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ProjLib_ComputeApprox.cxx

// File:    ProjLib_ComputeApprox.gxx
// Created: Tue Sep  7 16:37:49 1993
// Author:  Bruno DUMORTIER
//          <dub@topsn3>
// modified by NIZHNY-OFV  Thu Jan 20 11:04:19 2005

#include <ProjLib_ComputeApprox.hxx>

#include <GeomAbs_SurfaceType.hxx>
#include <GeomAbs_CurveType.hxx>
#include <AppCont_Function2d.hxx>
#include <Convert_CompBezierCurves2dToBSplineCurve2d.hxx>
#include <ElSLib.hxx>
#include <ElCLib.hxx>
#include <BSplCLib.hxx>
#include <Standard_NoSuchObject.hxx>
#include <Geom_UndefinedDerivative.hxx>
#include <gp.hxx>
#include <gp_Trsf.hxx>
#include <Precision.hxx>
#include <Approx_FitAndDivide2d.hxx>
#include <AppParCurves_MultiCurve.hxx>
#include <Handle_Adaptor3d_HCurve.hxx>
#include <Adaptor3d_HCurve.hxx>
#include <Handle_Adaptor3d_HSurface.hxx>
#include <Adaptor3d_HSurface.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array1OfInteger.hxx>
#include <Geom_BSplineCurve.hxx>
#include <Geom_BezierCurve.hxx>
#include <Geom2d_BSplineCurve.hxx>
#include <Geom2d_BezierCurve.hxx>

#ifdef DRAW
#include <DrawTrSurf.hxx>
#endif
#ifdef DEB
static Standard_Boolean AffichValue = Standard_False;
#endif    

static 
  void Parameters(const Handle(Adaptor3d_HCurve)&   myCurve,
              const Handle(Adaptor3d_HSurface)& mySurface,
              const gp_Pnt& aP1, 
              const Standard_Integer iFirst,
              const Standard_Real aTolU, 
              Standard_Real& aU, 
              Standard_Real& aV);

//=======================================================================
//function : IsEqual
//purpose  : 
//=======================================================================
// OFV:
static inline Standard_Boolean IsEqual(Standard_Real Check,Standard_Real With,Standard_Real Toler)
{
  return ((Abs(Check - With) < Toler) ? Standard_True : Standard_False);
}


//=======================================================================
//function : Value
//purpose  : 
//=======================================================================

static gp_Pnt2d Function_Value(const Standard_Real U,
                         const Handle(Adaptor3d_HCurve)&   myCurve,
                         const Handle(Adaptor3d_HSurface)& mySurface,
                         const Standard_Real U1,
                         const Standard_Real U2, 
                         const Standard_Real V1,
                         const Standard_Real V2,
                         const Standard_Boolean UCouture,
                         const Standard_Boolean VCouture ) 
{
  Standard_Real S, T;

  gp_Pnt P3d = myCurve->Value(U);
  GeomAbs_SurfaceType SType = mySurface->GetType();

  switch ( SType ) {
    
  case GeomAbs_Plane:
    {
      gp_Pln Plane = mySurface->Plane();
      ElSLib::Parameters( Plane, P3d, S, T);
      break;
    }
  case GeomAbs_Cylinder:
    {
      gp_Cylinder Cylinder = mySurface->Cylinder();
      ElSLib::Parameters( Cylinder, P3d, S, T);
      break;
    }
  case GeomAbs_Cone:
    {
      gp_Cone Cone = mySurface->Cone();
      ElSLib::Parameters( Cone, P3d, S, T);
      break;
    }
  case GeomAbs_Sphere:
    {
      gp_Sphere Sphere = mySurface->Sphere();
      ElSLib::Parameters(Sphere, P3d, S, T);
      break;
    }
  case GeomAbs_Torus:
    {
      gp_Torus Torus = mySurface->Torus();
      ElSLib::Parameters( Torus, P3d, S, T);
      break;
    }
  default:
    Standard_NoSuchObject::Raise("ProjLib_ComputeApprox::Value");
  }

  if ( UCouture) {
    S = ElCLib::InPeriod(S, U1, U2);
  }
 
  if ( VCouture) {
    if(SType == GeomAbs_Sphere) {
      if ( Abs( S - U1 ) > PI ) {
      T = PI - T;
      S = PI + S;
      }
      S = ElCLib::InPeriod(S, U1, U2);
    }
    T = ElCLib::InPeriod(T, V1, V2);
  }
  
  return gp_Pnt2d(S, T);
}
//=======================================================================
//function : D1
//purpose  : 
//=======================================================================
static Standard_Boolean Function_D1( const Standard_Real U, 
                            gp_Pnt2d&            P,
                            gp_Vec2d&            D,
                            const Handle(Adaptor3d_HCurve)&   myCurve,
                            const Handle(Adaptor3d_HSurface)& mySurface,
                            const Standard_Real U1,
                            const Standard_Real U2, 
                            const Standard_Real V1,
                            const Standard_Real V2,
                            const Standard_Boolean UCouture,
                            const Standard_Boolean VCouture )
{
  gp_Pnt P3d;
  Standard_Real dU, dV;
  
  P = Function_Value(U,myCurve,mySurface,U1,U2,V1,V2,UCouture,VCouture);

  GeomAbs_SurfaceType Type = mySurface->GetType();
  
  switch ( Type) {
  case GeomAbs_Plane:
  case GeomAbs_Cone:
  case GeomAbs_Cylinder:
  case GeomAbs_Sphere:
  case GeomAbs_Torus: 
    {
      gp_Vec D1U, D1V;
      gp_Vec T;
      myCurve->D1(U,P3d,T);
      mySurface->D1(P.X(),P.Y(),P3d,D1U,D1V);
      
      dU = T.Dot(D1U);
      dV = T.Dot(D1V);
      Standard_Real Nu = D1U.SquareMagnitude();
      Standard_Real Nv = D1V.SquareMagnitude(); 
      
      if ( Nu < Epsilon(1.) || Nv < Epsilon(1.))
      return Standard_False;
      
      dU /= Nu;
      dV /= Nv;
      D = gp_Vec2d( dU, dV);   
    }
    break;
    
  default:
    return Standard_False;
  }
  
  return Standard_True;
}

//=======================================================================
//function : Function_SetUVBounds
//purpose  : 
//=======================================================================
static void Function_SetUVBounds(Standard_Real& myU1, 
                         Standard_Real& myU2,
                         Standard_Real& myV1,
                         Standard_Real& myV2,
                         Standard_Boolean& UCouture,
                         Standard_Boolean& VCouture,
                         const Handle(Adaptor3d_HCurve)&   myCurve,
                         const Handle(Adaptor3d_HSurface)& mySurface) 
{
  Standard_Real W1, W2, W;
  gp_Pnt P1, P2, P;
  //
  W1 = myCurve->FirstParameter();
  W2 = myCurve->LastParameter ();
  W  = 0.5*(W1+W2);
  // on ouvre l`intervalle
  // W1 += 1.0e-9;
  // W2 -= 1.0e-9;
  P1 = myCurve->Value(W1);
  P2 = myCurve->Value(W2);
  P  = myCurve->Value(W);

  switch ( mySurface->GetType()) {

  case GeomAbs_Cone:    {
    gp_Cone Cone = mySurface->Cone();
    VCouture = Standard_False;
    
    switch( myCurve->GetType() ){
    case GeomAbs_Parabola:
    case GeomAbs_Hyperbola:
    case GeomAbs_Ellipse:{
      Standard_Real U1, U2, V1, V2, U , V;
      ElSLib::Parameters( Cone, P1, U1, V1);
      ElSLib::Parameters( Cone, P2, U2, V2);
      ElSLib::Parameters( Cone, P , U , V );
      myU1 = Min(U1,U2);
      myU2 = Max(U1,U2);
      if (  ( U1 < U  &&  U < U2 ) && !myCurve->IsClosed() ) {
      UCouture = Standard_False;
      }      
      else {
      UCouture = Standard_True;
      myU2 = myU1 + 2*PI;
      }
      
    }
      break;
    default:        { 
      Standard_Real U1, V1, U , V, Delta = 0., d = 0., pmin = W1, pmax = W1, dmax = 0., Uf, Ul;
      ElSLib::Parameters( Cone, P1, U1, V1);
      ElSLib::Parameters( Cone, P2, Ul, V1);
      myU1 = U1; myU2 = U1; Uf = U1; 
      Standard_Real Step = .1;
      Standard_Integer nbp = (Standard_Integer)((W2 - W1) / Step + 1);
      nbp = Max(nbp, 3);
      Step = (W2 - W1) / (nbp - 1);
      Standard_Boolean isclandper = (!(myCurve->IsClosed()) && !(myCurve->IsPeriodic()));
      for(Standard_Real par = W1 + Step; par <= W2; par += Step) {
      if(!isclandper) par += Step;
      P = myCurve->Value(par);
      ElSLib::Parameters( Cone, P, U, V);
      U += Delta;
      d = U - U1;
      if(d > PI)  {
        if( ( (IsEqual(U,(2*PI),1.e-10) && (U1 >= 0. && U1 <= PI)) && 
             (IsEqual(U,Ul,1.e-10) && !IsEqual(Uf,0.,1.e-10)) ) && isclandper ) U = 0.;
        else Delta -= 2*PI;
        U += Delta;
        d = U - U1;
      }
      else if(d < -PI)    {
        if( ( (IsEqual(U,0.,1.e-10) && (U1 >= PI && U1 <= (2*PI))) &&
             (IsEqual(U,Ul,1.e-10) && !IsEqual(Uf,(2*PI),1.e-10)) ) && isclandper ) U = 2*PI;
        else Delta += 2*PI;
        U += Delta;
        d = U - U1;
      }
      dmax = Max(dmax, Abs(d));
      if(U < myU1) {myU1 = U; pmin = par;}
      if(U > myU2) {myU2 = U; pmax = par;}
      U1 = U;
      }
      
      if(!(Abs(pmin - W1) <= Precision::PConfusion() || Abs(pmin - W2) <= Precision::PConfusion()) ) myU1 -= dmax*.5;
      if(!(Abs(pmax - W1) <= Precision::PConfusion() || Abs(pmax - W2) <= Precision::PConfusion()) ) myU2 += dmax*.5;

      if((myU1 >=0. && myU1 <= 2*PI) && (myU2 >=0. && myU2 <= 2*PI) ) UCouture = Standard_False;
      else{
      U = ( myU1 + myU2 ) /2.;
      myU1 = U - PI;
      myU2 = U + PI;
      UCouture = Standard_True;
      }
    }
      break;
    }// switch curve type
  }// case Cone
    break;
      
  case GeomAbs_Cylinder:    {
    gp_Cylinder Cylinder = mySurface->Cylinder();
    VCouture = Standard_False;
    
    if (myCurve->GetType() == GeomAbs_Ellipse) {
      
      Standard_Real U1, U2, V1, V2, U , V;
      ElSLib::Parameters( Cylinder, P1, U1, V1);
      ElSLib::Parameters( Cylinder, P2, U2, V2);
      ElSLib::Parameters( Cylinder, P , U , V );
      myU1 = Min(U1,U2);
      myU2 = Max(U1,U2);
      
      if ( !myCurve->IsClosed()) {
      if ( myU1 < U && U < myU2) {
        U = ( myU1 + myU2 ) /2.;
        myU1 = U - PI;
        myU2 = U + PI;
      }
      else {
        U = ( myU1 + myU2 ) /2.;
        if ( myU1 < U) {
          myU1 = U - 2*PI;
          myU2 = U;
        }
        else {
          myU1 = U;
          myU2 = U + 2*PI;
        }
      }
      UCouture = Standard_True;
      }
      else {
      gp_Vec D1U, D1V;
      gp_Vec T;
      gp_Pnt P3d;
      myCurve->D1(W1,P3d,T);
        mySurface->D1(U1,U2,P3d,D1U,D1V);
      Standard_Real dU = T.Dot(D1U);
      
      UCouture = Standard_True;
      if ( dU > 0.) {
        myU2 = myU1 + 2*PI;
      }
      else {
        myU2 = myU1;
        myU1 -= 2*PI;
      }
      }
    }
    else {
      Standard_Real U1, V1, U , V;
      ElSLib::Parameters( Cylinder, P1, U1, V1);
      Standard_Real Step = .1, Delta = 0.;
      Standard_Real eps = PI, dmax = 0., d = 0.;
      Standard_Integer nbp = (Standard_Integer)((W2 - W1) / Step + 1);
      nbp = Max(nbp, 3);
      Step = (W2 - W1) / (nbp - 1);
      myU1 = U1; myU2 = U1;
      Standard_Real pmin = W1, pmax = W1, plim = W2+.1*Step;
      for(Standard_Real par = W1 + Step; par <= plim; par += Step) {
      P = myCurve->Value(par);
        ElSLib::Parameters( Cylinder, P, U, V);
      U += Delta;
      d = U - U1;
      if(d > eps) {
        U -= Delta;
        Delta -= 2*PI;
        U += Delta;
        d = U - U1;
        }
      else if(d < -eps) {
        U -= Delta;
        Delta += 2*PI;
        U += Delta;
        d = U - U1;
      }
      dmax = Max(dmax, Abs(d));
      if(U < myU1) {myU1 = U; pmin = par;}
      if(U > myU2) {myU2 = U; pmax = par;}
        U1 = U;
      }
      
      if(!(Abs(pmin - W1) <= Precision::PConfusion() ||
         Abs(pmin - W2) <= Precision::PConfusion())  ) myU1 -= dmax*.5;
      if(!(Abs(pmax - W1) <= Precision::PConfusion() ||
         Abs(pmax - W2) <= Precision::PConfusion())  ) myU2 += dmax*.5;
      
      if((myU1 >=0. && myU1 <= 2*PI) &&
       (myU2 >=0. && myU2 <= 2*PI)    ) {
      UCouture = Standard_False;
      }
      else {
      U = ( myU1 + myU2 ) /2.;
      myU1 = U - PI;
      myU2 = U + PI;
      UCouture = Standard_True;
      }
    }
  }
    break;
    //    
  case GeomAbs_Sphere:{
    VCouture = Standard_False;
    gp_Sphere SP = mySurface->Sphere();
    if ( myCurve->GetType() == GeomAbs_Circle) {
      UCouture = Standard_True;
      
      // on cherche a savoir le nombre de fois que la couture est
      // traversee.
      // si 0 ou 2 fois : la PCurve est fermee et dans l`intervalle 
      //                  [Uc-PI, Uc+PI] (Uc: U du centre du cercle)
      // si 1 fois      : la PCurve est ouverte et dans l`intervalle
      //                  [U1, U1 +/- 2*PI]

      // pour determiner le nombre de solution, on resoud le systeme
      // x^2 + y^2 + z^2     = R^2  (1)
      // A x + B y + C z + D = 0    (2)
      // x > 0                      (3)
      // y = 0                      (4)
      // REM : (1) (2)     : equation du cercle
      //       (1) (3) (4) : equation de la couture.
      Standard_Integer NbSolutions = 0;
      Standard_Real A, B, C, D, R, Tol = 1.e-10;
      Standard_Real U1, U2, V1, V2, aTPC;
      gp_Trsf Trsf;
      //
      aTPC=Precision::PConfusion();
      //
      gp_Circ Circle = myCurve->Circle();
      Trsf.SetTransformation(SP.Position());
      Circle.Transform(Trsf);
      //
      R = SP.Radius();
      gp_Pln Plane( gp_Ax3(Circle.Position()));
      Plane.Coefficients(A,B,C,D);
      //
      if ( Abs(C) < Tol) {
      if ( Abs(A) > Tol) {
        if ( (D/A) < 0.) {
          if      ( ( R - Abs(D/A))  > Tol)  NbSolutions = 2;
          else if ( Abs(R - Abs(D/A))< Tol)  NbSolutions = 1;
          else                               NbSolutions = 0;
        }
      }
      }
      else {
      Standard_Real delta = R*R*(A*A+C*C) - D*D;
      delta *= C*C;
      if ( Abs(delta) < Tol*Tol) {
        if ( A*D > 0.) NbSolutions = 1;
      }
      else if ( delta > 0) {
        Standard_Real xx;
        delta = Sqrt(delta);
        xx = -A*D+delta;
        //    
        if ( xx > Tol) NbSolutions++;
        xx = -A*D-delta;
        //  
        if ( xx > Tol) NbSolutions++;
      }
      }
      //

      // box+sphere >>
      Standard_Real UU = 0.;
      ElSLib::Parameters(SP, P1, U1, V1);
      ElSLib::Parameters(SP, P2, U2, V1);
      ElSLib::Parameters(SP, P, UU, V1);
      Standard_Real UUmi = Min(Min(U1,UU),Min(UU,U2));
      Standard_Real UUma = Max(Max(U1,UU),Max(UU,U2));
      Standard_Boolean reCalc = ((UUmi >= 0. && UUmi <= PI) && (UUma >= 0. && UUma <= PI));
      // box+sphere <<
      
      ElSLib::Parameters(SP, P1, U1, V1);//*
      //
      Parameters(myCurve, mySurface, P1, 1, aTPC, U1, V1);
      //
      //
      P2 = myCurve->Value(W1+PI/8);
      ElSLib::Parameters(SP,P2,U2,V2);
      //
      if ( NbSolutions == 1) {
      if ( Abs(U1-U2) > PI) { // on traverse la couture
        if ( U1 > PI) {
          myU1 = U1;
          myU2 = U1+2*PI;
        }
        else {
          myU2 = U1;
          myU1 = U1-2*PI;
        }
      }
      else { // on ne traverse pas la couture
        if ( U1 > U2) {
          myU2 = U1;
          myU1 = U1-2*PI;
        }
        else {
          myU1 = U1;
          myU2 = U1+2*PI;
        }
      }
      }
      else { // 0 ou 2 solutions
      gp_Pnt Center = Circle.Location();
      Standard_Real U,V;
      ElSLib::SphereParameters(gp_Ax3(gp::XOY()),1,Center, U, V);
      myU1 = U-PI;
      myU2 = U+PI;
      }
      //
      // eval the VCouture.
      if ( (C==0) || Abs(Abs(D/C)-R) > 1.e-10) {
      VCouture = Standard_False;
      }
      else {
      VCouture = Standard_True;
      UCouture = Standard_True;
      
      if ( D/C < 0.) {
        myV1 =   - PI / 2.;
        myV2 = 3 * PI / 2.;
      }
      else {
        myV1 = -3 * PI / 2.;
        myV2 =      PI / 2.;
      }
      
      // si P1.Z() vaut +/- R on est sur le sommet : pas significatif.
      gp_Pnt pp = P1.Transformed(Trsf);
      
      if ( Abs( Abs(pp.Z()) - R) < Tol) {
        gp_Pnt Center = Circle.Location();
        Standard_Real U,V;
        ElSLib::SphereParameters(gp_Ax3(gp::XOY()),1,Center, U, V);
        myU1 = U-PI;
        myU2 = U+PI;
        VCouture = Standard_False;
      }
      else {
        ElSLib::Parameters(SP,P1,U1,V1);//*
        //
        Parameters(myCurve, mySurface, P1, 1, aTPC, U1, V1);
        //
        P2 = myCurve->Value(W1+PI/8);
        ElSLib::Parameters(SP,P2,U2,V2);
        
        if ( Abs(U1-U2) > PI) { // on traverse la couture
          if ( U1 > PI) {
            myU1 = U1;
            myU2 = U1+2*PI;
          }
          else {
            myU2 = U1;
            myU1 = U1-2*PI;
          }
        }
        else { // on ne traverse pas la couture
          if ( U1 > U2) {
            myU2 = U1;
            myU1 = U1-2*PI;
          }
          else {
            myU1 = U1;
            myU2 = U1+2*PI;
          }
        }
      }
      }
      
      // box+sphere >>
      myV1 = -1.e+100; myV2 = 1.e+100;
      Standard_Real UU1 = myU1, UU2 = myU2;
      if((Abs(UU1) <= (2.*PI) && Abs(UU2) <= (2.*PI)) && NbSolutions == 1 && reCalc) {
      gp_Pnt Center = Circle.Location();
      Standard_Real U,V;
      ElSLib::SphereParameters(gp_Ax3(gp::XOY()),1,Center, U, V);
      myU1 = U-PI;
      myU2 = U+PI;
      myU1 = Min(UU1,myU1);
      myU2 = Max(UU2,myU2);
      }
      // box+sphere <<

    }//if ( myCurve->GetType() == GeomAbs_Circle)

    else {
      Standard_Real U1, V1, U , V;
      ElSLib::Parameters( SP, P1, U1, V1);
      Standard_Real Step = .1, Delta = 0.;
      Standard_Real eps = PI, dmax = 0., d = 0.;
      Standard_Integer nbp = (Standard_Integer)((W2 - W1) / Step + 1);
      nbp = Max(nbp, 3);
      Step = (W2 - W1) / (nbp - 1);
      myU1 = U1; myU2 = U1;
      Standard_Real pmin = W1, pmax = W1, plim = W2+.1*Step;
      for(Standard_Real par = W1 + Step; par <= plim; par += Step) {
      P = myCurve->Value(par);
      ElSLib::Parameters( SP, P, U, V);
      U += Delta;
      d = U - U1;
      if(d > eps) {
        U -= Delta;
        Delta -= 2*PI;
        U += Delta;
        d = U - U1;
      }
      else if(d < -eps) {
        U -= Delta;
        Delta += 2*PI;
        U += Delta;
        d = U - U1;
        }
      dmax = Max(dmax, Abs(d));
      if(U < myU1) {myU1 = U; pmin = par;}
      if(U > myU2) {myU2 = U; pmax = par;}
      U1 = U;
      }
      
      if(!(Abs(pmin - W1) <= Precision::PConfusion() ||
         Abs(pmin - W2) <= Precision::PConfusion())  ) myU1 -= dmax*.5;
      if(!(Abs(pmax - W1) <= Precision::PConfusion() ||
         Abs(pmax - W2) <= Precision::PConfusion())  ) myU2 += dmax*.5;
      
      if((myU1 >=0. && myU1 <= 2*PI) &&
       (myU2 >=0. && myU2 <= 2*PI)    ) {
      myU1 = 0.;
      myU2 = 2.*PI;
      UCouture = Standard_False;
      }
      else {
      U = ( myU1 + myU2 ) /2.;
      myU1 = U - PI;
      myU2 = U + PI;
      UCouture = Standard_True;
      }
      
      VCouture = Standard_False;
    }
  }
    break;
    //     
  case GeomAbs_Torus:{
    gp_Torus TR = mySurface->Torus();
    Standard_Real U1, V1, U , V;
    ElSLib::Parameters( TR, P1, U1, V1);
    Standard_Real Step = .1, DeltaU = 0., DeltaV = 0.;
    Standard_Real eps = PI, dmaxU = 0., dU = 0., dmaxV = 0., dV = 0.;
    Standard_Integer nbp = (Standard_Integer)((W2 - W1) / Step + 1);
    nbp = Max(nbp, 3);
    Step = (W2 - W1) / (nbp - 1);
    myU1 = U1; myU2 = U1;
    myV1 = V1; myV2 = V1;
    Standard_Real pminU = W1, pmaxU = W1, pminV = W1, pmaxV = W1,
    plim = W2+.1*Step;
    for(Standard_Real par = W1 + Step; par <= plim; par += Step) {
      P = myCurve->Value(par);
      ElSLib::Parameters( TR, P, U, V);
      U += DeltaU;
      V += DeltaV;
      dU = U - U1;
      dV = V - V1;
      if(dU > eps) {
      U -= DeltaU;
      DeltaU -= 2*PI;
      U += DeltaU;
      dU = U - U1;
      }
      else if(dU < -eps) {
      U -= DeltaU;
      DeltaU += 2*PI;
      U += DeltaU;
      dU = U - U1;
      }
      if(dV > eps) {
      V -= DeltaV;
      DeltaV -= 2*PI;
      V += DeltaV;
      dV = V - V1;
      }
      else if(dV < -eps) {
      V -= DeltaV;
      DeltaV += 2*PI;
      V += DeltaV;
      dV = V - V1;
      }
      dmaxU = Max(dmaxU, Abs(dU));
      dmaxV = Max(dmaxV, Abs(dV));
      if(U < myU1) {myU1 = U; pminU = par;}
      if(U > myU2) {myU2 = U; pmaxU = par;}
      if(V < myV1) {myV1 = V; pminV = par;}
      if(V > myV2) {myV2 = V; pmaxV = par;}
      U1 = U;
      V1 = V;
    }
    
    if(!(Abs(pminU - W1) <= Precision::PConfusion() ||
       Abs(pminU - W2) <= Precision::PConfusion())  ) myU1 -= dmaxU*.5;
    if(!(Abs(pmaxU - W1) <= Precision::PConfusion() ||
       Abs(pmaxU - W2) <= Precision::PConfusion())  ) myU2 += dmaxU*.5;
    if(!(Abs(pminV - W1) <= Precision::PConfusion() ||
       Abs(pminV - W2) <= Precision::PConfusion())  ) myV1 -= dmaxV*.5;
    if(!(Abs(pmaxV - W1) <= Precision::PConfusion() ||
       Abs(pmaxV - W2) <= Precision::PConfusion())  ) myV2 += dmaxV*.5;
    
    if((myU1 >=0. && myU1 <= 2*PI) &&
       (myU2 >=0. && myU2 <= 2*PI)    ) {
      myU1 = 0.;
      myU2 = 2.*PI;
      UCouture = Standard_False;
    }
    else {
      U = ( myU1 + myU2 ) /2.;
      myU1 = U - PI;
      myU2 = U + PI;
      UCouture = Standard_True;
    }
    if((myV1 >=0. && myV1 <= 2*PI) &&
       (myV2 >=0. && myV2 <= 2*PI)    ) {
      VCouture = Standard_False;
    }
    else {
      V = ( myV1 + myV2 ) /2.;
      myV1 = V - PI;
      myV2 = V + PI;
        VCouture = Standard_True;
    }
    
  }
    break;
    
  default:
    {
      UCouture = Standard_False;
      VCouture = Standard_False;
    }
    break;
  }
}
//
//=======================================================================
//function : Parameters
//purpose  : 
//=======================================================================
void Parameters(const Handle(Adaptor3d_HCurve)&   myCurve,
            const Handle(Adaptor3d_HSurface)& mySurface,
            const gp_Pnt& aP1, 
            const Standard_Integer iFirst,
            const Standard_Real aTolU, 
            Standard_Real& aU, 
            Standard_Real& aV)
{
  Standard_Real aTwoPI, aU1, aV1, aU2, aV2, aRSp, aTol3D;
  Standard_Real aTF, aTL, aT2, dT;
  GeomAbs_SurfaceType aSType;
  GeomAbs_CurveType aCType;
  gp_Pnt aP2;
  //
  aTwoPI=2.*PI;
  //
  aSType=mySurface->GetType();
  aCType=myCurve->GetType();
  //
  if (aSType==GeomAbs_Sphere && aCType==GeomAbs_Circle) {
    gp_Sphere aSp=mySurface->Sphere();
    //
    aRSp=aSp.Radius();
    aTol3D=aRSp*aTolU;
    //
    aTF = myCurve->FirstParameter();
    aTL = myCurve->LastParameter ();
    dT=myCurve->Resolution(aTol3D);
    //
    ElSLib::Parameters(aSp, aP1, aU1, aV1);
    if (fabs(aU)<aTolU || fabs(aU-aTwoPI)<aTolU){
      aT2=aTF+dT;
      if (!iFirst) {
      aT2=aTL-dT;
      }
      //
      aP2=myCurve->Value(aT2);
      ElSLib::Parameters(aSp, aP2, aU2, aV2);
      //
      aU1=0.;
      if (aU2>PI) {
      aU1=aTwoPI;
      }
    }
    aU=aU1;
    aV=aV1;
  }
}
//
//=======================================================================
//classn : ProjLib_Function
//purpose  : 
//=======================================================================
class ProjLib_Function : public AppCont_Function2d
{
  Handle(Adaptor3d_HCurve)   myCurve;
  Handle(Adaptor3d_HSurface) mySurface;

  public :

  Standard_Real    myU1,myU2,myV1,myV2;
  Standard_Boolean UCouture,VCouture;
  
  ProjLib_Function(const Handle(Adaptor3d_HCurve)&   C, 
               const Handle(Adaptor3d_HSurface)& S) :
  myCurve(C), mySurface(S),
  myU1(0.0),
  myU2(0.0),
  myV1(0.0),
  myV2(0.0),
  UCouture(Standard_False),
  VCouture(Standard_False)
    {Function_SetUVBounds(myU1,myU2,myV1,myV2,UCouture,VCouture,myCurve,mySurface);}
  
  Standard_Real FirstParameter() const
    {return (myCurve->FirstParameter() + 1.e-9);}
  
  Standard_Real LastParameter() const
    {return (myCurve->LastParameter() -1.e-9);}
  
  
  gp_Pnt2d Value(const Standard_Real t) const
    {return Function_Value(t,myCurve,mySurface,myU1,myU2,myV1,myV2,UCouture,VCouture);}
  
  Standard_Boolean D1(const Standard_Real t, gp_Pnt2d& P, gp_Vec2d& V) const
    {return Function_D1(t,P,V,myCurve,mySurface,myU1,myU2,myV1,myV2,UCouture,VCouture);}
};

//=======================================================================
//function : ProjLib_ComputeApprox
//purpose  : 
//=======================================================================

ProjLib_ComputeApprox::ProjLib_ComputeApprox
  (const Handle(Adaptor3d_HCurve)   & C,
   const Handle(Adaptor3d_HSurface) & S,
   const Standard_Real              Tol )
{
  // if the surface is a plane and the curve a BSpline or a BezierCurve,
  // don`t make an Approx but only the projection of the poles.

  myTolerance = Max(Precision::PApproximation(),Tol);
  Standard_Integer NbKnots, NbPoles ;
  GeomAbs_CurveType   CType = C->GetType();
  GeomAbs_SurfaceType SType = S->GetType();

  Standard_Boolean SurfIsAnal = (SType != GeomAbs_BSplineSurface) &&
                                (SType != GeomAbs_BezierSurface)  &&
                                (SType != GeomAbs_OtherSurface)     ;

  Standard_Boolean CurvIsAnal = (CType != GeomAbs_BSplineCurve) &&
                                (CType != GeomAbs_BezierCurve)  &&
                                (CType != GeomAbs_OtherCurve)     ;

  Standard_Boolean simplecase = SurfIsAnal && CurvIsAnal;

  if (CType == GeomAbs_BSplineCurve &&
      SType == GeomAbs_Plane ) {
    
    // get the poles and eventually the weights
    Handle(Geom_BSplineCurve) BS = C->BSpline();
    NbPoles = BS->NbPoles();
    TColgp_Array1OfPnt P3d( 1, NbPoles);
    TColgp_Array1OfPnt2d Poles( 1, NbPoles);
    TColStd_Array1OfReal Weights( 1, NbPoles);
    if ( BS->IsRational()) BS->Weights(Weights);
    BS->Poles( P3d);
    gp_Pln Plane = S->Plane();
    Standard_Real U,V;
    for ( Standard_Integer i = 1; i <= NbPoles; i++) {
      ElSLib::Parameters( Plane, P3d(i), U, V);
      Poles.SetValue(i,gp_Pnt2d(U,V));
    }
    NbKnots = BS->NbKnots();
    TColStd_Array1OfReal     Knots(1,NbKnots);
    TColStd_Array1OfInteger  Mults(1,NbKnots);
    BS->Knots(Knots) ;
    BS->Multiplicities(Mults) ; 
    // get the knots and mults if BSplineCurve
    if ( BS->IsRational()) {
      myBSpline = new Geom2d_BSplineCurve(Poles,
                                Weights,
                                Knots,
                                Mults,
                                BS->Degree(),
                                BS->IsPeriodic());
    }
    else {
      myBSpline = new Geom2d_BSplineCurve(Poles,
                                Knots,
                                Mults,
                                BS->Degree(),
                                BS->IsPeriodic());
    }
  }
  else if (CType == GeomAbs_BezierCurve &&
         SType == GeomAbs_Plane ) {
    
    // get the poles and eventually the weights
    Handle(Geom_BezierCurve) BezierCurvePtr = C->Bezier() ;
    NbPoles = BezierCurvePtr->NbPoles();
    TColgp_Array1OfPnt P3d( 1, NbPoles);
    TColgp_Array1OfPnt2d  Poles( 1, NbPoles);
    TColStd_Array1OfReal   Weights( 1, NbPoles);
    if ( BezierCurvePtr->IsRational()) {
      BezierCurvePtr->Weights(Weights);
    }
    BezierCurvePtr->Poles( P3d);  
    
    // project the 3D-Poles on the plane
    
    gp_Pln Plane = S->Plane();
    Standard_Real U,V;
    for ( Standard_Integer i = 1; i <= NbPoles; i++) {
      ElSLib::Parameters( Plane, P3d(i), U, V);
      Poles.SetValue(i,gp_Pnt2d(U,V));
    }
    if (  BezierCurvePtr->IsRational()) {
      myBezier =  new Geom2d_BezierCurve(Poles, Weights);
    }
    else {
      myBezier =  new Geom2d_BezierCurve(Poles);
    }
  }
  else {
    ProjLib_Function F( C, S);

#ifdef DEB
    if ( AffichValue) {
      Standard_Integer Nb = 20;
      Standard_Real U1, U2, dU, U;
      U1 = F.FirstParameter();
      U2 = F.LastParameter();
      dU = ( U2 - U1) / Nb;
      TColStd_Array1OfInteger Mults(1,Nb+1);
      TColStd_Array1OfReal    Knots(1,Nb+1);
      TColgp_Array1OfPnt2d    Poles(1,Nb+1);
      for ( Standard_Integer i = 1; i <= Nb+1; i++) {
      U = U1 + (i-1)*dU;
      Poles(i) = F.Value(U);
      Knots(i) = i;
      Mults(i) = 1;
      }
      Mults(1)    = 2;
      Mults(Nb+1) = 2;
#ifdef DRAW
// POP pour NT
      char* ResultName = "Result";
      DrawTrSurf::Set(ResultName,new Geom2d_BSplineCurve(Poles,Knots,Mults,1));
//      DrawTrSurf::Set("Result",new Geom2d_BSplineCurve(Poles,Knots,Mults,1));
#endif
    }
#endif    

//-----------
    Standard_Integer Deg1, Deg2;
    if(simplecase) {
      Deg1 = 8; 
      Deg2 = 10; 
    }
    else {
      Deg1 = 8; 
      Deg2 = 12; 
    }
//-------------
    Approx_FitAndDivide2d Fit(F,Deg1,Deg2,myTolerance,myTolerance,
                        Standard_True);
    if(Fit.IsAllApproximated()) {
      Standard_Integer i;
      Standard_Integer NbCurves = Fit.NbMultiCurves();
    
    // on essaie de rendre la courbe au moins C1
      Convert_CompBezierCurves2dToBSplineCurve2d Conv;

      myTolerance = 0;
      Standard_Real Tol3d,Tol2d;
      for (i = 1; i <= NbCurves; i++) {
      Fit.Error(i,Tol3d, Tol2d);
      myTolerance = Max(myTolerance, Tol2d);
      AppParCurves_MultiCurve MC = Fit.Value( i);       //Charge la Ieme Curve
      TColgp_Array1OfPnt2d Poles2d( 1, MC.Degree() + 1);//Recupere les poles
      MC.Curve(1, Poles2d);
      
      Conv.AddCurve(Poles2d);
      }
    
    //mise a jour des fields de ProjLib_Approx
      Conv.Perform();
    
      NbPoles    = Conv.NbPoles();
      NbKnots    = Conv.NbKnots();

      //7626
      if(NbPoles <= 0 || NbPoles > 100000)
      return;
      if(NbKnots <= 0 || NbKnots > 100000)
      return;

      TColgp_Array1OfPnt2d    NewPoles(1,NbPoles);
      TColStd_Array1OfReal    NewKnots(1,NbKnots);
      TColStd_Array1OfInteger NewMults(1,NbKnots);
    
      Conv.KnotsAndMults(NewKnots,NewMults);
      Conv.Poles(NewPoles);
    
      BSplCLib::Reparametrize(C->FirstParameter(),
                        C->LastParameter(),
                        NewKnots);
    
      // il faut recadrer les poles de debut et de fin:
      // ( Car pour les problemes de couture, on a du ouvrir l`intervalle
      // de definition de la courbe.)
      // On choisit de calculer ces poles par prolongement de la courbe
      // approximee.
    
      gp_Pnt2d P;
      Standard_Real U;
    
      U = C->FirstParameter() - 1.e-9;
      BSplCLib::D0(U, 
               0, 
               Conv.Degree(), 
               Standard_False,
               NewPoles, 
               BSplCLib::NoWeights(), 
               NewKnots, 
               NewMults,
               P);
      NewPoles.SetValue(1,P);
      U = C->LastParameter() + 1.e-9;
      BSplCLib::D0(U, 
               0, 
               Conv.Degree(), 
               Standard_False,
               NewPoles, 
               BSplCLib::NoWeights(), 
               NewKnots, 
               NewMults,
               P);
      NewPoles.SetValue(NbPoles,P);
      myBSpline = new Geom2d_BSplineCurve (NewPoles,
                                 NewKnots,
                                 NewMults,
                                 Conv.Degree());
    }
    else {
      Standard_Integer NbCurves = Fit.NbMultiCurves();
      if(NbCurves != 0) {
      Standard_Real Tol3d,Tol2d;
      Fit.Error(NbCurves,Tol3d, Tol2d);
      myTolerance = Tol2d;
      }
    }

    //Return curve home
    Standard_Real UFirst = F.FirstParameter();
    gp_Pnt P3d = C->Value( UFirst );
    Standard_Real u, v;
    switch (SType)
      {
      case GeomAbs_Plane:
      {
        gp_Pln Plane = S->Plane();
        ElSLib::Parameters( Plane, P3d, u, v );
        break;
      }
      case GeomAbs_Cylinder:
      {
        gp_Cylinder Cylinder = S->Cylinder();
        ElSLib::Parameters( Cylinder, P3d, u, v );
        break;
      }
      case GeomAbs_Cone:
      {
        gp_Cone Cone = S->Cone();
        ElSLib::Parameters( Cone, P3d, u, v );
        break;
      }
      case GeomAbs_Sphere:
      {
        gp_Sphere Sphere = S->Sphere();
        ElSLib::Parameters( Sphere, P3d, u, v );
        break;
      }
      case GeomAbs_Torus:
      {
        gp_Torus Torus = S->Torus();
        ElSLib::Parameters( Torus, P3d, u, v );
        break;
      }
      default:
      Standard_NoSuchObject::Raise("ProjLib_ComputeApprox::Value");
      }
    Standard_Boolean ToMirror = Standard_False;
    Standard_Real du = 0., dv = 0.;
    Standard_Integer number;
    if (F.VCouture)
      { 
      if (SType == GeomAbs_Sphere && Abs(u-F.myU1) > PI)
        {
          ToMirror = Standard_True;
          dv = -PI;
          v = PI - v;
        }
      Standard_Real newV = ElCLib::InPeriod( v, F.myV1, F.myV2 );
      number = (Standard_Integer) (Floor((newV-v)/(F.myV2-F.myV1)));
      dv -= number*(F.myV2-F.myV1);
      }
    if (F.UCouture || F.VCouture && SType == GeomAbs_Sphere)
      {
      gp_Pnt2d P2d = F.Value( UFirst );
      number = (Standard_Integer) (Floor((P2d.X()-u)/PI + Epsilon(PI)));
      du = -number*PI;
      }

    if (!myBSpline.IsNull())
      {
      if (du != 0. || dv != 0.)
        myBSpline->Translate( gp_Vec2d(du,dv) );
      if (ToMirror)
        {
          gp_Ax2d Axe( gp_Pnt2d(0.,0.), gp_Dir2d(1.,0.) );
          myBSpline->Mirror( Axe );
        }
      }
  }
}

//=======================================================================
//function : BSpline
//purpose  : 
//=======================================================================

Handle(Geom2d_BSplineCurve)  ProjLib_ComputeApprox::BSpline() const 

{
  return myBSpline ;
}

//=======================================================================
//function : Bezier
//purpose  : 
//=======================================================================

Handle(Geom2d_BezierCurve)  ProjLib_ComputeApprox::Bezier()  const 

{
  return myBezier ;
}


//=======================================================================
//function : Tolerance
//purpose  : 
//=======================================================================

Standard_Real ProjLib_ComputeApprox::Tolerance() const 
{
  return myTolerance;
}



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