src/StdPrs/StdPrs_Isolines.cxx

// Created on: 2014-10-14
// Created by: Anton POLETAEV
// Copyright (c) 2013-2014 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 <StdPrs_Isolines.hxx>

#include <Adaptor3d_IsoCurve.hxx>
#include <Bnd_Range.hxx>
#include <BRepTools.hxx>
#include <BRep_Tool.hxx>
#include <GCPnts_AbscissaPoint.hxx>
#include <GCPnts_QuasiUniformDeflection.hxx>
#include <Geom_BezierSurface.hxx>
#include <Geom_BSplineSurface.hxx>
#include <Geom_Plane.hxx>
#include <Geom_Line.hxx>
#include <Geom2d_Line.hxx>
#include <Geom2dAdaptor_Curve.hxx>
#include <GeomAdaptor_Curve.hxx>
#include <GeomLib_Tool.hxx>
#include <gp_Lin2d.hxx>
#include <Hatch_Hatcher.hxx>
#include <NCollection_Shared.hxx>
#include <Prs3d.hxx>
#include <Prs3d_IsoAspect.hxx>
#include <Poly_Array1OfTriangle.hxx>
#include <Poly_Triangulation.hxx>
#include <StdPrs_DeflectionCurve.hxx>
#include <StdPrs_ToolRFace.hxx>
#include <TColgp_SequenceOfPnt2d.hxx>
#include <Standard_ErrorHandler.hxx>
#include <Geom_Surface.hxx>
#include <Geom_OffsetSurface.hxx>
#include <Geom_RectangularTrimmedSurface.hxx>
#include <algorithm>

namespace
{
  const gp_Lin2d isoU (const Standard_Real theU) { return gp_Lin2d (gp_Pnt2d (theU, 0.0), gp::DY2d()); }
  const gp_Lin2d isoV (const Standard_Real theV) { return gp_Lin2d (gp_Pnt2d (0.0, theV), gp::DX2d()); }

  typedef NCollection_Shared< NCollection_Vector<StdPrs_Isolines::SegOnIso> > VecOfSegments;
  typedef NCollection_Sequence<Handle(VecOfSegments)> SeqOfVecOfSegments;

  //! Pack isoline segments into polylines.
  static void sortSegments (const SeqOfVecOfSegments&   theSegments,
                            Prs3d_NListOfSequenceOfPnt& thePolylines)
  {
    for (SeqOfVecOfSegments::Iterator aLineIter (theSegments); aLineIter.More(); aLineIter.Next())
    {
      Handle(VecOfSegments)& anIsoSegs = aLineIter.ChangeValue();
      std::stable_sort (anIsoSegs->begin(), anIsoSegs->end());

      Handle(TColgp_HSequenceOfPnt) aPolyline = new TColgp_HSequenceOfPnt();
      thePolylines.Append (aPolyline);
      Standard_Real aLast = 0.0;
      for (VecOfSegments::Iterator aSegIter (*anIsoSegs); aSegIter.More(); aSegIter.Next())
      {
        if (!aPolyline->IsEmpty()
         && Abs (aSegIter.Value()[0].Param - aLast) > Precision::PConfusion())
        {
          aPolyline = new TColgp_HSequenceOfPnt();
          thePolylines.Append (aPolyline);
        }

        aPolyline->Append (aSegIter.Value()[0].Pnt);
        aPolyline->Append (aSegIter.Value()[1].Pnt);
        aLast = aSegIter.Value()[1].Param;
      }
    }
  }

  //! Reorder and adjust to the limit a curve's parameter values.
  //! @param theCurve [in] the curve.
  //! @param theLimit [in] the parameter limit value.
  //! @param theFirst [in/out] the first parameter value.
  //! @param theLast  [in/out] the last parameter value.
  static void findLimits (const Adaptor3d_Curve& theCurve,
                          const Standard_Real    theLimit,
                          Standard_Real&         theFirst,
                          Standard_Real&         theLast)
  {
    theFirst = Max (theCurve.FirstParameter(), theFirst);
    theLast  = Min (theCurve.LastParameter(), theLast);

    Standard_Boolean isFirstInf = Precision::IsNegativeInfinite (theFirst);
    Standard_Boolean isLastInf  = Precision::IsPositiveInfinite (theLast);

    if (!isFirstInf && !isLastInf)
    {
      return;
    }

    gp_Pnt aP1, aP2;
    Standard_Real aDelta = 1.0;
    if (isFirstInf && isLastInf)
    {
      do
      {
        aDelta *= 2.0;
        theFirst = -aDelta;
        theLast  =  aDelta;
        theCurve.D0 (theFirst, aP1);
        theCurve.D0 (theLast,  aP2);
      }
      while (aP1.Distance (aP2) < theLimit);
    }
    else if (isFirstInf)
    {
      theCurve.D0 (theLast, aP2);
      do
      {
        aDelta *= 2.0;
        theFirst = theLast - aDelta;
        theCurve.D0 (theFirst, aP1);
      }
      while (aP1.Distance (aP2) < theLimit);
    }
    else if (isLastInf)
    {
      theCurve.D0 (theFirst, aP1);
      do
      {
        aDelta *= 2.0;
        theLast = theFirst + aDelta;
        theCurve.D0 (theLast, aP2);
      }
      while (aP1.Distance (aP2) < theLimit);
    }
  }

}

//==================================================================
// function : AddOnTriangulation
// purpose  :
//==================================================================
void StdPrs_Isolines::AddOnTriangulation (const Handle(Prs3d_Presentation)& thePresentation,
                                          const TopoDS_Face&                theFace,
                                          const Handle(Prs3d_Drawer)&       theDrawer)
{
  Prs3d_NListOfSequenceOfPnt aUPolylines, aVPolylines;
  AddOnTriangulation (theFace, theDrawer, aUPolylines, aVPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->UIsoAspect(), aUPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->VIsoAspect(), aVPolylines);
}

//==================================================================
// function : AddOnTriangulation
// purpose  :
//==================================================================
void StdPrs_Isolines::AddOnTriangulation (const TopoDS_Face&          theFace,
                                          const Handle(Prs3d_Drawer)& theDrawer,
                                          Prs3d_NListOfSequenceOfPnt& theUPolylines,
                                          Prs3d_NListOfSequenceOfPnt& theVPolylines)
{
  const Standard_Integer aNbIsoU = theDrawer->UIsoAspect()->Number();
  const Standard_Integer aNbIsoV = theDrawer->VIsoAspect()->Number();
  if (aNbIsoU < 1 && aNbIsoV < 1)
  {
    return;
  }

  // Evaluate parameters for uv isolines.
  TColStd_SequenceOfReal aUIsoParams;
  TColStd_SequenceOfReal aVIsoParams;
  Standard_Real aUmin = 0., aUmax = 0., aVmin = 0., aVmax = 0.;
  UVIsoParameters (theFace, aNbIsoU, aNbIsoV, theDrawer->MaximalParameterValue(), aUIsoParams, aVIsoParams,
                   aUmin, aUmax, aVmin, aVmax);

  // Access surface definition.
  TopLoc_Location aLocSurface;
  Handle(Geom_Surface) aSurface = BRep_Tool::Surface (theFace, aLocSurface);
  if (aSurface.IsNull())
  {
    return;
  }

  // Access triangulation.
  TopLoc_Location aLocTriangulation;
  const Handle(Poly_Triangulation)& aTriangulation = BRep_Tool::Triangulation (theFace, aLocTriangulation);
  if (aTriangulation.IsNull())
  {
    return;
  }

  // Setup equal location for surface and triangulation.
  if (!aLocTriangulation.IsEqual (aLocSurface))
  {
    aSurface = Handle (Geom_Surface)::DownCast (
      aSurface->Transformed ((aLocSurface / aLocTriangulation).Transformation()));
  }

  const Handle(Standard_Type)& TheType = aSurface->DynamicType();
  if (TheType == STANDARD_TYPE(Geom_OffsetSurface))
  {
    Standard_Real u1, u2, v1, v2;
    aSurface->Bounds(u1, u2, v1, v2);
    //Isolines of Offset surfaces are calculated by approximation and
    //cannot be calculated for infinite limits.
    if (Precision::IsInfinite(u1) || Precision::IsInfinite(u2) ||
      Precision::IsInfinite(v1) || Precision::IsInfinite(v2))
    {
      u1 = Max(aUmin, u1);
      u2 = Min(aUmax, u2);
      v1 = Max(aVmin, v1);
      v2 = Min(aVmax, v2);
      aSurface = new Geom_RectangularTrimmedSurface(aSurface, u1, u2, v1, v2);
    }
  }

  addOnTriangulation (aTriangulation, aSurface, aLocTriangulation, aUIsoParams, aVIsoParams, theUPolylines, theVPolylines);
}

//==================================================================
// function : AddOnTriangulation
// purpose  :
//==================================================================
void StdPrs_Isolines::AddOnTriangulation (const Handle(Prs3d_Presentation)& thePresentation,
                                          const Handle(Poly_Triangulation)& theTriangulation,
                                          const Handle(Geom_Surface)&       theSurface,
                                          const TopLoc_Location&            theLocation,
                                          const Handle(Prs3d_Drawer)&       theDrawer,
                                          const TColStd_SequenceOfReal&     theUIsoParams,
                                          const TColStd_SequenceOfReal&     theVIsoParams)
{
  Prs3d_NListOfSequenceOfPnt aUPolylines, aVPolylines;
  addOnTriangulation (theTriangulation, theSurface, theLocation, theUIsoParams, theVIsoParams, aUPolylines, aVPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->UIsoAspect(), aUPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->VIsoAspect(), aVPolylines);
}

//==================================================================
// function : addOnTriangulation
// purpose  :
//==================================================================
void StdPrs_Isolines::addOnTriangulation (const Handle(Poly_Triangulation)& theTriangulation,
                                          const Handle(Geom_Surface)&       theSurface,
                                          const TopLoc_Location&            theLocation,
                                          const TColStd_SequenceOfReal&     theUIsoParams,
                                          const TColStd_SequenceOfReal&     theVIsoParams,
                                          Prs3d_NListOfSequenceOfPnt&       theUPolylines,
                                          Prs3d_NListOfSequenceOfPnt&       theVPolylines)
{
  for (Standard_Integer anUVIter = 0; anUVIter < 2; ++anUVIter)
  {
    const Standard_Boolean        isUIso      = anUVIter == 0;
    const TColStd_SequenceOfReal& anIsoParams = isUIso ? theUIsoParams : theVIsoParams;
    const Standard_Integer aNbIsolines = anIsoParams.Length();
    if (aNbIsolines == 0)
    {
      continue;
    }

    SeqOfVecOfSegments aPolylines;
    TColStd_Array1OfInteger anIsoIndexes (1, aNbIsolines);
    anIsoIndexes.Init (-1);
    for (Standard_Integer anIsoIdx = 1; anIsoIdx <= aNbIsolines; ++anIsoIdx)
    {
      const gp_Lin2d anIsolineUV = isUIso ? isoU (anIsoParams.Value (anIsoIdx)) : isoV (anIsoParams.Value (anIsoIdx));
      Handle(VecOfSegments) anIsoPnts;
      if (anIsoIndexes.Value (anIsoIdx) != -1)
      {
        anIsoPnts = aPolylines.ChangeValue (anIsoIndexes.Value (anIsoIdx));
      }

      for (Standard_Integer aTriIter = 1; aTriIter <= theTriangulation->NbTriangles(); ++aTriIter)
      {
        Standard_Integer aNodeIdxs[3];
        theTriangulation->Triangle (aTriIter).Get (aNodeIdxs[0], aNodeIdxs[1],aNodeIdxs[2]);
        const gp_Pnt aNodesXYZ[3] = { theTriangulation->Node (aNodeIdxs[0]),
                                      theTriangulation->Node (aNodeIdxs[1]),
                                      theTriangulation->Node (aNodeIdxs[2]) };
        const gp_Pnt2d aNodesUV[3] = { theTriangulation->UVNode (aNodeIdxs[0]),
                                       theTriangulation->UVNode (aNodeIdxs[1]),
                                       theTriangulation->UVNode (aNodeIdxs[2]) };

        // Find intersections with triangle in uv space and its projection on triangulation.
        SegOnIso aSegment;
        if (!findSegmentOnTriangulation (theSurface, isUIso, anIsolineUV, aNodesXYZ, aNodesUV, aSegment))
        {
          continue;
        }

        if (anIsoPnts.IsNull())
        {
          aPolylines.Append (new VecOfSegments());
          anIsoIndexes.SetValue (anIsoIdx, aPolylines.Size());
          anIsoPnts = aPolylines.ChangeValue (anIsoIndexes.Value (anIsoIdx));
        }

        if (!theLocation.IsIdentity())
        {
          aSegment[0].Pnt.Transform (theLocation);
          aSegment[1].Pnt.Transform (theLocation);
        }
        anIsoPnts->Append (aSegment);
      }
    }

    sortSegments (aPolylines, isUIso ? theUPolylines : theVPolylines);
  }
}

//==================================================================
// function : AddOnSurface
// purpose  :
//==================================================================
void StdPrs_Isolines::AddOnSurface (const Handle(Prs3d_Presentation)& thePresentation,
                                    const TopoDS_Face&                theFace,
                                    const Handle(Prs3d_Drawer)&       theDrawer,
                                    const Standard_Real               theDeflection)
{
  Prs3d_NListOfSequenceOfPnt aUPolylines, aVPolylines;
  AddOnSurface (theFace, theDrawer, theDeflection, aUPolylines, aVPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->UIsoAspect(), aUPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->VIsoAspect(), aVPolylines);
}

//==================================================================
// function : AddOnSurface
// purpose  :
//==================================================================
void StdPrs_Isolines::AddOnSurface (const TopoDS_Face&          theFace,
                                    const Handle(Prs3d_Drawer)& theDrawer,
                                    const Standard_Real         theDeflection,
                                    Prs3d_NListOfSequenceOfPnt& theUPolylines,
                                    Prs3d_NListOfSequenceOfPnt& theVPolylines)
{
  const Standard_Integer aNbIsoU = theDrawer->UIsoAspect()->Number();
  const Standard_Integer aNbIsoV = theDrawer->VIsoAspect()->Number();
  if (aNbIsoU < 1 && aNbIsoV < 1)
  {
    return;
  }

  // Evaluate parameters for uv isolines.
  TColStd_SequenceOfReal aUIsoParams, aVIsoParams;
  Standard_Real aUmin = 0., aUmax = 0., aVmin = 0., aVmax = 0.;
  UVIsoParameters (theFace, aNbIsoU, aNbIsoV, theDrawer->MaximalParameterValue(), aUIsoParams, aVIsoParams,
                   aUmin, aUmax, aVmin, aVmax);

  BRepAdaptor_Surface aSurface (theFace);
  addOnSurface (new BRepAdaptor_Surface (aSurface),
                theDrawer,
                theDeflection,
                aUIsoParams,
                aVIsoParams,
                theUPolylines,
                theVPolylines);
}

//==================================================================
// function : AddOnSurface
// purpose  :
//==================================================================
void StdPrs_Isolines::AddOnSurface (const Handle(Prs3d_Presentation)&   thePresentation,
                                    const Handle(BRepAdaptor_Surface)& theSurface,
                                    const Handle(Prs3d_Drawer)&         theDrawer,
                                    const Standard_Real                 theDeflection,
                                    const TColStd_SequenceOfReal&       theUIsoParams,
                                    const TColStd_SequenceOfReal&       theVIsoParams)
{
  Prs3d_NListOfSequenceOfPnt aUPolylines, aVPolylines;
  addOnSurface (theSurface, theDrawer, theDeflection, theUIsoParams, theVIsoParams, aUPolylines, aVPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->UIsoAspect(), aUPolylines);
  Prs3d::AddPrimitivesGroup (thePresentation, theDrawer->VIsoAspect(), aVPolylines);
}

//==================================================================
// function : addOnSurface
// purpose  :
//==================================================================
void StdPrs_Isolines::addOnSurface (const Handle(BRepAdaptor_Surface)& theSurface,
                                    const Handle(Prs3d_Drawer)&         theDrawer,
                                    const Standard_Real                 theDeflection,
                                    const TColStd_SequenceOfReal&       theUIsoParams,
                                    const TColStd_SequenceOfReal&       theVIsoParams,
                                    Prs3d_NListOfSequenceOfPnt&         theUPolylines,
                                    Prs3d_NListOfSequenceOfPnt&         theVPolylines)
{
  // Choose a deflection for sampling edge uv curves.
  Standard_Real aUVLimit = theDrawer->MaximalParameterValue();
  Standard_Real aUmin  = Max (theSurface->FirstUParameter(), -aUVLimit);
  Standard_Real aUmax  = Min (theSurface->LastUParameter(),   aUVLimit);
  Standard_Real aVmin  = Max (theSurface->FirstVParameter(), -aUVLimit);
  Standard_Real aVmax  = Min (theSurface->LastVParameter(),   aUVLimit);
  Standard_Real aSamplerDeflection = Max (aUmax - aUmin, aVmax - aVmin) * theDrawer->DeviationCoefficient();
  Standard_Real aHatchingTolerance = RealLast();

  try
  {
    OCC_CATCH_SIGNALS
    // Determine edge points for trimming uv hatch region.
    TColgp_SequenceOfPnt2d aTrimPoints;
    StdPrs_ToolRFace anEdgeTool (theSurface);
    for (anEdgeTool.Init(); anEdgeTool.More(); anEdgeTool.Next())
    {
      TopAbs_Orientation anOrientation = anEdgeTool.Orientation();
      const Adaptor2d_Curve2d* anEdgeCurve = &anEdgeTool.Value();
      if (anEdgeCurve->GetType() != GeomAbs_Line)
      {
        GCPnts_QuasiUniformDeflection aSampler (*anEdgeCurve, aSamplerDeflection);
        if (!aSampler.IsDone())
        {
#ifdef OCCT_DEBUG
          std::cout << "Cannot evaluate curve on surface" << std::endl;
#endif
          continue;
        }

        Standard_Integer aNumberOfPoints = aSampler.NbPoints();
        if (aNumberOfPoints < 2)
        {
          continue;
        }

        for (Standard_Integer anI = 1; anI < aNumberOfPoints; ++anI)
        {
          gp_Pnt2d aP1 (aSampler.Value (anI    ).X(), aSampler.Value (anI    ).Y());
          gp_Pnt2d aP2 (aSampler.Value (anI + 1).X(), aSampler.Value (anI + 1).Y());

          aHatchingTolerance = Min (aP1.SquareDistance (aP2), aHatchingTolerance);

          aTrimPoints.Append (anOrientation == TopAbs_FORWARD ? aP1 : aP2);
          aTrimPoints.Append (anOrientation == TopAbs_FORWARD ? aP2 : aP1);
        }
      }
      else
      {
        Standard_Real aU1 = anEdgeCurve->FirstParameter();
        Standard_Real aU2 = anEdgeCurve->LastParameter();

        // MSV 17.08.06 OCC13144: U2 occurred less than U1, to overcome it
        // ensure that distance U2-U1 is not greater than aLimit*2,
        // if greater then choose an origin and use aLimit to define
        // U1 and U2 anew.
        Standard_Real anOrigin = 0.0;

        if (!Precision::IsNegativeInfinite (aU1) || !Precision::IsPositiveInfinite(aU2))
        {
          if (Precision::IsNegativeInfinite (aU1))
          {
            anOrigin = aU2 - aUVLimit;
          }
          else if (Precision::IsPositiveInfinite (aU2))
          {
            anOrigin = aU1 + aUVLimit;
          }
          else
          {
            anOrigin = (aU1 + aU2) * 0.5;
          }
        }

        aU1 = Max (anOrigin - aUVLimit, aU1);
        aU2 = Min (anOrigin + aUVLimit, aU2);

        gp_Pnt2d aP1 = anEdgeCurve->Value (aU1);
        gp_Pnt2d aP2 = anEdgeCurve->Value (aU2);

        aHatchingTolerance = Min (aP1.SquareDistance(aP2), aHatchingTolerance);

        aTrimPoints.Append (anOrientation == TopAbs_FORWARD ? aP1 : aP2);
        aTrimPoints.Append (anOrientation == TopAbs_FORWARD ? aP2 : aP1);
      }
    }

    // re-calculate UV-range basing on p-curves tessellation
    Bnd_Range aTrimU, aTrimV;
    for (Standard_Integer anI = 1; anI <= aTrimPoints.Length(); ++anI)
    {
      const gp_Pnt2d& aTrimPnt = aTrimPoints.Value (anI);
      aTrimU.Add (aTrimPnt.X());
      aTrimV.Add (aTrimPnt.Y());
    }
    // ignore p-curves tessellation under sampler deflection - it might clamp range
    if (!aTrimU.IsVoid() && aTrimU.Delta() <= aSamplerDeflection)
    {
      aTrimU.SetVoid();
    }
    if (!aTrimV.IsVoid() && aTrimV.Delta() <= aSamplerDeflection)
    {
      aTrimV.SetVoid();
    }

    // Compute a hatching tolerance.
    aHatchingTolerance *= 0.1;
    aHatchingTolerance = Max (Precision::Confusion(), aHatchingTolerance);
    aHatchingTolerance = Min (1.0E-5, aHatchingTolerance);

    // Load isolines into hatcher.
    Hatch_Hatcher aHatcher (aHatchingTolerance, anEdgeTool.IsOriented());

    for (Standard_Integer anIso = 1; anIso <= theUIsoParams.Length(); ++anIso)
    {
      const Standard_Real anIsoParamU = theUIsoParams.Value (anIso);
      if (aTrimU.IsVoid()
      || !aTrimU.IsOut (anIsoParamU))
      {
        aHatcher.AddXLine (anIsoParamU);
      }
    }
    for (Standard_Integer anIso = 1; anIso <= theVIsoParams.Length(); ++anIso)
    {
      const Standard_Real anIsoParamV = theVIsoParams.Value (anIso);
      if (aTrimV.IsVoid()
      || !aTrimV.IsOut (anIsoParamV))
      {
        aHatcher.AddYLine (anIsoParamV);
      }
    }

    // Trim hatching region.
    for (Standard_Integer anI = 1; anI <= aTrimPoints.Length(); anI += 2)
    {
      aHatcher.Trim (aTrimPoints (anI), aTrimPoints (anI + 1));
    }

    // Use surface definition for evaluation of Bezier, B-spline surface.
    // Use isoline adapter for other types of surfaces.
    GeomAbs_SurfaceType  aSurfType = theSurface->GetType();
    Handle(Geom_Surface) aBSurface;
    GeomAdaptor_Curve    aBSurfaceCurve;
    Adaptor3d_IsoCurve   aCanonicalCurve;
    if (aSurfType == GeomAbs_BezierSurface)
    {
      aBSurface = theSurface->Bezier();
    }
    else if (aSurfType == GeomAbs_BSplineSurface)
    {
      aBSurface = theSurface->BSpline();
    }
    else
    {
      aCanonicalCurve.Load (theSurface);
    }

    // For each isoline: compute its segments.
    for (Standard_Integer anI = 1; anI <= aHatcher.NbLines(); anI++)
    {
      Standard_Real anIsoParam = aHatcher.Coordinate (anI);
      Standard_Boolean isIsoU  = aHatcher.IsXLine (anI);

      // For each isoline's segment: evaluate its points.
      for (Standard_Integer aJ = 1; aJ <= aHatcher.NbIntervals (anI); aJ++)
      {
        Standard_Real aSegmentP1 = aHatcher.Start (anI, aJ);
        Standard_Real aSegmentP2 = aHatcher.End (anI, aJ);

        if (!aBSurface.IsNull())
        {
          aBSurfaceCurve.Load (isIsoU ? aBSurface->UIso (anIsoParam) : aBSurface->VIso (anIsoParam));

          findLimits (aBSurfaceCurve, aUVLimit, aSegmentP1, aSegmentP2);

          if (aSegmentP2 - aSegmentP1 <= Precision::Confusion())
          {
            continue;
          }
        }
        else
        {
          aCanonicalCurve.Load (isIsoU ? GeomAbs_IsoU : GeomAbs_IsoV, anIsoParam, aSegmentP1, aSegmentP2);

          findLimits (aCanonicalCurve, aUVLimit, aSegmentP1, aSegmentP2);

          if (aSegmentP2 - aSegmentP1 <= Precision::Confusion())
          {
            continue;
          }
        }
        Adaptor3d_Curve* aCurve = aBSurface.IsNull() ? (Adaptor3d_Curve*) &aCanonicalCurve
          : (Adaptor3d_Curve*) &aBSurfaceCurve;

        Handle(TColgp_HSequenceOfPnt) aPoints = new TColgp_HSequenceOfPnt();
        StdPrs_DeflectionCurve::Add (Handle(Prs3d_Presentation)(),
                                     *aCurve,
                                     aSegmentP1,
                                     aSegmentP2,
                                     theDeflection,
                                     aPoints->ChangeSequence(),
                                     theDrawer->DeviationAngle(),
                                     Standard_False);
        if (aPoints->IsEmpty())
        {
          continue;
        }

        if (isIsoU)
        {
          theUPolylines.Append (aPoints);
        }
        else
        {
          theVPolylines.Append (aPoints);
        }
      }
    }
  }
  catch (Standard_Failure const&)
  {
    // ...
  }
}

//==================================================================
// function : UVIsoParameters
// purpose  :
//==================================================================
void StdPrs_Isolines::UVIsoParameters (const TopoDS_Face&      theFace,
                                       const Standard_Integer  theNbIsoU,
                                       const Standard_Integer  theNbIsoV,
                                       const Standard_Real     theUVLimit,
                                       TColStd_SequenceOfReal& theUIsoParams,
                                       TColStd_SequenceOfReal& theVIsoParams,
                                       Standard_Real& theUmin,
                                       Standard_Real& theUmax,
                                       Standard_Real& theVmin,
                                       Standard_Real& theVmax)
{

  TopLoc_Location aLocation;
  const Handle(Geom_Surface)& aSurface = BRep_Tool::Surface(theFace, aLocation);
  if (aSurface.IsNull())
  {
    return;
  }

  BRepTools::UVBounds (theFace, theUmin, theUmax, theVmin, theVmax);

  Standard_Real aUmin = theUmin;
  Standard_Real aUmax = theUmax;
  Standard_Real aVmin = theVmin;
  Standard_Real aVmax = theVmax;

  if (Precision::IsInfinite (aUmin))
    aUmin = -theUVLimit;
  if (Precision::IsInfinite (aUmax))
    aUmax = theUVLimit;
  if (Precision::IsInfinite (aVmin))
    aVmin = -theUVLimit;
  if (Precision::IsInfinite (aVmax))
    aVmax = theUVLimit;


  const Standard_Boolean isUClosed = aSurface->IsUClosed();
  const Standard_Boolean isVClosed = aSurface->IsVClosed();

  if (!isUClosed)
  {
    aUmin = aUmin + (aUmax - aUmin) / 1000.0;
    aUmax = aUmax - (aUmax - aUmin) / 1000.0;
  }

  if (!isVClosed)
  {
    aVmin = aVmin + (aVmax - aVmin) / 1000.0;
    aVmax = aVmax - (aVmax - aVmin) / 1000.0;
  }

  Standard_Real aUstep = (aUmax - aUmin) / (1 + theNbIsoU);
  Standard_Real aVstep = (aVmax - aVmin) / (1 + theNbIsoV);

  for (Standard_Integer anIso = 1; anIso <= theNbIsoU; ++anIso)
  {
    theUIsoParams.Append (aUmin + aUstep * anIso);
  }

  for (Standard_Integer anIso = 1; anIso <= theNbIsoV; ++anIso)
  {
    theVIsoParams.Append (aVmin + aVstep * anIso);
  }
}

//==================================================================
// function : FindSegmentOnTriangulation
// purpose  :
//==================================================================
Standard_Boolean StdPrs_Isolines::findSegmentOnTriangulation (const Handle(Geom_Surface)& theSurface,
                                                              const bool                  theIsU,
                                                              const gp_Lin2d&             theIsoline,
                                                              const gp_Pnt*               theNodesXYZ,
                                                              const gp_Pnt2d*             theNodesUV,
                                                              SegOnIso&                   theSegment)
{
  Standard_Integer aNPoints = 0;

  for (Standard_Integer aLinkIter = 0; aLinkIter < 3 && aNPoints < 2; ++aLinkIter)
  {
    // ...
    // Check that uv isoline crosses the triangulation link in parametric space
    // ...

    const gp_Pnt2d& aNodeUV1 = theNodesUV[aLinkIter];
    const gp_Pnt2d& aNodeUV2 = theNodesUV[(aLinkIter + 1) % 3];
    const gp_Pnt& aNode1 = theNodesXYZ[aLinkIter];
    const gp_Pnt& aNode2 = theNodesXYZ[(aLinkIter + 1) % 3];

    // Compute distance of uv points to isoline taking into consideration their relative
    // location against the isoline (left or right). Null value for a node means that the
    // isoline crosses the node. Both positive or negative means that the isoline does not
    // cross the segment.
    Standard_Boolean isLeftUV1 = (theIsoline.Direction().XY() ^ gp_Vec2d (theIsoline.Location(), aNodeUV1).XY()) > 0.0;
    Standard_Boolean isLeftUV2 = (theIsoline.Direction().XY() ^ gp_Vec2d (theIsoline.Location(), aNodeUV2).XY()) > 0.0;
    Standard_Real aDistanceUV1 = isLeftUV1 ? theIsoline.Distance (aNodeUV1) : -theIsoline.Distance (aNodeUV1);
    Standard_Real aDistanceUV2 = isLeftUV2 ? theIsoline.Distance (aNodeUV2) : -theIsoline.Distance (aNodeUV2);

    // Isoline crosses first point of an edge.
    if (Abs (aDistanceUV1) < Precision::PConfusion())
    {
      theSegment[aNPoints].Param = theIsU ? aNodeUV1.Y() : aNodeUV1.X();
      theSegment[aNPoints].Pnt   = aNode1;
      ++aNPoints;
      continue;
    }

    // Isoline crosses second point of an edge.
    if (Abs (aDistanceUV2) < Precision::PConfusion())
    {
      theSegment[aNPoints].Param = theIsU ? aNodeUV2.Y() : aNodeUV2.X();
      theSegment[aNPoints].Pnt   = aNode2;

      ++aNPoints;
      ++aLinkIter;
      continue;
    }

    // Isoline does not cross the triangle link.
    if (aDistanceUV1 * aDistanceUV2 > 0.0)
    {
      continue;
    }

    // Isoline crosses degenerated link.
    if (aNode1.SquareDistance (aNode2) < Precision::PConfusion())
    {
      theSegment[aNPoints].Param = theIsU ? aNodeUV1.Y() : aNodeUV1.X();
      theSegment[aNPoints].Pnt   = aNode1;
      ++aNPoints;
      continue;
    }

    // ...
    // Derive cross-point from parametric coordinates
    // ...

    Standard_Real anAlpha = Abs (aDistanceUV1) / (Abs (aDistanceUV1) + Abs (aDistanceUV2));

    gp_Pnt aCross (0.0, 0.0, 0.0);
    Standard_Real aCrossU = aNodeUV1.X() + anAlpha * (aNodeUV2.X() - aNodeUV1.X());
    Standard_Real aCrossV = aNodeUV1.Y() + anAlpha * (aNodeUV2.Y() - aNodeUV1.Y());
    Standard_Real aCrossParam = theIsU ? aCrossV : aCrossU;
    if (theSurface.IsNull())
    {
      // Do linear interpolation of point coordinates using triangulation nodes.
      aCross.SetX (aNode1.X() + anAlpha * (aNode2.X() - aNode1.X()));
      aCross.SetY (aNode1.Y() + anAlpha * (aNode2.Y() - aNode1.Y()));
      aCross.SetZ (aNode1.Z() + anAlpha * (aNode2.Z() - aNode1.Z()));
    }
    else
    {
      // Do linear interpolation of point coordinates by triangulation nodes.
      // Get 3d point on surface.
      Handle(Geom_Curve) anIso1, anIso2;
      Standard_Real aPntOnNode1Iso = 0.0;
      Standard_Real aPntOnNode2Iso = 0.0;
      Standard_Real aPntOnNode3Iso = 0.0;

      if (theIsoline.Direction().X() == 0.0)
      {
        aPntOnNode1Iso = aNodeUV1.X();
        aPntOnNode2Iso = aNodeUV2.X();
        aPntOnNode3Iso = aCrossU;
        anIso1 = theSurface->VIso (aNodeUV1.Y());
        anIso2 = theSurface->VIso (aNodeUV2.Y());
      }
      else if (theIsoline.Direction().Y() == 0.0)
      {
        aPntOnNode1Iso = aNodeUV1.Y();
        aPntOnNode2Iso = aNodeUV2.Y();
        aPntOnNode3Iso = aCrossV;
        anIso1 = theSurface->UIso (aNodeUV1.X());
        anIso2 = theSurface->UIso (aNodeUV2.X());
      }

      GeomAdaptor_Curve aCurveAdaptor1 (anIso1);
      GeomAdaptor_Curve aCurveAdaptor2 (anIso2);
      Standard_Real aLength1 = GCPnts_AbscissaPoint::Length (aCurveAdaptor1, aPntOnNode1Iso, aPntOnNode3Iso, 1e-2);
      Standard_Real aLength2 = GCPnts_AbscissaPoint::Length (aCurveAdaptor2, aPntOnNode2Iso, aPntOnNode3Iso, 1e-2);
      if (Abs (aLength1) < Precision::Confusion() || Abs (aLength2) < Precision::Confusion())
      {
        theSegment[aNPoints].Param = aCrossParam;
        theSegment[aNPoints].Pnt   = (aNode2.XYZ() - aNode1.XYZ()) * anAlpha + aNode1.XYZ();
        ++aNPoints;
        continue;
      }

      aCross = (aNode2.XYZ() - aNode1.XYZ()) * (aLength1 / (aLength1 + aLength2)) + aNode1.XYZ();
    }

    theSegment[aNPoints].Param = aCrossParam;
    theSegment[aNPoints].Pnt   = aCross;
    ++aNPoints;
  }

  if (aNPoints != 2
   || Abs (theSegment[1].Param - theSegment[0].Param) <= Precision::PConfusion())
  {
    return false;
  }

  if (theSegment[1].Param < theSegment[0].Param)
  {
    std::swap (theSegment[0], theSegment[1]);
  }
  return true;
}