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ed4415982c
License statement text corrected; compiler warnings caused by Bison 2.41 disabled for MSVC; a few other compiler warnings on 54-bit Windows eliminated by appropriate type cast Wrong license statements corrected in several files. Copyright and license statements added in XSD and GLSL files. Copyright year updated in some files. Obsolete documentation files removed from DrawResources.
505 lines
14 KiB
Plaintext
505 lines
14 KiB
Plaintext
// Created on: 1995-03-14
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// Created by: Modelistation
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// Copyright (c) 1995-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#ifndef DEB
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#define No_Standard_OutOfRange
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#define No_Standard_RangeError
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#endif
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#include <math.hxx>
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#include <math_Vector.hxx>
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#include <math_Matrix.hxx>
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#include <TColgp_Array1OfPnt.hxx>
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#include <TColgp_Array1OfPnt2d.hxx>
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#include <gp_Pnt2d.hxx>
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#include <gp_Pnt.hxx>
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#include <gp_Vec.hxx>
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#include <gp_Vec2d.hxx>
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#include <TColgp_Array1OfVec.hxx>
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#include <TColgp_Array1OfVec2d.hxx>
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#include <AppParCurves_MultiPoint.hxx>
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#include <AppCont_ContMatrices.hxx>
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#include <PLib.hxx>
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//=======================================================================
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//function : AppCont_LeastSquare
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//purpose :
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//=======================================================================
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AppCont_LeastSquare::AppCont_LeastSquare
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(const MultiLine& SSP,
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const Standard_Real U0,
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const Standard_Real U1,
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const AppParCurves_Constraint FirstCons,
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const AppParCurves_Constraint LastCons,
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const Standard_Integer Deg,
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const Standard_Integer NbPoints):
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SCU(Deg+1),
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Points(1, NbPoints, 1, NbBColumns(SSP)),
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Poles(1, Deg+1, 1, NbBColumns(SSP), 0.0),
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myParam(1, NbPoints),
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VB(1, Deg+1, 1, NbPoints)
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{
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Done = Standard_False;
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Degre = Deg;
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math_Matrix InvM(1, Deg+1, 1, Deg+1);
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Standard_Integer i, j, k, c, i2;
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Standard_Integer classe = Deg+1, cl1 = Deg;
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Standard_Real U, dU, Coeff, Coeff2;
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Standard_Real IBij, IBPij;
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Standard_Integer FirstP = 1, LastP = NbPoints;
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Standard_Integer nbcol = NbBColumns(SSP);
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math_Matrix B(1, classe, 1, nbcol, 0.0);
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Standard_Integer bdeb = 1, bfin = classe;
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AppParCurves_Constraint myFirstC = FirstCons, myLastC = LastCons;
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nbP = LineTool::NbP3d(SSP);
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nbP2d = LineTool::NbP2d(SSP);
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Standard_Integer mynbP = nbP, mynbP2d = nbP2d;
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if (nbP == 0) mynbP = 1;
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if (nbP2d == 0) mynbP2d = 1;
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Standard_Integer i2plus1, i2plus2;
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Nbdiscret = NbPoints;
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TColgp_Array1OfPnt TabP(1, mynbP);
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TColgp_Array1OfVec TabV(1, mynbP);
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TColgp_Array1OfPnt2d TabP2d(1, mynbP2d);
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TColgp_Array1OfVec2d TabV2d(1, mynbP2d);
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Standard_Boolean Ok;
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if (myFirstC == AppParCurves_TangencyPoint) {
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if (nbP != 0 && nbP2d != 0) Ok=LineTool::D1(SSP, U0, TabV, TabV2d);
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else if (nbP != 0) Ok=LineTool::D1(SSP, U0, TabV);
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else Ok=LineTool::D1(SSP, U0, TabV2d);
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if (!Ok) myFirstC = AppParCurves_PassPoint;
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}
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if (myLastC == AppParCurves_TangencyPoint) {
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if (nbP != 0 && nbP2d != 0) Ok=LineTool::D1(SSP, U1, TabV, TabV2d);
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else if (nbP != 0) Ok=LineTool::D1(SSP, U1, TabV);
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else Ok=LineTool::D1(SSP, U1, TabV2d);
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if (!Ok) myLastC = AppParCurves_PassPoint;
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}
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math_Vector GaussP(1, NbPoints), GaussW(1, NbPoints);
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math::GaussPoints(NbPoints, GaussP);
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math::GaussWeights(NbPoints, GaussW);
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math_Vector TheWeights(1, NbPoints), VBParam(1, NbPoints);
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dU = 0.5*(U1-U0);
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// calcul et mise en ordre des parametres et des poids:
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for (i = FirstP; i <= LastP; i++) {
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U = 0.5*(U1+U0) + dU*GaussP(i);
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if (i <= (NbPoints+1)/2) {
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myParam(LastP-i+1) = U;
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VBParam(LastP-i+1) = 0.5*(1 + GaussP(i));
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TheWeights(LastP-i+1) = 0.5*GaussW(i);
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}
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else {
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VBParam(i-(NbPoints+1)/2) = 0.5*(1 + GaussP(i));
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myParam(i-(NbPoints+1)/2) = U;
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TheWeights(i-(NbPoints+1)/2) = 0.5*GaussW(i);
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}
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}
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for (i = FirstP; i <= LastP; i++) {
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U = myParam(i);
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if (nbP != 0 && nbP2d != 0) LineTool::Value(SSP, U, TabP, TabP2d);
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else if (nbP != 0) LineTool::Value(SSP, U, TabP);
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else LineTool::Value(SSP, U, TabP2d);
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i2 = 1;
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for (j = 1; j <= nbP; j++) {
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(TabP(j)).Coord(Points(i, i2), Points(i, i2+1), Points(i, i2+2));
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i2 += 3;
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}
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for (j = 1; j <= nbP2d; j++) {
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(TabP2d(j)).Coord(Points(i, i2), Points(i, i2+1));
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i2 += 2;
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}
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}
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// Calcul du VB ( Valeur des fonctions de Bernstein):
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// for (i = 1; i <= classe; i++) {
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// for (j = 1; j <= NbPoints; j++) {
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// VB(i,j)=PLib::Binomial(cl1,i-1)*Pow((1-VBParam(j)),classe-i)*
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// Pow(VBParam(j),i-1);
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// }
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// }
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VBernstein(classe, NbPoints, VB);
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// Traitement du second membre:
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Standard_Real *tmppoints, *tmpbis;
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tmppoints = new Standard_Real[nbcol];
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for (c = 1; c <= classe; c++) {
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tmpbis = tmppoints;
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for (k = 1; k <= nbcol; k++, tmpbis++) {
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*tmpbis = 0.0;
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}
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for (i = 1; i <= NbPoints; i++) {
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Coeff = TheWeights(i)*VB(c, i);
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tmpbis = tmppoints;
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for (j = 1; j <= nbcol; j++, tmpbis++) {
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*tmpbis += Points(i, j)*Coeff;
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//B(c, j) += Points(i, j)*Coeff;
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}
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}
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tmpbis = tmppoints;
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for (k = 1; k <= nbcol; k++, tmpbis++) {
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B(c, k) += *tmpbis;
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}
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}
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delete [] tmppoints;
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if (myFirstC == AppParCurves_NoConstraint &&
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myLastC == AppParCurves_NoConstraint) {
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math_Matrix InvM(1, classe, 1, classe);
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InvMMatrix(classe, InvM);
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// Calcul direct des poles:
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for (i = 1; i <= classe; i++) {
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for (j = 1; j <= classe; j++) {
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IBij = InvM(i, j);
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for (k = 1; k <= nbcol; k++) {
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Poles(i, k) += IBij * B(j, k);
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}
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}
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}
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}
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else {
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math_Matrix M(1, classe, 1, classe);
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MMatrix(classe, M);
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if (myFirstC == AppParCurves_PassPoint ||
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myFirstC == AppParCurves_TangencyPoint) {
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if (nbP != 0 && nbP2d != 0) LineTool::Value(SSP, U0, TabP, TabP2d);
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else if (nbP != 0) LineTool::Value(SSP, U0, TabP);
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else LineTool::Value(SSP, U0, TabP2d);
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i2 =1;
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for (k = 1; k<= nbP; k++) {
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(TabP(k)).Coord(Poles(1, i2), Poles(1, i2+1), Poles(1, i2+2));
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i2 += 3;
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}
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for (k = 1; k<= nbP2d; k++) {
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(TabP2d(k)).Coord(Poles(1, i2), Poles(1, i2+1));
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i2 += 2;
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}
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}
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if (myLastC == AppParCurves_PassPoint ||
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myLastC == AppParCurves_TangencyPoint) {
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i2 = 1;
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if (nbP != 0 && nbP2d != 0) LineTool::Value(SSP, U1, TabP, TabP2d);
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else if (nbP != 0) LineTool::Value(SSP, U1, TabP);
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else LineTool::Value(SSP, U1, TabP2d);
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for (k = 1; k<= nbP; k++) {
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(TabP(k)).Coord(Poles(classe,i2),
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Poles(classe,i2+1),
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Poles(classe,i2+2));
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i2 += 3;
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}
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for (k = 1; k<= nbP2d; k++) {
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(TabP2d(k)).Coord(Poles(classe, i2), Poles(classe, i2+1));
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i2 += 2;
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}
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}
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if (myFirstC == AppParCurves_PassPoint) {
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bdeb = 2;
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// mise a jour du second membre:
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for (i = 1; i <= classe; i++) {
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Coeff = M(i, 1);
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for (k = 1; k <= nbcol; k++) {
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B(i, k) -= Poles(1, k)*Coeff;
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}
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}
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}
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if (myLastC == AppParCurves_PassPoint) {
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bfin = cl1;
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for (i = 1; i <= classe; i++) {
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Coeff = M(i, classe);
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for (k = 1; k <= nbcol; k++) {
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B(i, k) -= Poles(classe, k)*Coeff;
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}
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}
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}
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if (myFirstC == AppParCurves_TangencyPoint) {
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// On fixe le second pole::
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bdeb = 3;
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if (nbP != 0 && nbP2d != 0) LineTool::D1(SSP, U0, TabV, TabV2d);
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else if (nbP != 0) LineTool::D1(SSP, U0, TabV);
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else LineTool::D1(SSP, U0, TabV2d);
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i2 = 1;
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Coeff = (U1-U0)/Degre;
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for (k = 1; k<= nbP; k++) {
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i2plus1 = i2+1; i2plus2 = i2+2;
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Poles(2, i2) = Poles(1, i2) + TabV(k).X()*Coeff;
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Poles(2, i2plus1) = Poles(1, i2plus1) + TabV(k).Y()*Coeff;
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Poles(2, i2plus2) = Poles(1, i2plus2) + TabV(k).Z()*Coeff;
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i2 += 3;
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}
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for (k = 1; k<= nbP2d; k++) {
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i2plus1 = i2+1;
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Poles(2, i2) = Poles(1, i2) + TabV2d(k).X()*Coeff;
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Poles(2, i2plus1) = Poles(1, i2plus1) + TabV2d(k).Y()*Coeff;
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i2 += 2;
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}
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for (i = 1; i <= classe; i++) {
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Coeff = M(i, 1); Coeff2 = M(i, 2);
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for (k = 1; k <= nbcol; k++) {
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B(i, k) -= Poles(1, k)*Coeff+Poles(2, k)*Coeff2;
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}
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}
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}
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if (myLastC == AppParCurves_TangencyPoint) {
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bfin = classe-2;
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if (nbP != 0 && nbP2d != 0) LineTool::D1(SSP, U1, TabV, TabV2d);
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else if (nbP != 0) LineTool::D1(SSP, U1, TabV);
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else LineTool::D1(SSP, U1, TabV2d);
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i2 = 1;
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Coeff = (U1-U0)/Degre;
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for (k = 1; k<= nbP; k++) {
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i2plus1 = i2+1; i2plus2 = i2+2;
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Poles(cl1,i2) = Poles(classe, i2) - TabV(k).X()*Coeff;
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Poles(cl1,i2plus1) = Poles(classe, i2plus1) - TabV(k).Y()*Coeff;
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Poles(cl1,i2plus2) = Poles(classe, i2plus2) - TabV(k).Z()*Coeff;
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i2 += 3;
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}
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for (k = 1; k<= nbP2d; k++) {
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i2plus1 = i2+1;
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Poles(cl1,i2) = Poles(classe, i2) - TabV2d(k).X()*Coeff;
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Poles(cl1,i2plus1) = Poles(classe, i2plus1) - TabV2d(k).Y()*Coeff;
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i2 += 2;
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}
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for (i = 1; i <= classe; i++) {
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Coeff = M(i, classe); Coeff2 = M(i, cl1);
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for (k = 1; k <= nbcol; k++) {
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B(i, k) -= Poles(classe, k)*Coeff + Poles(cl1, k)*Coeff2;
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}
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}
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}
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if (bdeb <= bfin) {
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math_Matrix B2(bdeb, bfin, 1, B.UpperCol(), 0.0);
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for (i = bdeb; i <= bfin; i++) {
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for (j = 1; j <= classe; j++) {
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Coeff = M(i, j);
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for (k = 1; k <= nbcol; k++) {
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B2(i, k) += B(j, k)*Coeff;
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}
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}
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}
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// Resolution:
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// ===========
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math_Matrix IBP(bdeb, bfin, bdeb, bfin);
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// dans IBPMatrix at IBTMatrix ne sont stockees que les resultats pour
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// une classe inferieure ou egale a 26 (pour l instant du moins.)
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if (bdeb == 2 && bfin == classe-1 && classe <= 26) {
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IBPMatrix(classe, IBP);
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}
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else if (bdeb == 3 && bfin == classe-2 && classe <= 26) {
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IBTMatrix(classe, IBP);
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}
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else {
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math_Matrix MP(1, classe, bdeb, bfin);
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for (i = 1; i <= classe; i++) {
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for (j = bdeb; j <= bfin; j++) {
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MP(i, j) = M(i, j);
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}
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}
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math_Matrix IBP1(bdeb, bfin, bdeb, bfin);
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IBP1 = MP.Transposed()*MP;
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IBP = IBP1.Inverse();
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}
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Done = Standard_True;
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for (i = bdeb; i <= bfin; i++) {
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for (j = bdeb; j <= bfin; j++) {
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IBPij = IBP(i, j);;
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for (k = 1; k<= nbcol; k++) {
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Poles(i, k) += IBPij * B2(j, k);
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}
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}
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}
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}
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}
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}
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//=======================================================================
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//function : NbBColumns
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//purpose :
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//=======================================================================
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Standard_Integer AppCont_LeastSquare::NbBColumns(
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const MultiLine& SSP) const
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{
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Standard_Integer BCol;
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BCol = (LineTool::NbP3d(SSP))*3 +
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(LineTool::NbP2d(SSP))*2;
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return BCol;
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}
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//=======================================================================
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//function : Value
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//purpose :
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//=======================================================================
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const AppParCurves_MultiCurve& AppCont_LeastSquare::Value()
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{
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Standard_Integer i, j, j2;
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gp_Pnt Pt;
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gp_Pnt2d Pt2d;
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Standard_Integer ideb = 1, ifin = Degre+1;
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// On met le resultat dans les curves correspondantes
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for (i = ideb; i <= ifin; i++) {
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j2 = 1;
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AppParCurves_MultiPoint MPole(nbP, nbP2d);
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for (j = 1; j <= nbP; j++) {
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Pt.SetCoord(Poles(i, j2), Poles(i, j2+1), Poles(i,j2+2));
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MPole.SetPoint(j, Pt);
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j2 += 3;
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}
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for (j = nbP+1;j <= nbP+nbP2d; j++) {
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Pt2d.SetCoord(Poles(i, j2), Poles(i, j2+1));
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MPole.SetPoint2d(j, Pt2d);
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j2 += 2;
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}
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SCU.SetValue(i, MPole);
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}
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return SCU;
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}
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//=======================================================================
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//function : Error
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//purpose :
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//=======================================================================
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void AppCont_LeastSquare::Error(Standard_Real& F,
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Standard_Real& MaxE3d,
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Standard_Real& MaxE2d) const
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{
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Standard_Integer i, j, k, c, i2, classe = Degre+1;
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// Standard_Real Coeff, val = 0.0, err3d = 0.0, err2d =0.0;
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Standard_Real Coeff, err3d = 0.0, err2d =0.0;
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Standard_Integer ncol = Points.UpperCol()-Points.LowerCol()+1;
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math_Matrix MyPoints(1, Nbdiscret, 1, ncol);
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MyPoints = Points;
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MaxE3d = MaxE2d = F = 0.0;
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Standard_Real *tmppoles, *tmpbis;
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tmppoles = new Standard_Real[ncol];
|
|
|
|
for (c = 1; c <= classe; c++) {
|
|
tmpbis = tmppoles;
|
|
for (k = 1; k <= ncol; k++, tmpbis++) {
|
|
*tmpbis = Poles(c, k);
|
|
}
|
|
for (i = 1; i <= Nbdiscret; i++) {
|
|
Coeff = VB(c, i);
|
|
tmpbis = tmppoles;
|
|
for (j = 1; j <= ncol; j++, tmpbis++) {
|
|
MyPoints(i, j) -= (*tmpbis)*Coeff; // Poles(c, j)*Coeff;
|
|
}
|
|
}
|
|
}
|
|
delete [] tmppoles;
|
|
|
|
Standard_Real e1, e2, e3;
|
|
for (i = 1; i <= Nbdiscret; i++) {
|
|
i2 = 1;
|
|
for (j = 1; j<= nbP; 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<= nbP2d; 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 Done;
|
|
}
|