src/ApproxInt/ApproxInt_Approx.gxx

   1 // Created on: 1993-03-30
   2 // Created by: Laurent BUCHARD
   3 // Copyright (c) 1993-1999 Matra Datavision
   4 // Copyright (c) 1999-2014 OPEN CASCADE SAS
   5 //
   6 // This file is part of Open CASCADE Technology software library.
   7 //
   8 // This library is free software; you can redistribute it and/or modify it under
   9 // the terms of the GNU Lesser General Public License version 2.1 as published
  10 // by the Free Software Foundation, with special exception defined in the file
  11 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
  12 // distribution for complete text of the license and disclaimer of any warranty.
  13 //
  14 // Alternatively, this file may be used under the terms of Open CASCADE
  15 // commercial license or contractual agreement.
  16
  17 #include <AppParCurves_Constraint.hxx>
  18 #include <GeomAbs_SurfaceType.hxx>
  19 #include <IntSurf_Quadric.hxx>
  20 #include <gp_Trsf.hxx>
  21 #include <gp_Trsf2d.hxx>
  22 #include <IntSurf_PntOn2S.hxx>
  23 #include <Precision.hxx>
  24
  25 const Standard_Integer LimRajout = 5;
  26 const Standard_Integer NbPntMaxDecoupage = 30 ;
  27 const Standard_Real RatioTol = 1.5 ;
  28
  29 static Standard_Real MINABS3(Standard_Real a, Standard_Real b,Standard_Real c) {
  30   if(a<0.0) a=-a;
  31   if(b<0.0) b=-b;
  32   if(c<0.0) c=-c;
  33   if(a>c) a=c;
  34   if(a>b) a=b;
  35   return(a);
  36 }
  37
  38 static Standard_Real MINABS4(Standard_Real a, Standard_Real b,Standard_Real c,Standard_Real d) {
  39   if(a<0.0) a=-a;
  40   if(b<0.0) b=-b;
  41   if(c<0.0) c=-c;
  42   if(d<0.0) d=-d;
  43   if(a>c) a=c;
  44   if(a>b) a=b;
  45   if(a>d) a=d;
  46   return(a);
  47 }
  48
  49 static void  ComputeTrsf3d(const Handle(TheWLine)& theline,
  50                            Standard_Real& Xo, Standard_Real& Ax,
  51                            Standard_Real& Yo, Standard_Real& Ay,
  52                            Standard_Real& Zo, Standard_Real& Az) {
  53
  54   Standard_Integer nbp = theline->NbPnts();
  55   Standard_Real z0,z1,x0,x1,y0,y1;
  56   z0=y0=x0=RealLast();
  57   z1=y1=x1=RealFirst();
  58   for(Standard_Integer i=1;i<=nbp;i++) {
  59     const gp_Pnt& P = theline->Point(i).Value();
  60     Standard_Real  X = P.X();
  61     Standard_Real  Y = P.Y();
  62     Standard_Real  Z = P.Z();
  63     if(X<x0) x0=X;
  64     if(X>x1) x1=X;
  65     if(Y<y0) y0=Y;
  66     if(Y>y1) y1=Y;
  67     if(Z<z0) z0=Z;
  68     if(Z>z1) z1=Z;
  69   }
  70 //-deb-  cout << "ComputeTrsf3d -- NbPnt = " << nbp << endl ;
  71 //-deb-  cout << "ComputeTrsf3d -- Xm = " << x0 << " Ym = " << y0 << " Zm = " << z0 << endl ;
  72 //-deb-  cout << "ComputeTrsf3d -- XM = " << x1 << " YM = " << y1 << " ZM = " << z1 << endl ;
  73   Standard_Real dx = x1-x0;
  74   Standard_Real dy = y1-y0;
  75   Standard_Real dz = z1-z0;
  76   Standard_Real MaxD = dx;
  77   if(MaxD < dy) MaxD=dy;
  78   if(MaxD < dz) MaxD=dz;
  79   Standard_Real MaxDF = 0.01*MaxD;
  80
  81   //-- lbr le 22 fev99 : FPE
  82   if(MaxDF<1e-12)
  83     MaxDF=1.0;
  84
  85
  86   if(dx > MaxDF) { Ax = 1.0 / dx;    Xo = -Ax * x0;  }
  87   else {     Ax = 1.0/( MaxDF) ; Xo = -Ax*x0;   }
  88   if(dy > MaxDF) { Ay = 1.0 / dy;    Yo = -Ay * y0;  }
  89   else {     Ay = 1.0/( MaxDF); Yo = -Ay*y0;   }
  90   if(dz > MaxDF) { Az = 1.0 / dz;    Zo = -Az * z0;     }
  91   else {     Az = 1.0/(MaxDF); Zo = -Az*z0;   }
  92 }
  93
  94 static void  ComputeTrsf2d(const Handle(TheWLine)& theline,
  95                            Standard_Real& Uo, Standard_Real& Au,
  96                            Standard_Real& Vo, Standard_Real& Av,
  97                            const Standard_Boolean onFirst,
  98                            const Standard_Real UVResRatio = 1.) {
  99   Standard_Integer nbp = theline->NbPnts();
 100   Standard_Real u0,u1,v0,v1;
 101   u0 = v0 = RealLast();
 102   u1 = v1 = RealFirst();
 103   // pointer to a member-function
 104   void (IntSurf_PntOn2S::* pfunc)(Standard_Real&,Standard_Real&) const;
 105   if (onFirst)
 106     pfunc = &IntSurf_PntOn2S::ParametersOnS1;
 107   else
 108     pfunc = &IntSurf_PntOn2S::ParametersOnS2;
 109   for(Standard_Integer i=1;i<=nbp;i++) {
 110     const IntSurf_PntOn2S&  POn2S = theline->Point(i);
 111     Standard_Real  U,V;
 112     (POn2S.*pfunc)(U,V);
 113     if(U<u0) u0=U;
 114     if(U>u1) u1=U;
 115     if(V<v0) v0=V;
 116     if(V>v1) v1=V;
 117   }
 118
 119   Standard_Real du = (u1-u0);
 120   Standard_Real dv = (v1-v0);
 121
 122   if (UVResRatio > 1.)
 123     du *= UVResRatio;
 124   else if (UVResRatio < 1.)
 125     dv /= UVResRatio;
 126
 127   Standard_Real MaxUV=du;
 128   if(MaxUV<dv) MaxUV=dv;
 129
 130   Standard_Real MaxUVF=0.01*MaxUV;
 131
 132   //-- lbr le 22 fev 99 (FPE)
 133   if(MaxUVF<1e-12)
 134     MaxUVF=1.0;
 135
 136   if(du > MaxUVF) { Au = 1.0 / du;    Uo = -Au * u0;  }
 137   else {     Au = 1.0/(MaxUVF); Uo = -Au*u0;  }
 138   if(dv > MaxUVF) { Av = 1.0 / dv;    Vo = -Av * v0;  }
 139   else {     Av = 1.0/(MaxUVF); Vo = -Av*v0;  }
 140 }
 141
 142
 143
 144 ApproxInt_Approx::ApproxInt_Approx():
 145        myComputeLine(4,
 146                      8,
 147                      0.001,
 148                      0.001,
 149                      5,
 150                      Standard_True),
 151        myComputeLineBezier(4,
 152                            8,
 153                            0.001,
 154                            0.001,
 155                            5,
 156                            Standard_True)
 157 {
 158   myComputeLine.SetContinuity(2);
 159   //-- myComputeLineBezier.SetContinuity(2);
 160   myApproxBez = Standard_True;
 161
 162   myRelativeTol = Standard_True ;
 163   myNbPntMax = NbPntMaxDecoupage ;
 164   myMinFactorXYZ = 0.0;
 165   myMinFactorUV  = 0.0;
 166   myTolReached3d = myTolReached2d = 0.;
 167 }
 168
 169
 170 void ApproxInt_Approx::Perform(const Handle(TheWLine)& theline,
 171                                const Standard_Boolean ApproxXYZ,
 172                                const Standard_Boolean ApproxU1V1,
 173                                const Standard_Boolean ApproxU2V2,
 174                                const Standard_Integer indicemin,
 175                                const Standard_Integer indicemax) {
 176
 177   myMinFactorXYZ = 0.0;
 178   myMinFactorUV  = 0.0;
 179   myTolReached3d = myTolReached2d = 0.;
 180
 181
 182   Standard_Integer nbpntbez = indicemax-indicemin;
 183   Standard_Integer nbpntmax = myNbPntMax;
 184   Standard_Boolean OtherInter = Standard_False;
 185   if(nbpntbez < LimRajout)
 186     myApproxBez = Standard_False;
 187   else
 188     myApproxBez = Standard_True;
 189   if(myApproxBez) {
 190     myBezToBSpl.Reset();
 191     Standard_Integer nbi = (indicemax-indicemin)/nbpntmax;
 192     if(nbi>1)  {
 193       nbpntbez = (indicemax-indicemin)/nbi;
 194     }
 195   }
 196   Standard_Integer imin = indicemin;
 197   Standard_Integer imax = imin + nbpntbez;
 198   myTolReached = Standard_True;
 199
 200   Standard_Real Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v;
 201   if(ApproxXYZ) {
 202     ComputeTrsf3d(theline,Xo,Ax,Yo,Ay,Zo,Az);
 203   }
 204   else {
 205     Xo=Yo=Zo=0.0; Ax=Ay=Az=1.0;;
 206   }
 207   if(ApproxU1V1) {
 208     ComputeTrsf2d(theline,U1o,A1u,V1o,A1v,Standard_True);
 209   }
 210   else {
 211     U1o=V1o=0.0; A1u=A1v=1.0;
 212   }
 213   if(ApproxU2V2) {
 214     ComputeTrsf2d(theline,U2o,A2u,V2o,A2v,Standard_False);
 215   }
 216   else {
 217     U2o=V2o=0.0; A2u=A2v=1.0;
 218   }
 219
 220   //-deb-  cout << "ApproxInt_Approx -- NbPntMax = " << myNbPntMax    << endl ;
 221   //-deb-  cout << "ApproxInt_Approx -- Tol3D    = " << myTol3d       << endl ;
 222   //-deb-  cout << "ApproxInt_Approx -- Tol2D    = " << myTol2d       << endl ;
 223   //-deb-  cout << "ApproxInt_Approx -- RelTol   = " << (myRelativeTol ? "RELATIVE" : "ABSOLUTE") << endl ;
 224   //-deb-  cout << "ApproxInt_Approx -- Xo = " << Xo << " Yo = " << Yo << " Zo = " << Zo << endl ;
 225   //-deb-  cout << "ApproxInt_Approx -- Ax = " << Ax << " Ay = " << Ay << " Az = " << Az << endl ;
 226   //-deb-  cout << "ApproxInt_Approx -- U1o = " << U1o << " V1o = " << V1o << " A1u = " << A1u << " A1v = " << A1v << endl ;
 227   //-deb-  cout << "ApproxInt_Approx -- U2o = " << U2o << " V2o = " << V2o << " A2u = " << A2u << " A2v = " << A2v << endl ;
 228
 229   Standard_Real A3d = MINABS3(Ax,Ay,Az);
 230   if((A3d < myMinFactorXYZ) || (myMinFactorXYZ == 0.0)) {
 231     myMinFactorXYZ = A3d;
 232   }
 233
 234   Standard_Real A2d = MINABS4(A1u,A1v,A2u,A2v);
 235   if((A2d < myMinFactorUV) || (myMinFactorUV == 0.0)) {
 236     myMinFactorUV = A2d;
 237   }
 238
 239   Standard_Boolean cut=Standard_True;
 240   Approx_ParametrizationType parametrization;
 241   myComputeLineBezier.Parametrization(parametrization);
 242
 243   if(myRelativeTol==Standard_False) {
 244
 245     myComputeLine.Init(myDegMin,
 246                        myDegMax,
 247                        myTol3d*myMinFactorXYZ,
 248                        myTol2d*myMinFactorUV,
 249                        myNbIterMax,
 250                        cut,
 251                        parametrization);
 252     myComputeLineBezier.Init(myDegMin,
 253                              myDegMax,
 254                              myTol3d*myMinFactorXYZ,
 255                              myTol2d*myMinFactorUV,
 256                              myNbIterMax,
 257                              cut,
 258                              parametrization);
 259   }
 260
 261   do {
 262     ApproxInt_TheMultiLine myMultiLine(theline,
 263                                        ((ApproxXYZ)? 1 : 0),
 264                                        ((ApproxU1V1)? 1: 0) + ((ApproxU2V2)? 1: 0),
 265                                        Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v,
 266                                        ApproxU1V1,
 267                                        imin,
 268                                        imax);
 269
 270     if(myApproxBez) {
 271       myComputeLineBezier.Perform(myMultiLine);
 272       if (myComputeLineBezier.NbMultiCurves() == 0)
 273         return;
 274       myTolReached&=myComputeLineBezier.IsToleranceReached();
 275     }
 276     else {
 277       myComputeLine.Perform(myMultiLine);
 278     }
 279     UpdateTolReached();
 280
 281     Standard_Integer indice3d,indice2d1,indice2d2;
 282     indice3d = 1;
 283     indice2d1= 2;
 284     indice2d2= 3;
 285     if(!ApproxXYZ)  { indice2d1--; indice2d2--; }
 286     if(!ApproxU1V1) { indice2d2--; }
 287     if(ApproxXYZ) {
 288       Standard_Real ax,bx,ay,by,az,bz;
 289       ax = 1.0/Ax;   bx = -Xo*ax;
 290       ay = 1.0/Ay;   by = -Yo*ay;
 291       az = 1.0/Az;   bz = -Zo*az;
 292       if(myApproxBez) {
 293         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 294           myComputeLineBezier.ChangeValue(nbmc).Transform(indice3d,bx,ax,by,ay,bz,az);
 295         }
 296       }
 297       else {
 298         myComputeLine.ChangeValue().Transform(indice3d,bx,ax,by,ay,bz,az);
 299       }
 300     }
 301     if(ApproxU1V1) {
 302       Standard_Real ax,bx,ay,by;
 303       ax = 1.0/A1u;   bx = -U1o*ax;
 304       ay = 1.0/A1v;   by = -V1o*ay;
 305       if(myApproxBez) {
 306         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 307           myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d1,bx,ax,by,ay);
 308         }
 309       }
 310       else {
 311         myComputeLine.ChangeValue().Transform2d(indice2d1,bx,ax,by,ay);
 312       }
 313     }
 314     if(ApproxU2V2) {
 315       Standard_Real ax,bx,ay,by;
 316       ax = 1.0/A2u;   bx = -U2o*ax;
 317       ay = 1.0/A2v;   by = -V2o*ay;
 318       if(myApproxBez) {
 319         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 320           myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d2,bx,ax,by,ay);
 321         }
 322       }
 323       else {
 324         myComputeLine.ChangeValue().Transform2d(indice2d2,bx,ax,by,ay);
 325       }
 326     }
 327
 328     OtherInter = Standard_False;
 329     if(myApproxBez) {
 330       for(Standard_Integer nbmc = 1;
 331           nbmc <= myComputeLineBezier.NbMultiCurves() ;
 332           nbmc++) {
 333         myBezToBSpl.Append(myComputeLineBezier.Value(nbmc));
 334       }
 335       if(imax<indicemax) {
 336         imin = imax;
 337         imax = imin+nbpntbez;
 338         OtherInter = Standard_True;
 339         if((indicemax-imax)<(nbpntbez/2)) {
 340           imax = indicemax;
 341         }
 342       }
 343     }
 344   }
 345   while(OtherInter);
 346   if(myApproxBez) {
 347     myBezToBSpl.Perform();
 348   }
 349 }
 350
 351 void ApproxInt_Approx::Perform(const ThePSurface& Surf1,
 352                                const ThePSurface& Surf2,
 353                                const Handle(TheWLine)& theline,
 354                                const Standard_Boolean ApproxXYZ,
 355                                const Standard_Boolean ApproxU1V1,
 356                                const Standard_Boolean ApproxU2V2,
 357                                const Standard_Integer indicemin,
 358                                const Standard_Integer indicemax) {
 359   myMinFactorXYZ = 0.0;
 360   myMinFactorUV  = 0.0;
 361   myTolReached3d = myTolReached2d = 0.;
 362
 363   GeomAbs_SurfaceType typeS1 = ThePSurfaceTool::GetType(Surf1);
 364   GeomAbs_SurfaceType typeS2 = ThePSurfaceTool::GetType(Surf2);
 365   if ((typeS1 != GeomAbs_Plane    &&
 366        typeS1 != GeomAbs_Cylinder &&
 367        typeS1 != GeomAbs_Sphere   &&
 368        typeS1 != GeomAbs_Cone)
 369       &&
 370       (typeS2 != GeomAbs_Plane    &&
 371        typeS2 != GeomAbs_Cylinder &&
 372        typeS2 != GeomAbs_Sphere   &&
 373        typeS2 != GeomAbs_Cone)) {
 374
 375     //------------------------------------------------------------
 376     //-- Construction du SvSurfaces
 377     //------------------------------------------------------------
 378     ApproxInt_ThePrmPrmSvSurfaces myPrmPrmSvSurfaces(Surf1,Surf2);
 379     //------------------------------------------------------------
 380     //-- Construction de la MultiLine
 381     //------------------------------------------------------------
 382     Standard_Integer nbpntbez = indicemax-indicemin;
 383     Standard_Integer nbpntmax = myNbPntMax;
 384     Standard_Boolean OtherInter = Standard_False;
 385
 386     if(nbpntbez < LimRajout)
 387       myApproxBez = Standard_False;
 388     else
 389       myApproxBez = Standard_True;
 390
 391     Standard_Address ptrsvsurf = NULL;
 392     Standard_Boolean cut = Standard_True;
 393     if(nbpntbez < LimRajout) {
 394       cut = Standard_False;
 395       //-- cout<<" ApproxInt : Nb de points = "<<nbpntbez<<" Pas de rajout "<<endl;
 396     }
 397     ptrsvsurf = &myPrmPrmSvSurfaces;
 398
 399
 400     if(myApproxBez) {
 401       myBezToBSpl.Reset();
 402       Standard_Integer nbi = (indicemax-indicemin)/nbpntmax;
 403       if(nbi>1)  {
 404         nbpntbez = (indicemax-indicemin)/nbi;
 405       }
 406     }
 407     Standard_Integer imin = indicemin;
 408     Standard_Integer imax = imin + nbpntbez;
 409     myTolReached = Standard_True;
 410
 411
 412     Standard_Real Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v;
 413     if(ApproxXYZ) {
 414       ComputeTrsf3d(theline,Xo,Ax,Yo,Ay,Zo,Az);
 415     }
 416     else {
 417       Xo=Yo=Zo=0.0; Ax=Ay=Az=1.0;;
 418     }
 419     if(ApproxU1V1) {
 420       Standard_Real UVResRatio = ThePSurfaceTool::UResolution(Surf1,1.)/
 421                                  ThePSurfaceTool::VResolution(Surf1,1.);
 422       ComputeTrsf2d(theline,U1o,A1u,V1o,A1v,Standard_True,UVResRatio);
 423     }
 424     else {
 425       U1o=V1o=0.0; A1u=A1v=1.0;
 426     }
 427     if(ApproxU2V2) {
 428       Standard_Real UVResRatio = ThePSurfaceTool::UResolution(Surf2,1.)/
 429                                  ThePSurfaceTool::VResolution(Surf2,1.);
 430       ComputeTrsf2d(theline,U2o,A2u,V2o,A2v,Standard_False,UVResRatio);
 431     }
 432     else {
 433       U2o=V2o=0.0; A2u=A2v=1.0;
 434     }
 435
 436 //-deb-  cout << "ApproxInt_Approx -- NbPntMax = " << myNbPntMax    << endl ;
 437 //-deb-  cout << "ApproxInt_Approx -- Tol3D    = " << myTol3d       << endl ;
 438 //-deb-  cout << "ApproxInt_Approx -- Tol2D    = " << myTol2d       << endl ;
 439 //-deb-  cout << "ApproxInt_Approx -- RelTol   = " << (myRelativeTol ? "RELATIVE" : "ABSOLUTE") << endl ;
 440 //-deb-  cout << "ApproxInt_Approx -- Xo = " << Xo << " Yo = " << Yo << " Zo = " << Zo << endl ;
 441 //-deb-  cout << "ApproxInt_Approx -- Ax = " << Ax << " Ay = " << Ay << " Az = " << Az << endl ;
 442 //-deb-  cout << "ApproxInt_Approx -- U1o = " << U1o << " V1o = " << V1o << " A1u = " << A1u << " A1v = " << A1v << endl ;
 443 //-deb-  cout << "ApproxInt_Approx -- U2o = " << U2o << " V2o = " << V2o << " A2u = " << A2u << " A2v = " << A2v << endl ;
 444
 445
 446     Standard_Real A3d = MINABS3(Ax,Ay,Az);
 447     if((A3d < myMinFactorXYZ) || (myMinFactorXYZ == 0.0)) {
 448       myMinFactorXYZ = A3d;
 449     }
 450
 451     Standard_Real A2d = MINABS4(A1u,A1v,A2u,A2v);
 452     if((A2d < myMinFactorUV) || (myMinFactorUV == 0.0)) {
 453       myMinFactorUV = A2d;
 454     }
 455
 456
 457     Approx_ParametrizationType parametrization;
 458     myComputeLineBezier.Parametrization(parametrization);
 459
 460     if(myRelativeTol==Standard_False) {
 461       myComputeLine.Init(myDegMin,
 462                          myDegMax,
 463                          myTol3d*myMinFactorXYZ,
 464                          myTol2d*myMinFactorUV,
 465                          myNbIterMax,
 466                          cut,
 467                          parametrization);
 468       myComputeLineBezier.Init(myDegMin,
 469                                myDegMax,
 470                                myTol3d*myMinFactorXYZ,
 471                                myTol2d*myMinFactorUV,
 472                                myNbIterMax,
 473                                cut,
 474                                parametrization);
 475     }
 476     else {
 477       myComputeLine.Init(myDegMin,
 478                          myDegMax,
 479                          myTol3d,
 480                          myTol2d,
 481                          myNbIterMax,
 482                          cut,
 483                          parametrization);
 484       myComputeLineBezier.Init(myDegMin,
 485                                myDegMax,
 486                                myTol3d,
 487                                myTol2d,
 488                                myNbIterMax,
 489                                cut,
 490                                parametrization);
 491     }
 492
 493
 494
 495
 496     do {
 497       ApproxInt_TheMultiLine myMultiLine(theline,
 498                                          ptrsvsurf,
 499                                          ((ApproxXYZ)? 1 : 0),
 500                                          ((ApproxU1V1)? 1: 0) + ((ApproxU2V2)? 1: 0),
 501                                          Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v,
 502                                          ApproxU1V1,
 503                                          imin,
 504                                          imax);
 505
 506       if(myApproxBez) {
 507         myComputeLineBezier.Perform(myMultiLine);
 508         if (myComputeLineBezier.NbMultiCurves() == 0)
 509           return;
 510         myTolReached&=myComputeLineBezier.IsToleranceReached();
 511       }
 512       else {
 513         myComputeLine.Perform(myMultiLine);
 514       }
 515       UpdateTolReached();
 516
 517       Standard_Integer indice3d,indice2d1,indice2d2;
 518       indice3d = 1;
 519       indice2d1= 2;
 520       indice2d2= 3;
 521       if(!ApproxXYZ)  { indice2d1--; indice2d2--; }
 522       if(!ApproxU1V1) { indice2d2--; }
 523       if(ApproxXYZ) {
 524         Standard_Real ax,bx,ay,by,az,bz;
 525         ax = 1.0/Ax;   bx = -Xo*ax;
 526         ay = 1.0/Ay;   by = -Yo*ay;
 527         az = 1.0/Az;   bz = -Zo*az;
 528         if(myApproxBez) {
 529           for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 530             myComputeLineBezier.ChangeValue(nbmc).Transform(indice3d,bx,ax,by,ay,bz,az);
 531           }
 532         }
 533         else {
 534           myComputeLine.ChangeValue().Transform(indice3d,bx,ax,by,ay,bz,az);
 535         }
 536       }
 537       if(ApproxU1V1) {
 538         Standard_Real ax,bx,ay,by;
 539         ax = 1.0/A1u;   bx = -U1o*ax;
 540         ay = 1.0/A1v;   by = -V1o*ay;
 541         if(myApproxBez) {
 542           for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 543             myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d1,bx,ax,by,ay);
 544           }
 545         }
 546         else {
 547           myComputeLine.ChangeValue().Transform2d(indice2d1,bx,ax,by,ay);
 548         }
 549       }
 550       if(ApproxU2V2) {
 551         Standard_Real ax,bx,ay,by;
 552         ax = 1.0/A2u;   bx = -U2o*ax;
 553         ay = 1.0/A2v;   by = -V2o*ay;
 554         if(myApproxBez) {
 555           for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 556             myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d2,bx,ax,by,ay);
 557           }
 558         }
 559         else {
 560           myComputeLine.ChangeValue().Transform2d(indice2d2,bx,ax,by,ay);
 561         }
 562       }
 563       OtherInter = Standard_False;
 564       if(myApproxBez) {
 565         for(Standard_Integer nbmc = 1;
 566           nbmc <= myComputeLineBezier.NbMultiCurves() ;
 567           nbmc++) {
 568           myBezToBSpl.Append(myComputeLineBezier.Value(nbmc));
 569         }
 570         if(imax<indicemax) {
 571           imin = imax;
 572           imax = imin+nbpntbez;
 573           OtherInter = Standard_True;
 574           if((indicemax-imax)<(nbpntbez/2)) {
 575             imax = indicemax;
 576           }
 577         }
 578       }
 579     }
 580     while(OtherInter);
 581     if(myApproxBez) {
 582       myBezToBSpl.Perform();
 583     }
 584
 585   }
 586   else {
 587     IntSurf_Quadric Quad;
 588     Standard_Boolean SecondIsImplicit=Standard_False;
 589     switch (typeS1) {
 590
 591     case GeomAbs_Plane:
 592       Quad.SetValue(ThePSurfaceTool::Plane(Surf1));
 593       break;
 594
 595     case GeomAbs_Cylinder:
 596       Quad.SetValue(ThePSurfaceTool::Cylinder(Surf1));
 597       break;
 598
 599     case GeomAbs_Sphere:
 600       Quad.SetValue(ThePSurfaceTool::Sphere(Surf1));
 601       break;
 602
 603     case GeomAbs_Cone:
 604       Quad.SetValue(ThePSurfaceTool::Cone(Surf1));
 605       break;
 606
 607     default:
 608       {
 609         SecondIsImplicit = Standard_True;
 610         switch (typeS2) {
 611         case GeomAbs_Plane:
 612           Quad.SetValue(ThePSurfaceTool::Plane(Surf2));
 613           break;
 614
 615         case GeomAbs_Cylinder:
 616           Quad.SetValue(ThePSurfaceTool::Cylinder(Surf2));
 617           break;
 618
 619         case GeomAbs_Sphere:
 620           Quad.SetValue(ThePSurfaceTool::Sphere(Surf2));
 621           break;
 622
 623         case GeomAbs_Cone:
 624           Quad.SetValue(ThePSurfaceTool::Cone(Surf2));
 625           break;
 626
 627         default:
 628           break;
 629         }
 630       }
 631       break;
 632     }
 633     if(SecondIsImplicit) {
 634       Perform(Surf1,Quad,theline,ApproxXYZ,ApproxU1V1,ApproxU2V2,indicemin,indicemax);
 635     }
 636     else {
 637       Perform(Quad,Surf2,theline,ApproxXYZ,ApproxU1V1,ApproxU2V2,indicemin,indicemax);
 638     }
 639   }
 640 }
 641 //--------------------------------------------------------------------------------
 642 void ApproxInt_Approx::SetParameters(const Standard_Real     Tol3d,
 643                                      const Standard_Real     Tol2d,
 644                                      const Standard_Integer  DegMin,
 645                                      const Standard_Integer  DegMax,
 646                                      const Standard_Integer  NbIterMax,
 647                                      const Standard_Boolean  ApproxWithTangency,
 648                                      const Approx_ParametrizationType Parametrization) {
 649   myWithTangency = ApproxWithTangency;
 650   myTol3d        = Tol3d / RatioTol;
 651   myTol2d        = Tol2d / RatioTol;
 652   myDegMin       = DegMin;
 653   myDegMax       = DegMax;
 654   myNbIterMax    = NbIterMax;
 655   myComputeLine.Init(myDegMin,
 656                      myDegMax,
 657                      myTol3d,
 658                      myTol2d,
 659                      myNbIterMax,
 660                      Standard_True,
 661                      Parametrization);
 662
 663   if(!ApproxWithTangency) {
 664     myComputeLine.SetConstraints(AppParCurves_PassPoint,AppParCurves_PassPoint);
 665   }
 666   myComputeLineBezier.Init(myDegMin,
 667                            myDegMax,
 668                            myTol3d,
 669                            myTol2d,
 670                            myNbIterMax,
 671                            Standard_True,
 672                            Parametrization);
 673   if(!ApproxWithTangency) {
 674     myComputeLineBezier.SetConstraints(AppParCurves_PassPoint,AppParCurves_PassPoint);
 675   }
 676   myApproxBez = Standard_True;
 677 }
 678
 679 void ApproxInt_Approx::SetParameters(const Standard_Real     Tol3d,
 680                                      const Standard_Real     Tol2d,
 681                                      const Standard_Boolean  RelativeTol,
 682                                      const Standard_Integer  DegMin,
 683                                      const Standard_Integer  DegMax,
 684                                      const Standard_Integer  NbIterMax,
 685                                      const Standard_Integer  NbPntMax,
 686                                      const Standard_Boolean  ApproxWithTangency,
 687                                      const Approx_ParametrizationType Parametrization)
 688 {
 689   myNbPntMax = NbPntMax ;
 690   myRelativeTol = RelativeTol ;
 691   SetParameters (Tol3d, Tol2d, DegMin, DegMax, NbIterMax, ApproxWithTangency, Parametrization) ;
 692 }
 693
 694 //--------------------------------------------------------------------------------
 695 void ApproxInt_Approx::Perform(const ThePSurface& PSurf,
 696                                const TheISurface& ISurf,
 697                                const Handle(TheWLine)& theline,
 698                                const Standard_Boolean ApproxXYZ,
 699                                const Standard_Boolean ApproxU1V1,
 700                                const Standard_Boolean ApproxU2V2,
 701                                const Standard_Integer indicemin,
 702                                const Standard_Integer indicemax)
 703 {
 704   myMinFactorXYZ = 0.0;
 705   myMinFactorUV  = 0.0;
 706   myTolReached3d = myTolReached2d = 0.;
 707
 708   ApproxInt_TheImpPrmSvSurfaces myImpPrmSvSurfaces(PSurf,ISurf);
 709   Standard_Integer nbpntbez = indicemax-indicemin;
 710   Standard_Integer nbpntmax = myNbPntMax;
 711   Standard_Boolean OtherInter = Standard_False;
 712   if(nbpntbez < LimRajout)
 713     myApproxBez = Standard_False;
 714   else
 715     myApproxBez = Standard_True;
 716
 717   Standard_Address ptrsvsurf = NULL;
 718   Standard_Boolean cut = Standard_True;
 719   if(nbpntbez < LimRajout) {
 720     cut = Standard_False;
 721     //-- cout<<" ApproxInt : Nb de points = "<<nbpntbez<<" Pas de rajout "<<endl;
 722   }
 723
 724
 725   Approx_ParametrizationType parametrization;
 726   myComputeLineBezier.Parametrization(parametrization);
 727
 728
 729   ptrsvsurf = &myImpPrmSvSurfaces;
 730   myComputeLine.Init(myDegMin,
 731                      myDegMax,
 732                      myTol3d,
 733                      myTol2d,
 734                      myNbIterMax,
 735                      cut,
 736                      parametrization);
 737
 738   myComputeLineBezier.Init(myDegMin,
 739                            myDegMax,
 740                            myTol3d,
 741                            myTol2d,
 742                            myNbIterMax,
 743                            cut,
 744                            parametrization);
 745   if(myApproxBez) {
 746     myBezToBSpl.Reset();
 747     Standard_Integer nbi = (indicemax-indicemin)/nbpntmax;
 748     if(nbi>1)  {
 749       nbpntbez = (indicemax-indicemin)/nbi;
 750     }
 751   }
 752   Standard_Integer imin = indicemin;
 753   Standard_Integer imax = imin + nbpntbez;
 754   myTolReached = Standard_True;
 755   Standard_Real Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v;
 756   if(ApproxXYZ) {
 757     ComputeTrsf3d(theline,Xo,Ax,Yo,Ay,Zo,Az);
 758   }
 759   else {
 760     Xo=Yo=Zo=0.0; Ax=Ay=Az=1.0;;
 761   }
 762   if(ApproxU1V1) {
 763     Standard_Real UVResRatio = ThePSurfaceTool::UResolution(PSurf,1.)/
 764                                ThePSurfaceTool::VResolution(PSurf,1.);
 765     ComputeTrsf2d(theline,U1o,A1u,V1o,A1v,Standard_True,UVResRatio);
 766   }
 767   else {
 768     U1o=V1o=0.0; A1u=A1v=1.0;
 769   }
 770   if(ApproxU2V2) {
 771     ComputeTrsf2d(theline,U2o,A2u,V2o,A2v,Standard_False);
 772   }
 773   else {
 774     U2o=V2o=0.0; A2u=A2v=1.0;
 775   }
 776
 777   //-deb-  cout << "ApproxInt_Approx -- NbPntMax = " << myNbPntMax    << endl ;
 778   //-deb-  cout << "ApproxInt_Approx -- Tol3D    = " << myTol3d       << endl ;
 779   //-deb-  cout << "ApproxInt_Approx -- Tol2D    = " << myTol2d       << endl ;
 780   //-deb-  cout << "ApproxInt_Approx -- RelTol   = " << (myRelativeTol ? "RELATIVE" : "ABSOLUTE") << endl ;
 781   //-deb-  cout << "ApproxInt_Approx -- Xo = " << Xo << " Yo = " << Yo << " Zo = " << Zo << endl ;
 782   //-deb-  cout << "ApproxInt_Approx -- Ax = " << Ax << " Ay = " << Ay << " Az = " << Az << endl ;
 783   //-deb-  cout << "ApproxInt_Approx -- U1o = " << U1o << " V1o = " << V1o << " A1u = " << A1u << " A1v = " << A1v << endl ;
 784   //-deb-  cout << "ApproxInt_Approx -- U2o = " << U2o << " V2o = " << V2o << " A2u = " << A2u << " A2v = " << A2v << endl ;
 785
 786
 787   Standard_Real A3d = MINABS3(Ax,Ay,Az);
 788   if((A3d < myMinFactorXYZ) || (myMinFactorXYZ == 0.0)) {
 789     myMinFactorXYZ = A3d;
 790   }
 791
 792   Standard_Real A2d = MINABS4(A1u,A1v,A2u,A2v);
 793   if((A2d < myMinFactorUV) || (myMinFactorUV == 0.0)) {
 794     myMinFactorUV = A2d;
 795   }
 796
 797   myComputeLineBezier.Parametrization(parametrization);
 798
 799   if(myRelativeTol==Standard_False) {
 800     myComputeLine.Init(myDegMin,
 801                        myDegMax,
 802                        myTol3d*myMinFactorXYZ,
 803                        myTol2d*myMinFactorUV,
 804                        myNbIterMax,
 805                        cut,
 806                        parametrization);
 807     myComputeLineBezier.Init(myDegMin,
 808                              myDegMax,
 809                              myTol3d*myMinFactorXYZ,
 810                              myTol2d*myMinFactorUV,
 811                              myNbIterMax,
 812                              cut,
 813                              parametrization);
 814   }
 815   else {
 816     myComputeLine.Init(myDegMin,
 817                        myDegMax,
 818                        myTol3d,
 819                        myTol2d,
 820                        myNbIterMax,
 821                        cut,
 822                        parametrization);
 823     myComputeLineBezier.Init(myDegMin,
 824                              myDegMax,
 825                              myTol3d,
 826                              myTol2d,
 827                              myNbIterMax,
 828                              cut,
 829                              parametrization);
 830   }
 831
 832
 833   do {
 834
 835     ApproxInt_TheMultiLine myMultiLine(theline,
 836                                        ptrsvsurf,
 837                                        ((ApproxXYZ)? 1 : 0),
 838                                        ((ApproxU1V1)? 1: 0) + ((ApproxU2V2)? 1: 0),
 839                                        Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v,
 840                                        ApproxU1V1,
 841                                        imin,
 842                                        imax);
 843     if(myApproxBez) {
 844       myComputeLineBezier.Perform(myMultiLine);
 845       if (myComputeLineBezier.NbMultiCurves() == 0)
 846         return;
 847       myTolReached&=myComputeLineBezier.IsToleranceReached();
 848     }
 849     else {
 850       myComputeLine.Perform(myMultiLine);
 851     }
 852     UpdateTolReached();
 853     Standard_Integer indice3d,indice2d1,indice2d2;
 854     indice3d = 1;
 855     indice2d1= 2;
 856     indice2d2= 3;
 857     if(!ApproxXYZ)  { indice2d1--; indice2d2--; }
 858     if(!ApproxU1V1) { indice2d2--; }
 859     if(ApproxXYZ) {
 860       Standard_Real ax,bx,ay,by,az,bz;
 861       ax = 1.0/Ax;   bx = -Xo*ax;
 862       ay = 1.0/Ay;   by = -Yo*ay;
 863       az = 1.0/Az;   bz = -Zo*az;
 864       if(myApproxBez) {
 865         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 866           myComputeLineBezier.ChangeValue(nbmc).Transform(indice3d,bx,ax,by,ay,bz,az);
 867         }
 868       }
 869       else {
 870         myComputeLine.ChangeValue().Transform(indice3d,bx,ax,by,ay,bz,az);
 871       }
 872     }
 873     if(ApproxU1V1) {
 874       Standard_Real ax,bx,ay,by;
 875       ax = 1.0/A1u;   bx = -U1o*ax;
 876       ay = 1.0/A1v;   by = -V1o*ay;
 877       if(myApproxBez) {
 878         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 879           myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d1,bx,ax,by,ay);
 880         }
 881       }
 882       else {
 883         myComputeLine.ChangeValue().Transform2d(indice2d1,bx,ax,by,ay);
 884       }
 885     }
 886     if(ApproxU2V2) {
 887       Standard_Real ax,bx,ay,by;
 888       ax = 1.0/A2u;   bx = -U2o*ax;
 889       ay = 1.0/A2v;   by = -V2o*ay;
 890       if(myApproxBez) {
 891         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
 892           myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d2,bx,ax,by,ay);
 893         }
 894       }
 895       else {
 896         myComputeLine.ChangeValue().Transform2d(indice2d2,bx,ax,by,ay);
 897       }
 898     }
 899     OtherInter = Standard_False;
 900     if(myApproxBez) {
 901       for(Standard_Integer nbmc = 1;
 902           nbmc <= myComputeLineBezier.NbMultiCurves() ;
 903           nbmc++) {
 904         myBezToBSpl.Append(myComputeLineBezier.Value(nbmc));
 905       }
 906       if(imax<indicemax) {
 907         imin = imax;
 908         imax = imin+nbpntbez;
 909         OtherInter = Standard_True;
 910         if((indicemax-imax)<(nbpntbez/2)) {
 911           imax = indicemax;
 912         }
 913       }
 914     }
 915   }
 916   while(OtherInter);
 917   if(myApproxBez) {
 918     myBezToBSpl.Perform();
 919   }
 920 }
 921 //--------------------------------------------------------------------------------
 922 void ApproxInt_Approx::Perform(const TheISurface& ISurf,
 923                                const ThePSurface& PSurf,
 924                                const Handle(TheWLine)& theline,
 925                                const Standard_Boolean ApproxXYZ,
 926                                const Standard_Boolean ApproxU1V1,
 927                                const Standard_Boolean ApproxU2V2,
 928                                const Standard_Integer indicemin,
 929                                const Standard_Integer indicemax)
 930 {
 931
 932   myMinFactorXYZ = 0.0;
 933   myMinFactorUV  = 0.0;
 934   myTolReached3d = myTolReached2d = 0.;
 935
 936   ApproxInt_TheImpPrmSvSurfaces myImpPrmSvSurfaces(ISurf,PSurf);
 937   Standard_Integer nbpntbez = indicemax-indicemin;
 938
 939   Standard_Boolean cut = Standard_True;
 940   if(nbpntbez < LimRajout)
 941     myApproxBez = Standard_False;
 942   else
 943     myApproxBez = Standard_True;
 944
 945   if(nbpntbez < LimRajout) {
 946     cut = Standard_False;
 947     //-- cout<<" ApproxInt : Nb de points = "<<nbpntbez<<" Pas de rajout "<<endl;
 948   }
 949   Standard_Address ptrsvsurf = &myImpPrmSvSurfaces;
 950
 951   if(nbpntbez < LimRajout) myApproxBez = Standard_False;
 952
 953   Standard_Integer nbpntmax = myNbPntMax;
 954   Standard_Boolean OtherInter = Standard_False;
 955   if(myApproxBez) {
 956     myBezToBSpl.Reset();
 957     Standard_Integer nbi = (indicemax-indicemin)/nbpntmax;
 958     if(nbi>1)  {
 959       nbpntbez = (indicemax-indicemin)/nbi;
 960     }
 961   }
 962   Standard_Integer imin = indicemin;
 963   Standard_Integer imax = imin + nbpntbez;
 964   myTolReached = Standard_True;
 965
 966   Standard_Real Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v;
 967   if(ApproxXYZ) {
 968     ComputeTrsf3d(theline,Xo,Ax,Yo,Ay,Zo,Az);
 969   }
 970   else {
 971     Xo=Yo=Zo=0.0; Ax=Ay=Az=1.0;;
 972   }
 973   if(ApproxU1V1) {
 974     ComputeTrsf2d(theline,U1o,A1u,V1o,A1v,Standard_True);
 975   }
 976   else {
 977     U1o=V1o=0.0; A1u=A1v=1.0;
 978   }
 979   if(ApproxU2V2) {
 980     Standard_Real UVResRatio = ThePSurfaceTool::UResolution(PSurf,1.)/
 981                                ThePSurfaceTool::VResolution(PSurf,1.);
 982     ComputeTrsf2d(theline,U2o,A2u,V2o,A2v,Standard_False,UVResRatio);
 983   }
 984   else {
 985     U2o=V2o=0.0; A2u=A2v=1.0;
 986   }
 987
 988   //-deb-  cout << "ApproxInt_Approx -- NbPntMax = " << myNbPntMax    << endl ;
 989   //-deb-  cout << "ApproxInt_Approx -- Tol3D    = " << myTol3d       << endl ;
 990   //-deb-  cout << "ApproxInt_Approx -- Tol2D    = " << myTol2d       << endl ;
 991   //-deb-  cout << "ApproxInt_Approx -- RelTol   = " << (myRelativeTol ? "RELATIVE" : "ABSOLUTE") << endl ;
 992   //-deb-  cout << "ApproxInt_Approx -- Xo = " << Xo << " Yo = " << Yo << " Zo = " << Zo << endl ;
 993   //-deb-  cout << "ApproxInt_Approx -- Ax = " << Ax << " Ay = " << Ay << " Az = " << Az << endl ;
 994   //-deb-  cout << "ApproxInt_Approx -- U1o = " << U1o << " V1o = " << V1o << " A1u = " << A1u << " A1v = " << A1v << endl ;
 995   //-deb-  cout << "ApproxInt_Approx -- U2o = " << U2o << " V2o = " << V2o << " A2u = " << A2u << " A2v = " << A2v << endl ;
 996
 997
 998   Standard_Real A3d = MINABS3(Ax,Ay,Az);
 999   if((A3d < myMinFactorXYZ) || (myMinFactorXYZ == 0.0)) {
1000     myMinFactorXYZ = A3d;
1001   }
1002
1003   Standard_Real A2d = MINABS4(A1u,A1v,A2u,A2v);
1004   if((A2d < myMinFactorUV) || (myMinFactorUV == 0.0)) {
1005     myMinFactorUV = A2d;
1006   }
1007
1008   Approx_ParametrizationType parametrization;
1009   myComputeLineBezier.Parametrization(parametrization);
1010
1011
1012   if(myRelativeTol==Standard_False) {
1013     myComputeLine.Init(myDegMin,
1014                        myDegMax,
1015                        myTol3d*myMinFactorXYZ,
1016                        myTol2d*myMinFactorUV,
1017                        myNbIterMax,
1018                        cut,
1019                        parametrization);
1020     myComputeLineBezier.Init(myDegMin,
1021                              myDegMax,
1022                              myTol3d*myMinFactorXYZ,
1023                              myTol2d*myMinFactorUV,
1024                              myNbIterMax,
1025                              cut,
1026                              parametrization);
1027   }
1028   else {
1029     myComputeLine.Init(myDegMin,
1030                        myDegMax,
1031                        myTol3d,
1032                        myTol2d,
1033                        myNbIterMax,
1034                        cut,
1035                        parametrization);
1036     myComputeLineBezier.Init(myDegMin,
1037                              myDegMax,
1038                              myTol3d,
1039                              myTol2d,
1040                              myNbIterMax,
1041                              cut,
1042                              parametrization);
1043   }
1044
1045
1046
1047   do {
1048
1049     ApproxInt_TheMultiLine myMultiLine(theline,
1050                                        ptrsvsurf,
1051                                        ((ApproxXYZ)? 1 : 0),
1052                                        ((ApproxU1V1)? 1: 0) + ((ApproxU2V2)? 1: 0),
1053                                        Xo,Ax,Yo,Ay,Zo,Az,U1o,A1u,V1o,A1v,U2o,A2u,V2o,A2v,
1054                                        ApproxU1V1,
1055                                        imin,
1056                                        imax);
1057     if(myApproxBez) {
1058       myComputeLineBezier.Perform(myMultiLine);
1059
1060 #ifdef OCCT_DEBUG
1061       //myMultiLine.Dump();
1062 #endif
1063
1064       if (myComputeLineBezier.NbMultiCurves() == 0)
1065         return;
1066       myTolReached&=myComputeLineBezier.IsToleranceReached();
1067     }
1068     else {
1069       myComputeLine.Perform(myMultiLine);
1070     }
1071     UpdateTolReached();
1072
1073     Standard_Integer indice3d,indice2d1,indice2d2;
1074     indice3d = 1;
1075     indice2d1= 2;
1076     indice2d2= 3;
1077     if(!ApproxXYZ)  { indice2d1--; indice2d2--; }
1078     if(!ApproxU1V1) { indice2d2--; }
1079     if(ApproxXYZ) {
1080       Standard_Real ax,bx,ay,by,az,bz;
1081       ax = 1.0/Ax;   bx = -Xo*ax;
1082       ay = 1.0/Ay;   by = -Yo*ay;
1083       az = 1.0/Az;   bz = -Zo*az;
1084       if(myApproxBez) {
1085         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
1086           myComputeLineBezier.ChangeValue(nbmc).Transform(indice3d,bx,ax,by,ay,bz,az);
1087         }
1088       }
1089       else {
1090         myComputeLine.ChangeValue().Transform(indice3d,bx,ax,by,ay,bz,az);
1091       }
1092     }
1093     if(ApproxU1V1) {
1094       Standard_Real ax,bx,ay,by;
1095       ax = 1.0/A1u;   bx = -U1o*ax;
1096       ay = 1.0/A1v;   by = -V1o*ay;
1097       if(myApproxBez) {
1098         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
1099           myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d1,bx,ax,by,ay);
1100         }
1101       }
1102       else {
1103         myComputeLine.ChangeValue().Transform2d(indice2d1,bx,ax,by,ay);
1104       }
1105     }
1106     if(ApproxU2V2) {
1107       Standard_Real ax,bx,ay,by;
1108       ax = 1.0/A2u;   bx = -U2o*ax;
1109       ay = 1.0/A2v;   by = -V2o*ay;
1110       if(myApproxBez) {
1111         for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--) {
1112           myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d2,bx,ax,by,ay);
1113         }
1114       }
1115       else {
1116         myComputeLine.ChangeValue().Transform2d(indice2d2,bx,ax,by,ay);
1117       }
1118     }
1119     OtherInter = Standard_False;
1120     if(myApproxBez) {
1121       for(Standard_Integer nbmc = 1;
1122           nbmc <= myComputeLineBezier.NbMultiCurves() ;
1123           nbmc++) {
1124         myBezToBSpl.Append(myComputeLineBezier.Value(nbmc));
1125       }
1126       if(imax<indicemax) {
1127         imin = imax;
1128         imax = imin+nbpntbez;
1129         OtherInter = Standard_True;
1130         if((indicemax-imax)<(nbpntbez/2)) {
1131           imax = indicemax;
1132         }
1133       }
1134     }
1135   }
1136   while(OtherInter);
1137   if(myApproxBez) {
1138     myBezToBSpl.Perform();
1139   }
1140 }
1141 //--------------------------------------------------------------------------------
1142 Standard_Integer ApproxInt_Approx::NbMultiCurves() const {
1143   //  return(myComputeLine.NbMultiCurves());
1144   return 1;
1145 }
1146 //--------------------------------------------------------------------------------
1147 void ApproxInt_Approx::UpdateTolReached() {
1148
1149   if (myApproxBez) {
1150     Standard_Integer ICur ;
1151     Standard_Integer NbCurves = myComputeLineBezier.NbMultiCurves() ;
1152     for (ICur = 1 ; ICur <= NbCurves ; ICur++) {
1153       Standard_Real Tol3D, Tol2D ;
1154       myComputeLineBezier.Error (ICur, Tol3D, Tol2D) ;
1155       myTolReached3d = Max(myTolReached3d, Tol3D);
1156       myTolReached2d = Max(myTolReached2d, Tol2D);
1157     }
1158   } else {
1159     myComputeLine.Error (myTolReached3d, myTolReached2d);
1160   }
1161 }
1162 //--------------------------------------------------------------------------------
1163 Standard_Real ApproxInt_Approx::TolReached3d() const {
1164
1165   Standard_Real TheTol3D = RatioTol * myTolReached3d ;
1166   //modified by NIZNHY-PKV Mon Aug 27 14:21:33 2007f
1167   //if (myMinFactorXYZ)
1168   //TheTol3D = TheTol3D / myMinFactorXYZ ;
1169   if (myMinFactorXYZ>1.5e-7) {
1170     TheTol3D = TheTol3D / myMinFactorXYZ ;
1171   }
1172   //modified by NIZNHY-PKV Mon Aug 27 14:21:50 2007t
1173   return TheTol3D ;
1174 }
1175 //--------------------------------------------------------------------------------
1176 Standard_Real ApproxInt_Approx::TolReached2d() const {
1177
1178   Standard_Real TheTol2D = RatioTol * myTolReached2d ;
1179   //modified by NIZNHY-PKV Mon Aug 27 14:20:50 2007f
1180   //if (myMinFactorUV)
1181   //TheTol2D = TheTol2D / myMinFactorUV ;
1182   if (myMinFactorUV>1.5e-7) {
1183     TheTol2D = TheTol2D / myMinFactorUV ;
1184   }
1185   //modified by NIZNHY-PKV Mon Aug 27 14:20:55 2007t
1186   return TheTol2D ;
1187 }
1188 //--------------------------------------------------------------------------------
1189 Standard_Boolean ApproxInt_Approx::IsDone() const {
1190   if(myApproxBez) {
1191     return(myComputeLineBezier.NbMultiCurves() > 0);
1192                            //-- Lorsque la tolerance n est pas atteinte et qu il
1193                            //-- faudrait rajouter des points sur la ligne
1194                            //-- les approx sortent avec la meilleure tolerance
1195                            //-- atteinte.  ( Pas de rajout de points ds cette version)
1196     //-- return(myTolReached);
1197   }
1198   else {
1199     return(myComputeLine.IsToleranceReached());
1200   }
1201 }
1202 //--------------------------------------------------------------------------------
1203 const AppParCurves_MultiBSpCurve& ApproxInt_Approx::Value(const Standard_Integer ) const {
1204   if(myApproxBez) {
1205     return(myBezToBSpl.Value());
1206   }
1207   else {
1208     return(myComputeLine.Value());
1209   }
1210 }