// Copyright (c) 1995-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.


#include <Bnd_Box.hxx>
#include <Bnd_Box2d.hxx>
#include <BndLib.hxx>
#include <ElCLib.hxx>
#include <gp_Circ.hxx>
#include <gp_Circ2d.hxx>
#include <gp_Cone.hxx>
#include <gp_Cylinder.hxx>
#include <gp_Elips.hxx>
#include <gp_Elips2d.hxx>
#include <gp_Hypr.hxx>
#include <gp_Hypr2d.hxx>
#include <gp_Lin.hxx>
#include <gp_Lin2d.hxx>
#include <gp_Parab.hxx>
#include <gp_Parab2d.hxx>
#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Sphere.hxx>
#include <gp_Torus.hxx>
#include <gp_XY.hxx>
#include <gp_XYZ.hxx>
#include <Precision.hxx>
#include <Standard_Failure.hxx>
#include <ElSLib.hxx>

static 
  Standard_Integer ComputeBox(const gp_Hypr& aHypr, 
                              const Standard_Real aT1, 
                              const Standard_Real aT2, 
                              Bnd_Box& aBox);


namespace
{
  //! Compute method
  template<class PointType, class BndBoxType>
  void Compute (const Standard_Real theP1, const Standard_Real theP2,
                const Standard_Real theRa ,const Standard_Real theRb,
                const PointType& theXd, const PointType& theYd, const PointType& theO,
                BndBoxType& theB)
  {
    Standard_Real aTeta1;
    Standard_Real aTeta2;
    if(theP2 < theP1)
    { 
      aTeta1 = theP2;
      aTeta2 = theP1;
    }
    else
    {
      aTeta1 = theP1;
      aTeta2 = theP2;
    }

    Standard_Real aDelta = Abs(aTeta2-aTeta1); 
    if(aDelta > 2. * M_PI)
    {
      aTeta1 = 0.;
      aTeta2 = 2. * M_PI;
    }
    else
    {
      if(aTeta1 < 0.)
      {
        do{ aTeta1 += 2.*M_PI; } while (aTeta1 < 0.);
      }
      else if (aTeta1 > 2.*M_PI)
      {
        do { aTeta1 -= 2.*M_PI; } while (aTeta1 > 2.*M_PI);
      }
      aTeta2 = aTeta1 + aDelta;
    }

    // One places already both ends
    Standard_Real aCn1, aSn1 ,aCn2, aSn2;
    aCn1 = Cos(aTeta1); aSn1 = Sin(aTeta1);
    aCn2 = Cos(aTeta2); aSn2 = Sin(aTeta2);
    theB.Add(PointType( theO.Coord() +theRa*aCn1*theXd.Coord() +theRb*aSn1*theYd.Coord()));
    theB.Add(PointType(theO.Coord() +theRa*aCn2*theXd.Coord() +theRb*aSn2*theYd.Coord()));
    
    Standard_Real aRam, aRbm;
    if (aDelta > M_PI/8.)
    {
      // Main radiuses to take into account only 8 points (/cos(Pi/8.))
      aRam = theRa/0.92387953251128674;
      aRbm = theRb/0.92387953251128674;
    }
    else
    {
      // Main radiuses to take into account the arrow
      Standard_Real aTc = cos(aDelta/2);
      aRam = theRa/aTc;
      aRbm = theRb/aTc;
    }
    theB.Add(PointType(theO.Coord() + aRam*aCn1*theXd.Coord() + aRbm*aSn1*theYd.Coord()));
    theB.Add(PointType(theO.Coord() + aRam*aCn2*theXd.Coord() + aRbm*aSn2*theYd.Coord()));

// cos or sin M_PI/4.
#define PI4 0.70710678118654746

// 8 points of the polygon
#define addPoint0 theB.Add(PointType(theO.Coord() +aRam*theXd.Coord()))
#define addPoint1 theB.Add(PointType(theO.Coord() +aRam*PI4*theXd.Coord() +aRbm*PI4*theYd.Coord()))
#define addPoint2 theB.Add(PointType(theO.Coord() +aRbm*theYd.Coord()))
#define addPoint3 theB.Add(PointType(theO.Coord() -aRam*PI4*theXd.Coord() +aRbm*PI4*theYd.Coord()))
#define addPoint4 theB.Add(PointType(theO.Coord() -aRam*theXd.Coord() ))
#define addPoint5 theB.Add(PointType(theO.Coord() -aRam*PI4*theXd.Coord() -aRbm*PI4*theYd.Coord()))
#define addPoint6 theB.Add(PointType(theO.Coord() -aRbm*theYd.Coord()))
#define addPoint7 theB.Add(PointType(theO.Coord() +aRam*PI4*theXd.Coord() -aRbm*PI4*theYd.Coord()))

    Standard_Integer aDeb = (Standard_Integer )( aTeta1/(M_PI/4.));
    Standard_Integer aFin = (Standard_Integer )( aTeta2/(M_PI/4.));
    aDeb++;

    if (aDeb > aFin) return;

    switch (aDeb)
    {
    case 1:
      {
        addPoint1;
        if (aFin <= 1) break;
      }
      Standard_FALLTHROUGH
    case 2:
      {
        addPoint2;
        if (aFin <= 2) break;
      }
      Standard_FALLTHROUGH
    case 3:
      {
        addPoint3;
        if (aFin <= 3) break;
      }
      Standard_FALLTHROUGH
    case 4:
      {
        addPoint4;
        if (aFin <= 4) break;
      }
      Standard_FALLTHROUGH
    case 5:
      {
        addPoint5;
        if (aFin <= 5) break;
      }
      Standard_FALLTHROUGH
    case 6:
      {
        addPoint6;
        if (aFin <= 6) break;
      }
      Standard_FALLTHROUGH
    case 7:
      {
        addPoint7;
        if (aFin <= 7) break;
      }
      Standard_FALLTHROUGH
    case 8:
      {
        addPoint0;
        if (aFin <= 8) break;
      }
      Standard_FALLTHROUGH
    case 9:
      {
        addPoint1;
        if (aFin <= 9) break;
      }  
      Standard_FALLTHROUGH
    case 10:
      {
        addPoint2;
        if (aFin <= 10) break;
      }
      Standard_FALLTHROUGH
    case 11:
      {
        addPoint3;
        if (aFin <= 11) break;
      }  
      Standard_FALLTHROUGH
    case 12:
      {
        addPoint4;
        if (aFin <= 12) break;
      }  
      Standard_FALLTHROUGH
    case 13:
      {
        addPoint5;
        if (aFin <= 13) break;
      }
      Standard_FALLTHROUGH
    case 14:
      {
        addPoint6;
        if (aFin <= 14) break;
      }
      Standard_FALLTHROUGH
    case 15:
      {
        addPoint7;
        if (aFin <= 15) break;
      }
    }
  }
} // end namespace

static void OpenMin(const gp_Dir& V,Bnd_Box& B) {
  gp_Dir OX(1.,0.,0.);
  gp_Dir OY(0.,1.,0.);
  gp_Dir OZ(0.,0.,1.);
  if (V.IsParallel(OX,Precision::Angular())) 
    B.OpenXmin();
  else if (V.IsParallel(OY,Precision::Angular())) 
    B.OpenYmin();
  else if (V.IsParallel(OZ,Precision::Angular())) 
    B.OpenZmin();
  else {
    B.OpenXmin();B.OpenYmin();B.OpenZmin();
  }
}

static void OpenMax(const gp_Dir& V,Bnd_Box& B) {
  gp_Dir OX(1.,0.,0.);
  gp_Dir OY(0.,1.,0.);
  gp_Dir OZ(0.,0.,1.);
  if (V.IsParallel(OX,Precision::Angular())) 
    B.OpenXmax();
  else if (V.IsParallel(OY,Precision::Angular())) 
    B.OpenYmax();
  else if (V.IsParallel(OZ,Precision::Angular())) 
    B.OpenZmax();
  else {
    B.OpenXmax();B.OpenYmax();B.OpenZmax();
  }
}

static void OpenMinMax(const gp_Dir& V,Bnd_Box& B) {
  gp_Dir OX(1.,0.,0.);
  gp_Dir OY(0.,1.,0.);
  gp_Dir OZ(0.,0.,1.);
  if (V.IsParallel(OX,Precision::Angular())) {
    B.OpenXmax();B.OpenXmin();
  }
  else if (V.IsParallel(OY,Precision::Angular())) {
    B.OpenYmax();B.OpenYmin();
  }
  else if (V.IsParallel(OZ,Precision::Angular())) {
    B.OpenZmax();B.OpenZmin();
  }
  else {
    B.OpenXmin();B.OpenYmin();B.OpenZmin();
    B.OpenXmax();B.OpenYmax();B.OpenZmax();
  }
}

static void OpenMin(const gp_Dir2d& V,Bnd_Box2d& B) {
  gp_Dir2d OX(1.,0.);
  gp_Dir2d OY(0.,1.);
  if (V.IsParallel(OX,Precision::Angular())) 
    B.OpenXmin();
  else if (V.IsParallel(OY,Precision::Angular())) 
    B.OpenYmin();
  else {
    B.OpenXmin();B.OpenYmin();
  }
}

static void OpenMax(const gp_Dir2d& V,Bnd_Box2d& B) {
  gp_Dir2d OX(1.,0.);
  gp_Dir2d OY(0.,1.);
  if (V.IsParallel(OX,Precision::Angular())) 
    B.OpenXmax();
  else if (V.IsParallel(OY,Precision::Angular())) 
    B.OpenYmax();
  else {
    B.OpenXmax();B.OpenYmax();
  }
}

static void OpenMinMax(const gp_Dir2d& V,Bnd_Box2d& B) {
  gp_Dir2d OX(1.,0.);
  gp_Dir2d OY(0.,1.);
  if (V.IsParallel(OX,Precision::Angular())) {
    B.OpenXmax();B.OpenXmin();
  }
  else if (V.IsParallel(OY,Precision::Angular())) {
    B.OpenYmax();B.OpenYmin();
  }
  else {
    B.OpenXmin();B.OpenYmin();
    B.OpenXmax();B.OpenYmax();
  }
}


void BndLib::Add( const gp_Lin& L,const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, Bnd_Box& B) {

  if (Precision::IsNegativeInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      OpenMinMax(L.Direction(),B);
      B.Add(ElCLib::Value(0.,L));
    }
    else {
      OpenMin(L.Direction(),B);
      B.Add(ElCLib::Value(P2,L));
    }
  }
  else if (Precision::IsPositiveInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      OpenMinMax(L.Direction(),B);
      B.Add(ElCLib::Value(0.,L));
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else {
      OpenMax(L.Direction(),B);
      B.Add(ElCLib::Value(P2,L));
    }
  }
  else  {
    B.Add(ElCLib::Value(P1,L));
    if (Precision::IsNegativeInfinite(P2)) {
      OpenMin(L.Direction(),B);
    }
    else if (Precision::IsPositiveInfinite(P2)){
      OpenMax(L.Direction(),B);
    }
    else {
      B.Add(ElCLib::Value(P2,L));
    }
  }
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Lin2d& L,const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, Bnd_Box2d& B) {

  if (Precision::IsNegativeInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      OpenMinMax(L.Direction(),B);
      B.Add(ElCLib::Value(0.,L));
    }
    else {
      OpenMin(L.Direction(),B);
      B.Add(ElCLib::Value(P2,L));
    }
  }
  else if (Precision::IsPositiveInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      OpenMinMax(L.Direction(),B);
      B.Add(ElCLib::Value(0.,L));
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else {
      OpenMax(L.Direction(),B);
      B.Add(ElCLib::Value(P2,L));
    }
  }
  else  {
    B.Add(ElCLib::Value(P1,L));
    if (Precision::IsNegativeInfinite(P2)) {
      OpenMin(L.Direction(),B);
    }
    else if (Precision::IsPositiveInfinite(P2)){
      OpenMax(L.Direction(),B);
    }
    else {
      B.Add(ElCLib::Value(P2,L));
    }
  }
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Circ& C, const Standard_Real Tol, Bnd_Box& B) 
{
  Standard_Real U1 = 0., U2 = 2.*M_PI;
  Add(C, U1, U2, Tol, B);
}

void BndLib::Add(const gp_Circ& C,
                 const Standard_Real U1,
                 const Standard_Real U2,
                 const Standard_Real Tol, 
                 Bnd_Box& B) 
{
  Standard_Real period = 2.*M_PI - Epsilon(2.*M_PI);

  Standard_Real utrim1 = U1, utrim2 = U2;
  if(U2 - U1 > period)
  {
    utrim1 = 0.;
    utrim2 = 2.*M_PI;
  }
  else
  {
    Standard_Real tol = Epsilon(1.);
    ElCLib::AdjustPeriodic(0., 2.*M_PI,
                           tol,
                           utrim1, utrim2);
  }
  Standard_Real R = C.Radius();
  gp_XYZ O  = C.Location().XYZ();
  gp_XYZ Xd = C.XAxis().Direction().XYZ();
  gp_XYZ Yd = C.YAxis().Direction().XYZ();
  const gp_Ax2& pos = C.Position();
  //
  Standard_Real tt;
  Standard_Real xmin, xmax, txmin, txmax;
  if(Abs(Xd.X()) > gp::Resolution())
  {
    txmin = ATan(Yd.X() / Xd.X());
    txmin = ElCLib::InPeriod(txmin, 0., 2.*M_PI);
  }
  else
  {
    txmin = M_PI/ 2.;
  }
  txmax = txmin <= M_PI? txmin + M_PI : txmin - M_PI;
  xmin = R * Cos(txmin) * Xd.X() + R * Sin(txmin) * Yd.X() + O.X();
  xmax = R * Cos(txmax) * Xd.X() + R * Sin(txmax) * Yd.X() + O.X();
  if(xmin > xmax)
  {
    tt = xmin;
    xmin = xmax;
    xmax = tt;
    tt = txmin;
    txmin = txmax;
    txmax = tt;
  }
  //
  Standard_Real ymin, ymax, tymin, tymax;
  if(Abs(Xd.Y()) > gp::Resolution())
  {
    tymin = ATan(Yd.Y() / Xd.Y());
    tymin = ElCLib::InPeriod(tymin, 0., 2.*M_PI);
  }
  else
  {
    tymin = M_PI/ 2.;
  }
  tymax = tymin <= M_PI? tymin + M_PI : tymin - M_PI;
  ymin = R * Cos(tymin) * Xd.Y() + R * Sin(tymin) * Yd.Y() + O.Y();
  ymax = R * Cos(tymax) * Xd.Y() + R * Sin(tymax) * Yd.Y() + O.Y();
  if(ymin > ymax)
  {
    tt = ymin;
    ymin = ymax;
    ymax = tt;
    tt = tymin;
    tymin = tymax;
    tymax = tt;
  }
  //
  Standard_Real zmin, zmax, tzmin, tzmax;
  if(Abs(Xd.Z()) > gp::Resolution())
  {
    tzmin = ATan(Yd.Z() / Xd.Z());
    tzmin = ElCLib::InPeriod(tzmin, 0., 2.*M_PI);
  }
  else
  {
    tzmin = M_PI/ 2.;
  }
  tzmax = tzmin <= M_PI? tzmin + M_PI : tzmin - M_PI;
  zmin = R * Cos(tzmin) * Xd.Z() + R * Sin(tzmin) * Yd.Z() + O.Z();
  zmax = R * Cos(tzmax) * Xd.Z() + R * Sin(tzmax) * Yd.Z() + O.Z();
  if(zmin > zmax)
  {
    tt = zmin;
    zmin = zmax;
    zmax = tt;
    tt = tzmin;
    tzmin = tzmax;
    tzmax = tt;
  }
  //
  if(utrim2 - utrim1 >= period)
  {
    B.Update(xmin, ymin, zmin, xmax, ymax, zmax);
  }
  else
  {
    gp_Pnt P = ElCLib::CircleValue(utrim1, pos, R);
    B.Add(P);
    P = ElCLib::CircleValue(utrim2, pos, R);
    B.Add(P);
    Standard_Real Xmin, Ymin, Zmin, Xmax, Ymax, Zmax;
    B.FinitePart().Get(Xmin, Ymin, Zmin, Xmax, Ymax, Zmax);
    Standard_Real gap = B.GetGap();
    Xmin += gap;
    Ymin += gap;
    Zmin += gap;
    Xmax -= gap;
    Ymax -= gap;
    Zmax -= gap;
    //
    txmin = ElCLib::InPeriod(txmin, utrim1, utrim1 + 2. * M_PI);
    if(txmin >= utrim1 && txmin <= utrim2)
    {
      Xmin = Min(xmin, Xmin);
    }
    txmax = ElCLib::InPeriod(txmax, utrim1, utrim1 + 2. * M_PI);
    if(txmax >= utrim1 && txmax <= utrim2)
    {
      Xmax = Max(xmax, Xmax);
   }
    //
    tymin = ElCLib::InPeriod(tymin, utrim1, utrim1 + 2. * M_PI);
    if(tymin >= utrim1 && tymin <= utrim2)
    {
      Ymin = Min(ymin, Ymin);
    }
    tymax = ElCLib::InPeriod(tymax, utrim1, utrim1 + 2. * M_PI);
    if(tymax >= utrim1 && tymax <= utrim2)
    {
      Ymax = Max(ymax, Ymax);
    }
    //
    tzmin = ElCLib::InPeriod(tzmin, utrim1, utrim1 + 2. * M_PI);
    if(tzmin >= utrim1 && tzmin <= utrim2)
    {
      Zmin = Min(zmin, Zmin);
    }
    tzmax = ElCLib::InPeriod(tzmax, utrim1, utrim1 + 2. * M_PI);
    if(tzmax >= utrim1 && tzmax <= utrim2)
    {
      Zmax = Max(zmax, Zmax);
    }
    //
    B.Update(Xmin, Ymin, Zmin, Xmax, Ymax, Zmax);
  }
  //
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Circ2d& C,const Standard_Real Tol, Bnd_Box2d& B) {

  Standard_Real R = C.Radius();
  gp_XY O  = C.Location().XY();
  gp_XY Xd = C.XAxis().Direction().XY();
  gp_XY Yd = C.YAxis().Direction().XY();
  B.Add(gp_Pnt2d(O -R*Xd -R*Yd));
  B.Add(gp_Pnt2d(O -R*Xd +R*Yd));
  B.Add(gp_Pnt2d(O +R*Xd -R*Yd));
  B.Add(gp_Pnt2d(O +R*Xd +R*Yd));
  B.Enlarge(Tol);
}

void BndLib::Add(const gp_Circ2d& C,const Standard_Real P1,
   const Standard_Real P2,
   const Standard_Real Tol, Bnd_Box2d& B) {

       Compute(P1,P2,C.Radius(),C.Radius(),gp_Pnt2d(C.XAxis().Direction().XY()),
         gp_Pnt2d(C.YAxis().Direction().XY()),C.Location(),B);
  B.Enlarge(Tol);
}

void BndLib::Add(const gp_Elips& C, const Standard_Real Tol, Bnd_Box& B) 
{
  Standard_Real U1 = 0., U2 = 2.*M_PI;
  Add(C, U1, U2, Tol, B);
}

void BndLib::Add(const gp_Elips& C,
                 const Standard_Real U1,
                 const Standard_Real U2,
                 const Standard_Real Tol, 
                 Bnd_Box& B) 
{
  Standard_Real period = 2.*M_PI - Epsilon(2.*M_PI);

  Standard_Real utrim1 = U1, utrim2 = U2;
  if(U2 - U1 > period)
  {
    utrim1 = 0.;
    utrim2 = 2.*M_PI;
  }
  else
  {
    Standard_Real tol = Epsilon(1.);
    ElCLib::AdjustPeriodic(0., 2.*M_PI,
                           tol,
                           utrim1, utrim2);
  }
  Standard_Real MajR = C.MajorRadius();
  Standard_Real MinR = C.MinorRadius();
  gp_XYZ O  = C.Location().XYZ();
  gp_XYZ Xd = C.XAxis().Direction().XYZ();
  gp_XYZ Yd = C.YAxis().Direction().XYZ();
  const gp_Ax2& pos = C.Position();
  //
  Standard_Real tt;
  Standard_Real xmin, xmax, txmin, txmax;
  if(Abs(Xd.X()) > gp::Resolution())
  {
    txmin = ATan((MinR*Yd.X()) / (MajR*Xd.X()));
    txmin = ElCLib::InPeriod(txmin, 0., 2.*M_PI);
  }
  else
  {
    txmin = M_PI/ 2.;
  }
  txmax = txmin <= M_PI? txmin + M_PI : txmin - M_PI;
  xmin = MajR * Cos(txmin) * Xd.X() + MinR * Sin(txmin) * Yd.X() + O.X();
  xmax = MajR * Cos(txmax) * Xd.X() + MinR * Sin(txmax) * Yd.X() + O.X();
  if(xmin > xmax)
  {
    tt = xmin;
    xmin = xmax;
    xmax = tt;
    tt = txmin;
    txmin = txmax;
    txmax = tt;
  }
  //
  Standard_Real ymin, ymax, tymin, tymax;
  if(Abs(Xd.Y()) > gp::Resolution())
  {
    tymin = ATan((MinR*Yd.Y()) / (MajR*Xd.Y()));
    tymin = ElCLib::InPeriod(tymin, 0., 2.*M_PI);
  }
  else
  {
    tymin = M_PI/ 2.;
  }
  tymax = tymin <= M_PI? tymin + M_PI : tymin - M_PI;
  ymin = MajR * Cos(tymin) * Xd.Y() + MinR * Sin(tymin) * Yd.Y() + O.Y();
  ymax = MajR * Cos(tymax) * Xd.Y() + MinR * Sin(tymax) * Yd.Y() + O.Y();
  if(ymin > ymax)
  {
    tt = ymin;
    ymin = ymax;
    ymax = tt;
    tt = tymin;
    tymin = tymax;
    tymax = tt;
  }
  //
  Standard_Real zmin, zmax, tzmin, tzmax;
  if(Abs(Xd.Z()) > gp::Resolution())
  {
    tzmin = ATan((MinR*Yd.Z()) / (MajR*Xd.Z()));
    tzmin = ElCLib::InPeriod(tzmin, 0., 2.*M_PI);
  }
  else
  {
    tzmin = M_PI/ 2.;
  }
  tzmax = tzmin <= M_PI? tzmin + M_PI : tzmin - M_PI;
  zmin = MajR * Cos(tzmin) * Xd.Z() + MinR * Sin(tzmin) * Yd.Z() + O.Z();
  zmax = MajR * Cos(tzmax) * Xd.Z() + MinR * Sin(tzmax) * Yd.Z() + O.Z();
  if(zmin > zmax)
  {
    tt = zmin;
    zmin = zmax;
    zmax = tt;
    tt = tzmin;
    tzmin = tzmax;
    tzmax = tt;
  }
  //
  if(utrim2 - utrim1 >= period)
  {
    B.Update(xmin, ymin, zmin, xmax, ymax, zmax);
  }
  else
  {
    gp_Pnt P = ElCLib::EllipseValue(utrim1, pos, MajR, MinR);
    B.Add(P);
    P = ElCLib::EllipseValue(utrim2, pos, MajR, MinR);
    B.Add(P);
    Standard_Real Xmin, Ymin, Zmin, Xmax, Ymax, Zmax;
    B.FinitePart().Get(Xmin, Ymin, Zmin, Xmax, Ymax, Zmax);
    Standard_Real gap = B.GetGap();
    Xmin += gap;
    Ymin += gap;
    Zmin += gap;
    Xmax -= gap;
    Ymax -= gap;
    Zmax -= gap;
    //
    txmin = ElCLib::InPeriod(txmin, utrim1, utrim1 + 2. * M_PI);
    if(txmin >= utrim1 && txmin <= utrim2)
    {
      Xmin = Min(xmin, Xmin);
    }
    txmax = ElCLib::InPeriod(txmax, utrim1, utrim1 + 2. * M_PI);
    if(txmax >= utrim1 && txmax <= utrim2)
    {
      Xmax = Max(xmax, Xmax);
    }
    //
    tymin = ElCLib::InPeriod(tymin, utrim1, utrim1 + 2. * M_PI);
    if(tymin >= utrim1 && tymin <= utrim2)
    {
      Ymin = Min(ymin, Ymin);
    }
    tymax = ElCLib::InPeriod(tymax, utrim1, utrim1 + 2. * M_PI);
    if(tymax >= utrim1 && tymax <= utrim2)
    {
      Ymax = Max(ymax, Ymax);
    }
    //
    tzmin = ElCLib::InPeriod(tzmin, utrim1, utrim1 + 2. * M_PI);
    if(tzmin >= utrim1 && tzmin <= utrim2)
    {
      Zmin = Min(zmin, Zmin);
    }
    tzmax = ElCLib::InPeriod(tzmax, utrim1, utrim1 + 2. * M_PI);
    if(tzmax >= utrim1 && tzmax <= utrim2)
    {
      Zmax = Max(zmax, Zmax);
    }
    //
    B.Update(Xmin, Ymin, Zmin, Xmax, Ymax, Zmax);
  }
  //
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Elips2d& C,const Standard_Real Tol, Bnd_Box2d& B) {

  Standard_Real Ra= C.MajorRadius();
  Standard_Real Rb= C.MinorRadius();
  gp_XY Xd = C.XAxis().Direction().XY();
  gp_XY Yd = C.YAxis().Direction().XY();
  gp_XY O  = C.Location().XY();
  B.Add(gp_Pnt2d(O +Ra*Xd +Rb*Yd));
  B.Add(gp_Pnt2d(O -Ra*Xd +Rb*Yd));
  B.Add(gp_Pnt2d(O -Ra*Xd -Rb*Yd));
  B.Add(gp_Pnt2d(O +Ra*Xd -Rb*Yd));
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Elips2d& C,const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, Bnd_Box2d& B) {

  Compute(P1,P2,C.MajorRadius(),C.MinorRadius(),
   gp_Pnt2d(C.XAxis().Direction().XY()),
   gp_Pnt2d(C.YAxis().Direction().XY()),C.Location(),B);
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Parab& P,const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, Bnd_Box& B) {

  if (Precision::IsNegativeInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      B.OpenXmax();B.OpenYmax();B.OpenZmax();
    }
    else {
      B.Add(ElCLib::Value(P2,P));
    }
    B.OpenXmin();B.OpenYmin();B.OpenZmin();
  }
  else if (Precision::IsPositiveInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();B.OpenZmin();
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else {
      B.Add(ElCLib::Value(P2,P));
    }
    B.OpenXmax();B.OpenYmax();B.OpenZmax();
  }
  else  {
    B.Add(ElCLib::Value(P1,P));
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();B.OpenZmin();
    }
    else if (Precision::IsPositiveInfinite(P2)){
      B.OpenXmax();B.OpenYmax();B.OpenZmax();
    }
    else {
      B.Add(ElCLib::Value(P2,P));
      if (P1*P2<0) B.Add(ElCLib::Value(0.,P));
    }
  }
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Parab2d& P,const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, Bnd_Box2d& B) {

  if (Precision::IsNegativeInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      B.OpenXmax();B.OpenYmax();
    }
    else {
      B.Add(ElCLib::Value(P2,P));
    }
    B.OpenXmin();B.OpenYmin();
  }
  else if (Precision::IsPositiveInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else {
      B.Add(ElCLib::Value(P2,P));
    }
    B.OpenXmax();B.OpenYmax();
  }
  else  {
    B.Add(ElCLib::Value(P1,P));
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();
    }
    else if (Precision::IsPositiveInfinite(P2)){
      B.OpenXmax();B.OpenYmax();
    }
    else {
      B.Add(ElCLib::Value(P2,P));
      if (P1*P2<0) B.Add(ElCLib::Value(0.,P));
    }
  }
  B.Enlarge(Tol);
}

//=======================================================================
//function : Add
//purpose  : 
//=======================================================================
void BndLib::Add(const gp_Hypr& H,
                 const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, 
                 Bnd_Box& B) 
{
  if (Precision::IsNegativeInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      B.OpenXmax();B.OpenYmax();B.OpenZmax();
    }
    else {
      B.Add(ElCLib::Value(P2,H));
    }
    B.OpenXmin();B.OpenYmin();B.OpenZmin();
  }
  else if (Precision::IsPositiveInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();B.OpenZmin();
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else {
      B.Add(ElCLib::Value(P2,H));
    }
    B.OpenXmax();B.OpenYmax();B.OpenZmax();
  }
  else  {
    B.Add(ElCLib::Value(P1,H));
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();B.OpenZmin();
    }
    else if (Precision::IsPositiveInfinite(P2)){
      B.OpenXmax();B.OpenYmax();B.OpenZmax();
    }
    else {
      ComputeBox(H, P1, P2, B);
    }
  }
  B.Enlarge(Tol);
}

void BndLib::Add(const gp_Hypr2d& H,const Standard_Real P1,
                 const Standard_Real P2,
                 const Standard_Real Tol, Bnd_Box2d& B) {
  
  if (Precision::IsNegativeInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      B.OpenXmax();B.OpenYmax();
    }
    else {
      B.Add(ElCLib::Value(P2,H));
    }
    B.OpenXmin();B.OpenYmin();
  }
  else if (Precision::IsPositiveInfinite(P1)) {
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();
    }
    else if (Precision::IsPositiveInfinite(P2)) {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else {
      B.Add(ElCLib::Value(P2,H));
    }
    B.OpenXmax();B.OpenYmax();
  }
  else  {
    B.Add(ElCLib::Value(P1,H));
    if (Precision::IsNegativeInfinite(P2)) {
      B.OpenXmin();B.OpenYmin();
    }
    else if (Precision::IsPositiveInfinite(P2)){
      B.OpenXmax();B.OpenYmax();
    }
    else {
      B.Add(ElCLib::Value(P2,H));
      if (P1*P2<0) B.Add(ElCLib::Value(0.,H));
    }
  }
  B.Enlarge(Tol);
}

static void ComputeCyl(const gp_Cylinder& Cyl, 
                       const Standard_Real UMin, const Standard_Real UMax, 
                       const Standard_Real VMin, const Standard_Real VMax, 
                       Bnd_Box& B)
{
  gp_Circ aC = ElSLib::CylinderVIso(Cyl.Position(), Cyl.Radius(), VMin);
  BndLib::Add(aC, UMin, UMax, 0., B);
  //
  gp_Vec aT = (VMax - VMin) * Cyl.Axis().Direction();
  aC.Translate(aT);
  BndLib::Add(aC, UMin, UMax, 0., B);
}

void BndLib::Add( const gp_Cylinder& S,const Standard_Real UMin,
                 const Standard_Real UMax,const Standard_Real VMin,
                 const Standard_Real VMax,const Standard_Real Tol, Bnd_Box& B)
{
  if (Precision::IsNegativeInfinite(VMin))
  {
    if (Precision::IsNegativeInfinite(VMax))
    {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(VMax))
    {
      OpenMinMax(S.Axis().Direction(),B);
    }
    else
    {
      ComputeCyl(S, UMin, UMax, 0., VMax,B);
      OpenMin(S.Axis().Direction(),B);
    }
  }
  else if (Precision::IsPositiveInfinite(VMin)) 
  {
    if (Precision::IsNegativeInfinite(VMax)) 
    {
      OpenMinMax(S.Axis().Direction(),B);
    }
    else if (Precision::IsPositiveInfinite(VMax))
    {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else
    {
      ComputeCyl(S, UMin, UMax, 0., VMax, B);
      OpenMax(S.Axis().Direction(),B);
    }
  }
  else
  {
    if (Precision::IsNegativeInfinite(VMax))
    {
      ComputeCyl(S, UMin, UMax, VMin, 0., B);
      OpenMin(S.Axis().Direction(),B);
    }
    else if (Precision::IsPositiveInfinite(VMax)) 
    {
      ComputeCyl(S, UMin, UMax, VMin, 0., B);
      OpenMax(S.Axis().Direction(),B); 
    }
    else 
    {
      ComputeCyl(S, UMin, UMax, VMin, VMax, B);
    }
  }

  B.Enlarge(Tol);

}

void BndLib::Add( const gp_Cylinder& S,const Standard_Real VMin,
                 const Standard_Real VMax,const Standard_Real Tol, Bnd_Box& B) {

  BndLib::Add(S,0.,2.*M_PI,VMin,VMax,Tol,B);
}

static void ComputeCone (const gp_Cone& Cone, 
                         const Standard_Real UMin, const Standard_Real UMax, 
                         const Standard_Real VMin, const Standard_Real VMax, 
                         Bnd_Box& B)
{
  const gp_Ax3& aPos = Cone.Position();
  Standard_Real R = Cone.RefRadius();
  Standard_Real sang = Cone.SemiAngle();
  gp_Circ aC = ElSLib::ConeVIso(aPos, R, sang, VMin);
  if(aC.Radius() > Precision::Confusion())
  {
    BndLib::Add(aC, UMin, UMax, 0., B);
  }
  else
  {
    B.Add(aC.Location());
  }
  //
  aC = ElSLib::ConeVIso(aPos, R, sang, VMax);
  if(aC.Radius() > Precision::Confusion())
  {
    BndLib::Add(aC, UMin, UMax, 0., B);
  }
  else
  {
    B.Add(aC.Location());
  }
}

void BndLib::Add(const gp_Cone& S,const Standard_Real UMin,
                 const Standard_Real UMax,const Standard_Real VMin,
                 const Standard_Real VMax,const Standard_Real Tol, Bnd_Box& B) {

  Standard_Real A = S.SemiAngle();
  if (Precision::IsNegativeInfinite(VMin)) 
  {
    if (Precision::IsNegativeInfinite(VMax)) 
    {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else if (Precision::IsPositiveInfinite(VMax)) 
    {
      gp_Dir D(Cos(A)*S.Axis().Direction());
      OpenMinMax(D,B); 
    }
    else 
    {
      ComputeCone(S, UMin, UMax, 0., VMax, B);
      gp_Dir D(Cos(A)*S.Axis().Direction());
      OpenMin(D,B);     
    }

  }
  else if (Precision::IsPositiveInfinite(VMin)) 
  {
    if (Precision::IsNegativeInfinite(VMax))
    {
      gp_Dir D(Cos(A)*S.Axis().Direction());
      OpenMinMax(D,B);
    }
    else if (Precision::IsPositiveInfinite(VMax)) 
    {
      throw Standard_Failure("BndLib::bad parameter");
    }
    else 
    {
      ComputeCone(S, UMin, UMax, 0., VMax, B);
      gp_Dir D(Cos(A)*S.Axis().Direction());
      OpenMax(D,B);
    }
  }
  else 
  {
    if (Precision::IsNegativeInfinite(VMax)) 
    {
      ComputeCone(S, UMin, UMax, VMin, 0., B);
      gp_Dir D(Cos(A)*S.Axis().Direction());
      OpenMin(D,B);
    }
    else if (Precision::IsPositiveInfinite(VMax)) 
    {
      ComputeCone(S, UMin, UMax, VMin, 0., B);
      gp_Dir D(Cos(A)*S.Axis().Direction());
      OpenMax(D,B);
    }
    else 
    {
      ComputeCone(S, UMin, UMax, VMin, VMax, B);
    }
  }

  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Cone& S,const Standard_Real VMin,
                 const Standard_Real VMax,const Standard_Real Tol, Bnd_Box& B) {

  BndLib::Add(S,0.,2.*M_PI,VMin,VMax,Tol,B);
}

static void ComputeSphere (const gp_Sphere& Sphere, 
                           const Standard_Real UMin, const Standard_Real UMax, 
                           const Standard_Real VMin, const Standard_Real VMax, 
                           Bnd_Box& B)
{
  gp_Pnt P = Sphere.Location();
  Standard_Real R = Sphere.Radius();
  Standard_Real xmin, ymin, zmin, xmax, ymax, zmax;
  xmin = P.X() - R;
  xmax = P.X() + R;
  ymin = P.Y() - R;
  ymax = P.Y() + R;
  zmin = P.Z() - R;
  zmax = P.Z() + R;
  
  Standard_Real uper = 2. * M_PI - Precision::PConfusion();
  Standard_Real vper = M_PI - Precision::PConfusion();
  if (UMax - UMin >= uper && VMax - VMin >= vper)
  {
    // a whole sphere
    B.Update(xmin, ymin, zmin, xmax, ymax, zmax);
  }
  else
  {
    Standard_Real u, v;
    Standard_Real umax = UMin + 2. * M_PI;
    const gp_Ax3& Pos = Sphere.Position();
    gp_Pnt PExt = P;
    PExt.SetX(xmin);
    ElSLib::SphereParameters(Pos, R, PExt, u, v);
    u = ElCLib::InPeriod(u, UMin, umax);
    if(u >= UMin && u <= UMax && v >= VMin && v <= VMax)
    {
      B.Add(PExt);
    }
    //
    PExt.SetX(xmax);
    ElSLib::SphereParameters(Pos, R, PExt, u, v);
    u = ElCLib::InPeriod(u, UMin, umax);
    if(u >= UMin && u <= UMax && v >= VMin && v <= VMax)
    {
      B.Add(PExt);
    }
    PExt.SetX(P.X());
    //
    PExt.SetY(ymin);
    ElSLib::SphereParameters(Pos, R, PExt, u, v);
    u = ElCLib::InPeriod(u, UMin, umax);
    if(u >= UMin && u <= UMax && v >= VMin && v <= VMax)
    {
      B.Add(PExt);
    }
    //
    PExt.SetY(ymax);
    ElSLib::SphereParameters(Pos, R, PExt, u, v);
    u = ElCLib::InPeriod(u, UMin, umax);
    if(u >= UMin && u <= UMax && v >= VMin && v <= VMax)
    {
      B.Add(PExt);
    }
    PExt.SetY(P.Y());
    //
    PExt.SetZ(zmin);
    ElSLib::SphereParameters(Pos, R, PExt, u, v);
    u = ElCLib::InPeriod(u, UMin, umax);
    if(u >= UMin && u <= UMax && v >= VMin && v <= VMax)
    {
      B.Add(PExt);
    }
    //
    PExt.SetZ(zmax);
    ElSLib::SphereParameters(Pos, R, PExt, u, v);
    u = ElCLib::InPeriod(u, UMin, umax);
    if(u >= UMin && u <= UMax && v >= VMin && v <= VMax)
    {
      B.Add(PExt);
    }
    //
    // Add boundaries of patch
    // UMin, UMax
    gp_Circ aC = ElSLib::SphereUIso(Pos, R, UMin);
    BndLib::Add(aC, VMin, VMax, 0., B);
    aC = ElSLib::SphereUIso(Pos, R, UMax);
    BndLib::Add(aC, VMin, VMax, 0., B);
    // VMin, VMax
    aC = ElSLib::SphereVIso(Pos, R, VMin);
    BndLib::Add(aC, UMin, UMax, 0., B);
    aC = ElSLib::SphereVIso(Pos, R, VMax);
    BndLib::Add(aC, UMin, UMax, 0., B);
  }
}

void BndLib::Add(const gp_Sphere& S,const Standard_Real UMin,
                 const Standard_Real UMax,const Standard_Real VMin,
                 const Standard_Real VMax,const Standard_Real Tol, Bnd_Box& B) 
{
  ComputeSphere(S, UMin, UMax, VMin, VMax, B);
  B.Enlarge(Tol);
}

void BndLib::Add( const gp_Sphere& S,const Standard_Real Tol, Bnd_Box& B) 
{
  gp_Pnt P = S.Location();
  Standard_Real R = S.Radius();
  Standard_Real xmin, ymin, zmin, xmax, ymax, zmax;
  xmin = P.X() - R;
  xmax = P.X() + R;
  ymin = P.Y() - R;
  ymax = P.Y() + R;
  zmin = P.Z() - R;
  zmax = P.Z() + R;
  B.Update(xmin, ymin, zmin, xmax, ymax, zmax);
  B.Enlarge(Tol);
}

void BndLib::Add(const gp_Torus& S,const Standard_Real UMin,
   const Standard_Real UMax,const Standard_Real VMin,
   const Standard_Real VMax,const Standard_Real Tol, Bnd_Box& B) {

  Standard_Integer Fi1;
  Standard_Integer Fi2;
  if (VMax<VMin) {
    Fi1 = (Standard_Integer )( VMax/(M_PI/4.));
    Fi2 = (Standard_Integer )( VMin/(M_PI/4.));
  }
  else {
    Fi1 = (Standard_Integer )( VMin/(M_PI/4.));
    Fi2 = (Standard_Integer )( VMax/(M_PI/4.));
  }
  Fi2++;
  
  Standard_Real Ra = S.MajorRadius();
  Standard_Real Ri = S.MinorRadius();

  if (Fi2<Fi1) return;

#define SC 0.71
#define addP0    (Compute(UMin,UMax,Ra+Ri,Ra+Ri,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),S.Location(),B))
#define addP1    (Compute(UMin,UMax,Ra+Ri*SC,Ra+Ri*SC,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),gp_Pnt(S.Location().XYZ()+(Ri*SC)*S.Axis().Direction().XYZ()),B))
#define addP2    (Compute(UMin,UMax,Ra,Ra,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),gp_Pnt(S.Location().XYZ()+Ri*S.Axis().Direction().XYZ()),B))
#define addP3    (Compute(UMin,UMax,Ra-Ri*SC,Ra-Ri*SC,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),gp_Pnt(S.Location().XYZ()+(Ri*SC)*S.Axis().Direction().XYZ()),B))
#define addP4    (Compute(UMin,UMax,Ra-Ri,Ra-Ri,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),S.Location(),B))
#define addP5    (Compute(UMin,UMax,Ra-Ri*SC,Ra-Ri*SC,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),gp_Pnt(S.Location().XYZ()-(Ri*SC)*S.Axis().Direction().XYZ()),B))
#define addP6    (Compute(UMin,UMax,Ra,Ra,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),gp_Pnt(S.Location().XYZ()-Ri*S.Axis().Direction().XYZ()),B))
#define addP7    (Compute(UMin,UMax,Ra+Ri*SC,Ra+Ri*SC,gp_Pnt(S.XAxis().Direction().XYZ()),gp_Pnt(S.YAxis().Direction().XYZ()),gp_Pnt(S.Location().XYZ()-(Ri*SC)*S.Axis().Direction().XYZ()),B))
  
  switch (Fi1) {
  case 0 : 
    {
      addP0;
      if (Fi2 <= 0) break;
    }
    Standard_FALLTHROUGH
  case 1 : 
    {
      addP1;
      if (Fi2 <= 1) break;
    }
    Standard_FALLTHROUGH
  case 2 :  
    {
      addP2;
      if (Fi2 <= 2) break;
    }
    Standard_FALLTHROUGH
  case 3 :  
    {
      addP3;
      if (Fi2 <= 3) break;
    }
    Standard_FALLTHROUGH
  case 4 :  
    {
      addP4;
      if (Fi2 <= 4) break;
    }
    Standard_FALLTHROUGH
  case 5 :  
    {
      addP5;
      if (Fi2 <= 5) break;
    }
    Standard_FALLTHROUGH
  case 6 :  
    {
      addP6;
      if (Fi2 <= 6) break;
    }
    Standard_FALLTHROUGH
  case 7 :  
    {
      addP7;
      if (Fi2 <= 7) break;
    }
    Standard_FALLTHROUGH
  case 8 :  
  default :
    {
      addP0;
      switch (Fi2) {
      case 15 :  
        addP7;
        Standard_FALLTHROUGH
      case 14 :  
        addP6;
        Standard_FALLTHROUGH
      case 13 :  
        addP5;
        Standard_FALLTHROUGH
      case 12 :  
        addP4;
        Standard_FALLTHROUGH
      case 11 :  
        addP3;
        Standard_FALLTHROUGH
      case 10 :  
        addP2;
        Standard_FALLTHROUGH
      case 9 : 
        addP1;
        Standard_FALLTHROUGH
      case 8 : 
        break;
      }    
    }
  }    
  B.Enlarge(Tol);
}


void BndLib::Add( const gp_Torus& S,const Standard_Real Tol, Bnd_Box& B) {

  Standard_Real RMa = S.MajorRadius();
  Standard_Real Rmi = S.MinorRadius(); 
  gp_XYZ O = S.Location().XYZ();
  gp_XYZ Xd = S.XAxis().Direction().XYZ();
  gp_XYZ Yd = S.YAxis().Direction().XYZ();
  gp_XYZ Zd = S.Axis().Direction().XYZ();
  B.Add(gp_Pnt(O -(RMa+Rmi)*Xd -(RMa+Rmi)*Yd+ Rmi*Zd)); 
  B.Add(gp_Pnt(O -(RMa+Rmi)*Xd -(RMa+Rmi)*Yd- Rmi*Zd)); 
  B.Add(gp_Pnt(O +(RMa+Rmi)*Xd -(RMa+Rmi)*Yd+ Rmi*Zd)); 
  B.Add(gp_Pnt(O +(RMa+Rmi)*Xd -(RMa+Rmi)*Yd- Rmi*Zd)); 
  B.Add(gp_Pnt(O -(RMa+Rmi)*Xd +(RMa+Rmi)*Yd+ Rmi*Zd)); 
  B.Add(gp_Pnt(O -(RMa+Rmi)*Xd +(RMa+Rmi)*Yd- Rmi*Zd)); 
  B.Add(gp_Pnt(O +(RMa+Rmi)*Xd +(RMa+Rmi)*Yd+ Rmi*Zd)); 
  B.Add(gp_Pnt(O +(RMa+Rmi)*Xd +(RMa+Rmi)*Yd- Rmi*Zd)); 
  B.Enlarge(Tol);
}
//=======================================================================
//function : ComputeBox
//purpose  : 
//=======================================================================
Standard_Integer ComputeBox(const gp_Hypr& aHypr, 
                            const Standard_Real aT1, 
                            const Standard_Real aT2, 
                            Bnd_Box& aBox)
{
  Standard_Integer i, iErr;
  Standard_Real aRmaj, aRmin, aA, aB, aABP, aBAM, aT3, aCf, aEps;
  gp_Pnt aP1, aP2, aP3, aP0;
  //
  //
  aP1=ElCLib::Value(aT1, aHypr);
  aP2=ElCLib::Value(aT2, aHypr);
  //
  aBox.Add(aP1);
  aBox.Add(aP2);
  //
  if (aT1*aT2<0.) {
    aP0=ElCLib::Value(0., aHypr);
    aBox.Add(aP0);
  }
  //
  aEps=Epsilon(1.);
  iErr=1;
  //
  const gp_Ax2& aPos=aHypr.Position();
  const gp_XYZ& aXDir = aPos.XDirection().XYZ();
  const gp_XYZ& aYDir = aPos.YDirection().XYZ();
  aRmaj=aHypr.MajorRadius();
  aRmin=aHypr.MinorRadius();
  //
  aT3=0;
  for (i=1; i<=3; ++i) {
    aA=aRmin*aYDir.Coord(i);
    aB=aRmaj*aXDir.Coord(i);
    //
    aABP=aA+aB;
    aBAM=aB-aA;
    //
    aABP=fabs(aABP);
    aBAM=fabs(aBAM);
    //
    if (aABP<aEps || aBAM<aEps) {
      continue;
    }
    //
    aCf=aBAM/aABP;
    aT3=log(sqrt(aCf));
    //
    if (aT3<aT1 || aT3>aT2) {
      continue;
    }
    iErr=0;
    break;
  }
  //
  if (iErr) {
    return iErr;
  }
  //
  aP3=ElCLib::Value(aT3, aHypr);
  aBox.Add(aP3);
  //
  return iErr;
}