// Copyright (c) 1995-1999 Matra Datavision // Copyright (c) 1999-2014 OPEN CASCADE SAS // // This file is part of Open CASCADE Technology software library. // // This library is free software; you can redistribute it and/or modify it under // the terms of the GNU Lesser General Public License version 2.1 as published // by the Free Software Foundation, with special exception defined in the file // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT // distribution for complete text of the license and disclaimer of any warranty. // // Alternatively, this file may be used under the terms of Open CASCADE // commercial license or contractual agreement. // lpa, le 11/09/91 // Application de la methode du gradient corrige pour minimiser // F = somme(||C(ui, Poles(ui)) - ptli||2. // La methode de gradient conjugue est programmee dans la bibliotheque // mathematique: math_BFGS. // cet algorithme doit etre appele uniquement lorsque on a affaire a un set // de points contraints (ailleurs qu aux extremites). En effet, l appel de la // fonction F a minimiser implique un appel a ParLeastSquare et ResConstraint. // Si ce n est pas le cas, l appel a ResConstraint est equivalent a une // seconde resolution par les moindres carres donc beaucoup de temps perdu. #define No_Standard_RangeError #define No_Standard_OutOfRange #include #include #include #include #include #include #include #include #include #include #include #include #include #include // #define AppParCurves_Gradient_BFGS BFGS_/**/AppParCurves_Gradient AppParCurves_Gradient:: AppParCurves_Gradient(const MultiLine& SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints, math_Vector& Parameters, const Standard_Integer Deg, const Standard_Real Tol3d, const Standard_Real Tol2d, const Standard_Integer NbIterations): ParError(FirstPoint, LastPoint,0.0), AvError(0.0), MError3d(0.0), MError2d(0.0) { // Standard_Boolean grad = Standard_True; Standard_Integer j, k, i2, l; Standard_Real UF, DU, Fval = 0.0, FU, DFU; Standard_Integer nbP3d = ToolLine::NbP3d(SSP); Standard_Integer nbP2d = ToolLine::NbP2d(SSP); Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d; Standard_Integer nbP = nbP3d + nbP2d; // gp_Pnt Pt, P1, P2; gp_Pnt Pt; // gp_Pnt2d Pt2d, P12d, P22d; gp_Pnt2d Pt2d; // gp_Vec V1, V2, MyV; gp_Vec V1, MyV; // gp_Vec2d V12d, V22d, MyV2d; gp_Vec2d V12d, MyV2d; Done = Standard_False; if (nbP3d == 0) mynbP3d = 1; if (nbP2d == 0) mynbP2d = 1; TColgp_Array1OfPnt TabP(1, mynbP3d); TColgp_Array1OfPnt2d TabP2d(1, mynbP2d); TColgp_Array1OfVec TabV(1, mynbP3d); TColgp_Array1OfVec2d TabV2d(1, mynbP2d); // Calcul de la fonction F= somme(||C(ui)-Ptli||2): // Appel a une fonction heritant de MultipleVarFunctionWithGradient // pour calculer F et grad_F. // ================================================================ AppParCurves_ParFunction MyF(SSP, FirstPoint,LastPoint, TheConstraints, Parameters, Deg); if (!MyF.Value(Parameters, Fval)) { Done = Standard_False; return; } SCU = MyF.CurveValue(); Standard_Integer deg = SCU.NbPoles()-1; TColgp_Array1OfPnt TabPole(1, deg+1), TabCoef(1, deg+1); TColgp_Array1OfPnt2d TabPole2d(1, deg+1), TabCoef2d(1, deg+1); TColgp_Array1OfPnt TheCoef(1, (deg+1)*mynbP3d); TColgp_Array1OfPnt2d TheCoef2d(1, (deg+1)*mynbP2d); // Stockage des Poles des courbes pour projeter: // ============================================ i2 = 0; for (k = 1; k <= nbP3d; k++) { SCU.Curve(k, TabPole); BSplCLib::PolesCoefficients(TabPole, PLib::NoWeights(), TabCoef, PLib::NoWeights()); for (j=1; j<=deg+1; j++) TheCoef(j+i2) = TabCoef(j); i2 += deg+1; } i2 = 0; for (k = 1; k <= nbP2d; k++) { SCU.Curve(nbP3d+k, TabPole2d); BSplCLib::PolesCoefficients(TabPole2d, PLib::NoWeights(), TabCoef2d, PLib::NoWeights()); for (j=1; j<=deg+1; j++) TheCoef2d(j+i2) = TabCoef2d(j); i2 += deg+1; } // Une iteration rapide de projection est faite par la methode de // Rogers & Fog 89, methode equivalente a Hoschek 88 qui ne necessite pas // le calcul de D2. // Iteration de Projection: // ======================= for (j = FirstPoint+1; j <= LastPoint-1; j++) { UF = Parameters(j); if (nbP != 0 && nbP2d != 0) ToolLine::Value(SSP, j, TabP, TabP2d); else if (nbP2d != 0) ToolLine::Value(SSP, j, TabP2d); else ToolLine::Value(SSP, j, TabP); FU = 0.0; DFU = 0.0; i2 = 0; for (k = 1; k <= nbP3d; k++) { for (l=1; l<=deg+1; l++) TabCoef(l) = TheCoef(l+i2); i2 += deg+1; BSplCLib::CoefsD1(UF, TabCoef, BSplCLib::NoWeights(), Pt, V1); MyV = gp_Vec(Pt, TabP(k)); FU += MyV*V1; DFU += V1.SquareMagnitude(); } i2 = 0; for (k = 1; k <= nbP2d; k++) { for (l=1; l<=deg+1; l++) TabCoef2d(l) = TheCoef2d(l+i2); i2 += deg+1; BSplCLib::CoefsD1(UF, TabCoef2d, BSplCLib::NoWeights(), Pt2d, V12d); MyV2d = gp_Vec2d(Pt2d, TabP2d(k)); FU += MyV2d*V12d; DFU += V12d.SquareMagnitude(); } if (DFU >= RealEpsilon()) { DU = FU/DFU; DU = Sign(Min(5.e-02, Abs(DU)), DU); UF += DU; Parameters(j) = UF; } } if (!MyF.Value(Parameters, Fval)) { SCU = AppParCurves_MultiCurve(); Done = Standard_False; return; } MError3d = MyF.MaxError3d(); MError2d = MyF.MaxError2d(); if (MError3d<= Tol3d && MError2d <= Tol2d) { Done = Standard_True; SCU = MyF.CurveValue(); } else if (NbIterations != 0) { // NbIterations de gradient conjugue: // ================================= Standard_Real Eps = 1.e-07; AppParCurves_Gradient_BFGS FResol(MyF, Parameters, Tol3d, Tol2d, Eps, NbIterations); Parameters = MyF.NewParameters(); SCU = MyF.CurveValue(); } AvError = 0.; for (j = FirstPoint; j <= LastPoint; j++) { // Recherche des erreurs maxi et moyenne a un index donne: for (k = 1; k <= nbP; k++) { ParError(j) = Max(ParError(j), MyF.Error(j, k)); } AvError += ParError(j); } AvError = AvError/(LastPoint-FirstPoint+1); MError3d = MyF.MaxError3d(); MError2d = MyF.MaxError2d(); if (MError3d <= Tol3d && MError2d <= Tol2d) { Done = Standard_True; } } AppParCurves_MultiCurve AppParCurves_Gradient::Value() const { return SCU; } Standard_Boolean AppParCurves_Gradient::IsDone() const { return Done; } Standard_Real AppParCurves_Gradient::Error(const Standard_Integer Index) const { return ParError(Index); } Standard_Real AppParCurves_Gradient::AverageError() const { return AvError; } Standard_Real AppParCurves_Gradient::MaxError3d() const { return MError3d; } Standard_Real AppParCurves_Gradient::MaxError2d() const { return MError2d; }