+// Created on: 1995-03-14
+// Created by: Modelistation
+// 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.
+
+#ifndef OCCT_DEBUG
+#define No_Standard_OutOfRange
+#define No_Standard_RangeError
+#endif
+#include <AppCont_LeastSquare.hxx>
+
+#include <math.hxx>
+#include <AppParCurves_MultiPoint.hxx>
+#include <AppCont_ContMatrices.hxx>
+#include <PLib.hxx>
+
+
+//=======================================================================
+//function : AppCont_LeastSquare
+//purpose :
+//=======================================================================
+void AppCont_LeastSquare::FixSingleBorderPoint(const AppCont_Function& theSSP,
+ const Standard_Real theU,
+ const Standard_Real theU0,
+ const Standard_Real theU1,
+ NCollection_Array1<gp_Pnt2d>& theFix2d,
+ NCollection_Array1<gp_Pnt>& theFix)
+{
+ Standard_Real aMaxIter = 15.0;
+ Standard_Integer j, i2;
+ NCollection_Array1<gp_Pnt> aTabP(1, Max (myNbP, 1)), aPrevP(1, Max (myNbP, 1));
+ NCollection_Array1<gp_Pnt2d> aTabP2d(1, Max (myNbP2d, 1)), aPrevP2d(1, Max (myNbP2d, 1));
+ Standard_Real aMult = ((theU - theU0) > (theU1 - theU)) ? 1.0: -1.0;
+ Standard_Real aStartParam = (theU0 + theU1) / 2.0,
+ aCurrParam, aPrevDist = 1.0, aCurrDist = 1.0;
+
+ for (Standard_Real anIter = 1.0; anIter < aMaxIter; anIter += 1.0)
+ {
+ aCurrParam = aStartParam + aMult * (1 - pow(10, -anIter)) * (theU1 - theU0) / 2.0;
+ theSSP.Value(aCurrParam, aTabP2d, aTabP);
+
+ // from second iteration
+ if (anIter > 1.5)
+ {
+ aCurrDist = 0.0;
+
+ i2 = 1;
+ for (j = 1; j <= myNbP; j++)
+ {
+ aCurrDist += aTabP(j).Distance(aPrevP(j));
+ i2 += 3;
+ }
+ for (j = 1; j <= myNbP2d; j++)
+ {
+ aCurrDist += aTabP2d(j).Distance(aPrevP2d(j));
+ i2 += 2;
+ }
+
+ // from the third iteration
+ if (anIter > 2.5 && aCurrDist / aPrevDist > 10.0)
+ break;
+ }
+ aPrevP = aTabP;
+ aPrevP2d = aTabP2d;
+ aPrevDist = aCurrDist;
+ }
+ theFix2d = aPrevP2d;
+ theFix = aPrevP;
+}
+
+
+//=======================================================================
+//function : AppCont_LeastSquare
+//purpose :
+//=======================================================================
+
+AppCont_LeastSquare::AppCont_LeastSquare(const AppCont_Function& SSP,
+ const Standard_Real U0,
+ const Standard_Real U1,
+ const AppParCurves_Constraint FirstCons,
+ const AppParCurves_Constraint LastCons,
+ const Standard_Integer Deg,
+ const Standard_Integer myNbPoints)
+: mySCU(Deg+1),
+ myPoints(1, myNbPoints, 1, 3 * SSP.GetNbOf3dPoints() + 2 * SSP.GetNbOf2dPoints()),
+ myPoles(1, Deg + 1, 1, 3 * SSP.GetNbOf3dPoints() + 2 * SSP.GetNbOf2dPoints(), 0.0),
+ myParam(1, myNbPoints),
+ myVB(1, Deg+1, 1, myNbPoints),
+ myPerInfo(1, 3 * SSP.GetNbOf3dPoints() + 2 * SSP.GetNbOf2dPoints() )
+{
+ myDone = Standard_False;
+ myDegre = Deg;
+ math_Matrix InvM(1, Deg+1, 1, Deg + 1);
+ Standard_Integer i, j, k, c, i2;
+ Standard_Integer classe = Deg + 1, cl1 = Deg;
+ Standard_Real U, dU, Coeff, Coeff2;
+ Standard_Real IBij, IBPij;
+
+ Standard_Integer FirstP = 1, LastP = myNbPoints;
+ Standard_Integer nbcol = 3 * SSP.GetNbOf3dPoints() + 2 * SSP.GetNbOf2dPoints();
+ math_Matrix B(1, classe, 1, nbcol, 0.0);
+ Standard_Integer bdeb = 1, bfin = classe;
+ AppParCurves_Constraint myFirstC = FirstCons, myLastC = LastCons;
+ SSP.GetNumberOfPoints(myNbP, myNbP2d);
+
+ Standard_Integer i2plus1, i2plus2;
+ myNbdiscret = myNbPoints;
+ NCollection_Array1<gp_Pnt> aTabP(1, Max (myNbP, 1));
+ NCollection_Array1<gp_Pnt2d> aTabP2d(1, Max (myNbP2d, 1));
+ NCollection_Array1<gp_Vec> aTabV(1, Max (myNbP, 1));
+ NCollection_Array1<gp_Vec2d> aTabV2d(1, Max (myNbP2d, 1));
+
+ for(Standard_Integer aDimIdx = 1; aDimIdx <= myNbP * 3 + myNbP2d * 2; aDimIdx++)
+ {
+ SSP.PeriodInformation(aDimIdx,
+ myPerInfo(aDimIdx).isPeriodic,
+ myPerInfo(aDimIdx).myPeriod);
+ }
+
+ Standard_Boolean Ok;
+ if (myFirstC == AppParCurves_TangencyPoint)
+ {
+ Ok = SSP.D1(U0, aTabV2d, aTabV);
+ if (!Ok) myFirstC = AppParCurves_PassPoint;
+ }
+
+ if (myLastC == AppParCurves_TangencyPoint)
+ {
+ Ok = SSP.D1(U1, aTabV2d, aTabV);
+ if (!Ok) myLastC = AppParCurves_PassPoint;
+ }
+
+ // Compute control points params on which approximation will be built.
+ math_Vector GaussP(1, myNbPoints), GaussW(1, myNbPoints);
+ math::GaussPoints(myNbPoints, GaussP);
+ math::GaussWeights(myNbPoints, GaussW);
+ math_Vector TheWeights(1, myNbPoints), VBParam(1, myNbPoints);
+ dU = 0.5*(U1-U0);
+ for (i = FirstP; i <= LastP; i++)
+ {
+ U = 0.5 * (U1 + U0) + dU * GaussP(i);
+ if (i <= (myNbPoints+1)/2)
+ {
+ myParam(LastP - i + 1) = U;
+ VBParam(LastP - i + 1) = 0.5 * (1 + GaussP(i));
+ TheWeights(LastP - i + 1) = 0.5 * GaussW(i);
+ }
+ else
+ {
+ VBParam(i - (myNbPoints + 1) / 2) = 0.5*(1 + GaussP(i));
+ myParam(i - (myNbPoints + 1) / 2) = U;
+ TheWeights(i - (myNbPoints+ 1) / 2) = 0.5 * GaussW(i);
+ }
+ }
+
+ // Compute control points.
+ for (i = FirstP; i <= LastP; i++)
+ {
+ U = myParam(i);
+ SSP.Value(U, aTabP2d, aTabP);
+
+ i2 = 1;
+ for (j = 1; j <= myNbP; j++)
+ {
+ (aTabP(j)).Coord(myPoints(i, i2), myPoints(i, i2+1), myPoints(i, i2+2));
+ i2 += 3;
+ }
+ for (j = 1; j <= myNbP2d; j++)
+ {
+ (aTabP2d(j)).Coord(myPoints(i, i2), myPoints(i, i2+1));
+ i2 += 2;
+ }
+ }
+
+ // Fix possible "period jump".
+ Standard_Integer aMaxDim = 3 * myNbP + 2 * myNbP2d;
+ for(Standard_Integer aDimIdx = 1; aDimIdx <= aMaxDim; aDimIdx++)
+ {
+ if (myPerInfo(aDimIdx).isPeriodic &&
+ Abs (myPoints(1, aDimIdx) - myPoints(2, aDimIdx)) > myPerInfo(aDimIdx).myPeriod / 2.01 &&
+ Abs (myPoints(2, aDimIdx) - myPoints(3, aDimIdx)) < myPerInfo(aDimIdx).myPeriod / 2.01)
+ {
+ Standard_Real aPeriodMult = (myPoints(1, aDimIdx) < myPoints(2, aDimIdx)) ? 1.0 : -1.0;
+ Standard_Real aNewParam = myPoints(1, aDimIdx) + aPeriodMult * myPerInfo(aDimIdx).myPeriod;
+ myPoints(1, aDimIdx) = aNewParam;
+ }
+ }
+ for (Standard_Integer aPntIdx = 1; aPntIdx < myNbPoints; aPntIdx++)
+ {
+ for(Standard_Integer aDimIdx = 1; aDimIdx <= aMaxDim; aDimIdx++)
+ {
+ if (myPerInfo(aDimIdx).isPeriodic &&
+ Abs ( myPoints(aPntIdx, aDimIdx) - myPoints(aPntIdx + 1, aDimIdx) ) > myPerInfo(aDimIdx).myPeriod / 2.01)
+ {
+ Standard_Real aPeriodMult = (myPoints(aPntIdx, aDimIdx) > myPoints(aPntIdx + 1, aDimIdx)) ? 1.0 : -1.0;
+ Standard_Real aNewParam = myPoints(aPntIdx + 1, aDimIdx) + aPeriodMult * myPerInfo(aDimIdx).myPeriod;
+ myPoints(aPntIdx + 1, aDimIdx) = aNewParam;
+ }
+ }
+ }
+
+ VBernstein(classe, myNbPoints, myVB);
+
+ // Traitement du second membre:
+ NCollection_Array1<Standard_Real> tmppoints(1, nbcol);
+
+ for (c = 1; c <= classe; c++)
+ {
+ tmppoints.Init(0.0);
+ for (i = 1; i <= myNbPoints; i++)
+ {
+ Coeff = TheWeights(i) * myVB(c, i);
+ for (j = 1; j <= nbcol; j++)
+ {
+ tmppoints(j) += myPoints(i, j)*Coeff;
+ }
+ }
+ for (k = 1; k <= nbcol; k++)
+ {
+ B(c, k) += tmppoints(k);
+ }
+ }
+
+ if (myFirstC == AppParCurves_NoConstraint &&
+ myLastC == AppParCurves_NoConstraint) {
+
+ math_Matrix InvM(1, classe, 1, classe);
+ InvMMatrix(classe, InvM);
+ // Calcul direct des poles:
+
+ for (i = 1; i <= classe; i++) {
+ for (j = 1; j <= classe; j++) {
+ IBij = InvM(i, j);
+ for (k = 1; k <= nbcol; k++) {
+ myPoles(i, k) += IBij * B(j, k);
+ }
+ }
+ }
+ }
+
+
+ else
+ {
+ math_Matrix M(1, classe, 1, classe);
+ MMatrix(classe, M);
+ NCollection_Array1<gp_Pnt2d> aFixP2d(1, Max (myNbP2d, 1));
+ NCollection_Array1<gp_Pnt> aFixP(1, Max (myNbP, 1));
+
+ if (myFirstC == AppParCurves_PassPoint ||
+ myFirstC == AppParCurves_TangencyPoint)
+ {
+ SSP.Value(U0, aTabP2d, aTabP);
+ FixSingleBorderPoint(SSP, U0, U0, U1, aFixP2d, aFixP);
+
+ i2 = 1;
+ for (k = 1; k<= myNbP; k++)
+ {
+ if (aFixP(k).Distance(aTabP(k)) > 0.1)
+ (aFixP(k)).Coord(myPoles(1, i2), myPoles(1, i2 + 1), myPoles(1, i2 + 2));
+ else
+ (aTabP(k)).Coord(myPoles(1, i2), myPoles(1, i2 + 1), myPoles(1, i2 + 2));
+ i2 += 3;
+ }
+ for (k = 1; k<= myNbP2d; k++)
+ {
+ if (aFixP2d(k).Distance(aTabP2d(k)) > 0.1)
+ (aFixP2d(k)).Coord(myPoles(1, i2), myPoles(1, i2 + 1));
+ else
+ (aTabP2d(k)).Coord(myPoles(1, i2), myPoles(1, i2 + 1));
+ i2 += 2;
+ }
+
+ for (Standard_Integer aDimIdx = 1; aDimIdx <= aMaxDim; aDimIdx++)
+ {
+ if (myPerInfo(aDimIdx).isPeriodic &&
+ Abs ( myPoles(1, aDimIdx) - myPoints(1, aDimIdx) ) > myPerInfo(aDimIdx).myPeriod / 2.01 )
+ {
+ Standard_Real aMult = myPoles(1, aDimIdx) < myPoints(1, aDimIdx)? 1.0: -1.0;
+ myPoles(1,aDimIdx) += aMult * myPerInfo(aDimIdx).myPeriod;
+ }
+ }
+ }
+
+ if (myLastC == AppParCurves_PassPoint ||
+ myLastC == AppParCurves_TangencyPoint)
+ {
+ SSP.Value(U1, aTabP2d, aTabP);
+ FixSingleBorderPoint(SSP, U1, U0, U1, aFixP2d, aFixP);
+
+ i2 = 1;
+ for (k = 1; k<= myNbP; k++)
+ {
+ if (aFixP(k).Distance(aTabP(k)) > 0.1)
+ (aFixP(k)).Coord(myPoles(classe, i2), myPoles(classe, i2 + 1), myPoles(classe, i2 + 2));
+ else
+ (aTabP(k)).Coord(myPoles(classe, i2), myPoles(classe, i2 + 1), myPoles(classe, i2 + 2));
+ i2 += 3;
+ }
+ for (k = 1; k<= myNbP2d; k++)
+ {
+ if (aFixP2d(k).Distance(aTabP2d(k)) > 0.1)
+ (aFixP2d(k)).Coord(myPoles(classe, i2), myPoles(classe, i2 + 1));
+ else
+ (aTabP2d(k)).Coord(myPoles(classe, i2), myPoles(classe, i2 + 1));
+ i2 += 2;
+ }
+
+
+ for (Standard_Integer aDimIdx = 1; aDimIdx <= 2; aDimIdx++)
+ {
+ if (myPerInfo(aDimIdx).isPeriodic &&
+ Abs ( myPoles(classe, aDimIdx) - myPoints(myNbPoints, aDimIdx) ) > myPerInfo(aDimIdx).myPeriod / 2.01 )
+ {
+ Standard_Real aMult = myPoles(classe, aDimIdx) < myPoints(myNbPoints, aDimIdx)? 1.0: -1.0;
+ myPoles(classe,aDimIdx) += aMult * myPerInfo(aDimIdx).myPeriod;
+ }
+ }
+ }
+
+ if (myFirstC == AppParCurves_PassPoint) {
+ bdeb = 2;
+ // mise a jour du second membre:
+ for (i = 1; i <= classe; i++) {
+ Coeff = M(i, 1);
+ for (k = 1; k <= nbcol; k++) {
+ B(i, k) -= myPoles(1, k)*Coeff;
+ }
+ }
+ }
+
+ if (myLastC == AppParCurves_PassPoint) {
+ bfin = cl1;
+ for (i = 1; i <= classe; i++) {
+ Coeff = M(i, classe);
+ for (k = 1; k <= nbcol; k++) {
+ B(i, k) -= myPoles(classe, k)*Coeff;
+ }
+ }
+ }
+
+ if (myFirstC == AppParCurves_TangencyPoint) {
+ // On fixe le second pole::
+ bdeb = 3;
+ SSP.D1(U0, aTabV2d, aTabV);
+
+ i2 = 1;
+ Coeff = (U1-U0)/myDegre;
+ for (k = 1; k<= myNbP; k++) {
+ i2plus1 = i2+1; i2plus2 = i2+2;
+ myPoles(2, i2) = myPoles(1, i2) + aTabV(k).X()*Coeff;
+ myPoles(2, i2plus1) = myPoles(1, i2plus1) + aTabV(k).Y()*Coeff;
+ myPoles(2, i2plus2) = myPoles(1, i2plus2) + aTabV(k).Z()*Coeff;
+ i2 += 3;
+ }
+ for (k = 1; k<= myNbP2d; k++) {
+ i2plus1 = i2+1;
+ myPoles(2, i2) = myPoles(1, i2) + aTabV2d(k).X()*Coeff;
+ myPoles(2, i2plus1) = myPoles(1, i2plus1) + aTabV2d(k).Y()*Coeff;
+ i2 += 2;
+ }
+
+ for (i = 1; i <= classe; i++) {
+ Coeff = M(i, 1); Coeff2 = M(i, 2);
+ for (k = 1; k <= nbcol; k++) {
+ B(i, k) -= myPoles(1, k)*Coeff+myPoles(2, k)*Coeff2;
+ }
+ }
+ }
+
+ if (myLastC == AppParCurves_TangencyPoint) {
+ bfin = classe-2;
+ SSP.D1(U1, aTabV2d, aTabV);
+ i2 = 1;
+ Coeff = (U1-U0)/myDegre;
+ for (k = 1; k<= myNbP; k++) {
+ i2plus1 = i2+1; i2plus2 = i2+2;
+ myPoles(cl1,i2) = myPoles(classe, i2) - aTabV(k).X()*Coeff;
+ myPoles(cl1,i2plus1) = myPoles(classe, i2plus1) - aTabV(k).Y()*Coeff;
+ myPoles(cl1,i2plus2) = myPoles(classe, i2plus2) - aTabV(k).Z()*Coeff;
+ i2 += 3;
+ }
+ for (k = 1; k<= myNbP2d; k++) {
+ i2plus1 = i2+1;
+ myPoles(cl1,i2) = myPoles(classe, i2) - aTabV2d(k).X()*Coeff;
+ myPoles(cl1,i2plus1) = myPoles(classe, i2plus1) - aTabV2d(k).Y()*Coeff;
+ i2 += 2;
+ }
+
+ for (i = 1; i <= classe; i++) {
+ Coeff = M(i, classe); Coeff2 = M(i, cl1);
+ for (k = 1; k <= nbcol; k++) {
+ B(i, k) -= myPoles(classe, k)*Coeff + myPoles(cl1, k)*Coeff2;
+ }
+ }
+ }
+
+
+ if (bdeb <= bfin) {
+ math_Matrix B2(bdeb, bfin, 1, B.UpperCol(), 0.0);
+
+ for (i = bdeb; i <= bfin; i++) {
+ for (j = 1; j <= classe; j++) {
+ Coeff = M(i, j);
+ for (k = 1; k <= nbcol; k++) {
+ B2(i, k) += B(j, k)*Coeff;
+ }
+ }
+ }
+
+ // Resolution:
+ // ===========
+ math_Matrix IBP(bdeb, bfin, bdeb, bfin);
+
+ // dans IBPMatrix at IBTMatrix ne sont stockees que les resultats pour
+ // une classe inferieure ou egale a 26 (pour l instant du moins.)
+
+ if (bdeb == 2 && bfin == classe-1 && classe <= 26) {
+ IBPMatrix(classe, IBP);
+ }
+ else if (bdeb == 3 && bfin == classe-2 && classe <= 26) {
+ IBTMatrix(classe, IBP);
+ }
+ else {
+ math_Matrix MP(1, classe, bdeb, bfin);
+ for (i = 1; i <= classe; i++) {
+ for (j = bdeb; j <= bfin; j++) {
+ MP(i, j) = M(i, j);
+ }
+ }
+ math_Matrix IBP1(bdeb, bfin, bdeb, bfin);
+ IBP1 = MP.Transposed()*MP;
+ IBP = IBP1.Inverse();
+ }
+
+ myDone = Standard_True;
+ for (i = bdeb; i <= bfin; i++) {
+ for (j = bdeb; j <= bfin; j++) {
+ IBPij = IBP(i, j);;
+ for (k = 1; k<= nbcol; k++) {
+ myPoles(i, k) += IBPij * B2(j, k);
+ }
+ }
+ }
+ }
+ }
+}
+
+//=======================================================================
+//function : Value
+//purpose :
+//=======================================================================
+
+const AppParCurves_MultiCurve& AppCont_LeastSquare::Value()
+{
+
+ Standard_Integer i, j, j2;
+ gp_Pnt Pt;
+ gp_Pnt2d Pt2d;
+ Standard_Integer ideb = 1, ifin = myDegre+1;
+
+ // On met le resultat dans les curves correspondantes
+ for (i = ideb; i <= ifin; i++) {
+ j2 = 1;
+ AppParCurves_MultiPoint MPole(myNbP, myNbP2d);
+ for (j = 1; j <= myNbP; j++) {
+ Pt.SetCoord(myPoles(i, j2), myPoles(i, j2+1), myPoles(i,j2+2));
+ MPole.SetPoint(j, Pt);
+ j2 += 3;
+ }
+ for (j = myNbP+1;j <= myNbP+myNbP2d; j++) {
+ Pt2d.SetCoord(myPoles(i, j2), myPoles(i, j2+1));
+ MPole.SetPoint2d(j, Pt2d);
+ j2 += 2;
+ }
+ mySCU.SetValue(i, MPole);
+ }
+ return mySCU;
+}
+
+
+
+//=======================================================================
+//function : Error
+//purpose :
+//=======================================================================
+
+void AppCont_LeastSquare::Error(Standard_Real& F,
+ Standard_Real& MaxE3d,
+ Standard_Real& MaxE2d) const
+{
+ Standard_Integer i, j, k, c, i2, classe = myDegre + 1;
+ Standard_Real Coeff, err3d = 0.0, err2d = 0.0;
+ Standard_Integer ncol = myPoints.UpperCol() - myPoints.LowerCol() + 1;
+
+ math_Matrix MyPoints(1, myNbdiscret, 1, ncol);
+ MyPoints = myPoints;
+
+ MaxE3d = MaxE2d = F = 0.0;
+
+ NCollection_Array1<Standard_Real> tmppoles(1, ncol);
+
+ for (c = 1; c <= classe; c++)
+ {
+ for (k = 1; k <= ncol; k++)
+ {
+ tmppoles(k) = myPoles(c, k);
+ }
+ for (i = 1; i <= myNbdiscret; i++)
+ {
+ Coeff = myVB(c, i);
+ for (j = 1; j <= ncol; j++)
+ {
+ MyPoints(i, j) -= tmppoles(j) * Coeff;
+ }
+ }
+ }
+
+ Standard_Real e1, e2, e3;
+ for (i = 1; i <= myNbdiscret; i++)
+ {
+ i2 = 1;
+ for (j = 1; j<= myNbP; j++) {
+ e1 = MyPoints(i, i2);
+ e2 = MyPoints(i, i2+1);
+ e3 = MyPoints(i, i2+2);
+ err3d = e1*e1+e2*e2+e3*e3;
+ MaxE3d = Max(MaxE3d, err3d);
+ F += err3d;
+ i2 += 3;
+ }
+ for (j = 1; j<= myNbP2d; j++) {
+ e1 = MyPoints(i, i2);
+ e2 = MyPoints(i, i2+1);
+ err2d = e1*e1+e2*e2;
+ MaxE2d = Max(MaxE2d, err2d);
+ F += err2d;
+ i2 += 2;
+ }
+ }
+
+ MaxE3d = Sqrt(MaxE3d);
+ MaxE2d = Sqrt(MaxE2d);
+
+}
+
+
+//=======================================================================
+//function : IsDone
+//purpose :
+//=======================================================================
+
+Standard_Boolean AppCont_LeastSquare::IsDone() const
+{
+ return myDone;
+}
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