWithoutSmoothing() = 0;
/**
* Solve a regular system of equations
*/
virtual bool SolveWithSmoothing(double fWeight) = 0;
public:
/**
* Calculates a B-spline surface from the given points
*/
virtual Handle(Geom_BSplineSurface) CreateSurface(
const TColgp_Array1OfPnt& points,
int iIter,
bool bParaCor,
double fSizeFactor = 0.0f
);
/**
* Setting the u/v directions
* The third parameter specifies whether the directions should actually be used.
*/
virtual void SetUV(const Base::Vector3d& clU, const Base::Vector3d& clV, bool bUseDir = true);
/**
* Returns the u/v/w directions
*/
virtual void GetUVW(Base::Vector3d& clU, Base::Vector3d& clV, Base::Vector3d& clW) const;
/**
* Get the center of gravity
*/
virtual Base::Vector3d GetGravityPoint() const;
/**
* Use smoothing-terms
*/
virtual void EnableSmoothing(bool bSmooth = true, double fSmoothInfl = 1.0f);
protected:
bool _bGetUVDir; //! Determines whether u/v direction is given
bool _bSmoothing; //! Use smoothing
double _fSmoothInfluence; //! Influence of smoothing
unsigned _usUOrder; //! Order in u-direction
unsigned _usVOrder; //! Order in v-direction
unsigned _usUCtrlpoints; //! Number of control points in the u-direction
unsigned _usVCtrlpoints; //! Number of control points in the v-direction
Base::Vector3d _clU; //! u-direction
Base::Vector3d _clV; //! v-direction
Base::Vector3d _clW; //! w-direction (perpendicular to u & v directions)
TColgp_Array1OfPnt* _pvcPoints {nullptr}; //! Raw data point list
TColgp_Array1OfPnt2d* _pvcUVParam {nullptr}; //! Parameter value for the points in the list
TColgp_Array2OfPnt _vCtrlPntsOfSurf; //! Array of control points
TColStd_Array1OfReal _vUKnots; //! Knot vector of the B-spline surface in the u-direction
TColStd_Array1OfReal _vVKnots; //! Knot vector of the B-spline surface in the v-direction
TColStd_Array1OfInteger _vUMults; //! Multiplicity of the knots in the knot vector
TColStd_Array1OfInteger _vVMults; //! Multiplicity of the knots in the knot vector
};
///////////////////////////////////////////////////////////////////////////////////////////////
/**
* This class calculates a B-spline area on any point cloud (AKA scattered data).
* The surface is generated iteratively with the help of a parameter correction.
* See Hoschek/Lasser 2nd ed. (1992).
* The approximation is expanded to include smoothing terms so that smooth surfaces
* can be generated.
*/
class ReenExport BSplineParameterCorrection: public ParameterCorrection
{
public:
// Constructor
explicit BSplineParameterCorrection(
unsigned usUOrder = 4, // Order in u-direction (order = degree + 1)
unsigned usVOrder = 4, // Order in the v-direction
unsigned usUCtrlpoints = 6, // Qty. of the control points in u-direction
unsigned usVCtrlpoints = 6
); // Qty. of the control points in v-direction
~BSplineParameterCorrection() override = default;
protected:
/**
* Initialization
*/
virtual void Init();
/**
* Carries out a parameter correction.
*/
void DoParameterCorrection(int iIter) override;
/**
* Solve an overdetermined LGS with the help of the Householder-Tansformation
*/
bool SolveWithoutSmoothing() override;
/**
* Solve a regular system of equations by LU decomposition. Depending on the weighting,
* smoothing terms are included
*/
bool SolveWithSmoothing(double fWeight) override;
public:
/**
* Setting the knot vector
*/
void SetUKnots(const std::vector<double>& afKnots);
/**
* Setting the knot vector
*/
void SetVKnots(const std::vector<double>& afKnots);
/**
* Returns the first matrix of smoothing terms, if calculated
*/
virtual const math_Matrix& GetFirstSmoothMatrix() const;
/**
* Returns the second matrix of smoothing terms, if calculated
*/
virtual const math_Matrix& GetSecondSmoothMatrix() const;
/**
* Returns the third matrix of smoothing terms, if calculated
*/
virtual const math_Matrix& GetThirdSmoothMatrix() const;
/**
* Sets the first matrix of the smoothing terms
*/
virtual void SetFirstSmoothMatrix(const math_Matrix& rclMat);
/**
* Sets the second matrix of smoothing terms
*/
virtual void SetSecondSmoothMatrix(const math_Matrix& rclMat);
/**
* Sets the third matrix of smoothing terms
*/
virtual void SetThirdSmoothMatrix(const math_Matrix& rclMat);
/**
* Use smoothing-terms
*/
void EnableSmoothing(bool bSmooth = true, double fSmoothInfl = 1.0f) override;
/**
* Use smoothing-terms
*/
virtual void EnableSmoothing(bool bSmooth, double fSmoothInfl, double fFirst, double fSec, double fThird);
protected:
/**
* Calculates the matrix for the smoothing terms
* (see U.Dietz dissertation)
*/
virtual void CalcSmoothingTerms(bool bRecalc, double fFirst, double fSecond, double fThird);
/**
* Calculates the matrix for the first smoothing term
* (see U.Dietz dissertation)
*/
virtual void CalcFirstSmoothMatrix(Base::SequencerLauncher&);
/**
* Calculates the matrix for the second smoothing term
* (see U.Dietz dissertation)
*/
virtual void CalcSecondSmoothMatrix(Base::SequencerLauncher&);
/**
* Calculates the matrix for the third smoothing term
*/
virtual void CalcThirdSmoothMatrix(Base::SequencerLauncher&);
protected:
BSplineBasis _clUSpline; //! B-spline basic function in the u-direction
BSplineBasis _clVSpline; //! B-spline basic function in the v-direction
math_Matrix _clSmoothMatrix; //! Matrix of smoothing functionals
math_Matrix _clFirstMatrix; //! Matrix of the 1st smoothing functionals
math_Matrix _clSecondMatrix; //! Matrix of the 2nd smoothing functionals
math_Matrix _clThirdMatrix; //! Matrix of the 3rd smoothing functionals
};
} // namespace Reen
#endif // REEN_APPROXSURFACE_H
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