OpenCASCADE BRepTools

Abstract. OpenCASCADE BRepTools provides utilities for BRep data structure. OuterWire method to find the outer wire of a face. Dump method to dump a BRep object. It also can be used as the data exchange for OpenCASCADE native shapes.

Key Words. OpenCASCADE, BRepTools, BRep, Topology

1. Introduction

OpenCASCADE 提供了一个类BRepTools，其中有许多static函数，主要用来对BRep表示的拓朴形状的数据进行读写，也提供了查找一个面中外环（Outer Wire）的函数。因为OpenCASCADE中的边界表示法BRep的数据结构如下图1.1所示：

Figure 1.1 BRep Data Structure of OpenCASCADE

因为OpenCASCADE中拓朴结构采用了包含关系，当需要将TopoDS_Shape数据保存到文件时，如何保持TopoDS_Shape中的关系，以便于从文件读取这些数据时，可以重构出TopoDS_Shape中的各种关系？

参考opennurbs中的BRep表示时数据的存储方式，可知直接在BRep中保存拓朴及几何数据的索引，这样对数据的存储及读取时重构拓朴结构还是很方便的。而在OpenCASCADE中拓朴数据是以Handle来保存的，且为组合关系，即一个父结构中有一个列表（TopoDS_ListOfShape）给包含了子结构数据。对于没有索引的OpenCASCADE的拓朴结构，如何进行读写操作呢？

本文结合类BRepTools中的函数，对OpenCASCADE中TopoDS_Shape数据的保存和读取功能的代码进行分析，从而对ModelingData中的BRep数据做进一步的理解。

2.Topology Shape Serialization

OpenCASCADE的类BRepTools中提供了如下函数，可以TopoDS_Shape中的数据进行导入导出：

v BRepTools::Dump()；

v BRepTools::Read()；

v BRepTools::Write()；

这几个函数比较常用，因为可以方便地将TopoDS_Shape导出，或导入到OpenCASCADE的Draw Test Harness中，来对程序一些算法进行验证。对于使用了组合关系的TopoDS_Shape如何确保数据的保存及读取后，能够维持这些关系？带着这个问题去看BRep文件读写的功能，应该更为清晰。

还是看看代码，如下所示为输出TopoDS_Shape的函数，在程序Debug时比较常用：

//=======================================================================
//function : Dump
//purpose  :
//=======================================================================
void  BRepTools::Dump(const TopoDS_Shape& Sh, Standard_OStream& S)
{
  BRepTools_ShapeSet SS;
  SS.Add(Sh);
  SS.Dump(Sh,S);
  SS.Dump(S);
}

其中使用了类BRepTools_ShapeSet，这里的Set的意思我理解为集合的意思，其Add函数如下：

//=======================================================================
//function : Add
//purpose  :
//=======================================================================
Standard_Integer  TopTools_ShapeSet::Add(const TopoDS_Shape& S)
{
  if (S.IsNull()) return ;
  myLocations.Add(S.Location());
  TopoDS_Shape S2 = S;
  S2.Location(TopLoc_Location());
  Standard_Integer index = myShapes.FindIndex(S2);
  if (index == ) {
    AddGeometry(S2);
 
    for (TopoDS_Iterator its(S2,Standard_False,Standard_False);
         its.More(); its.Next())
      Add(its.Value());
    index = myShapes.Add(S2);
  }
  return index;
}

这是一个递归函数，通过AddGeometry函数，将TopoDS_Shape中的几何信息都保存到相应的集合Set中，Set中使用了Map，即给每个几何信息一个唯一的编号与之对应。

//=======================================================================
//function : AddGeometry
//purpose  :
//=======================================================================
 
void BRepTools_ShapeSet::AddGeometry(const TopoDS_Shape& S)
{
  // Add the geometry
 
  if (S.ShapeType() == TopAbs_VERTEX) {
 
    Handle(BRep_TVertex) TV = Handle(BRep_TVertex)::DownCast(S.TShape());
    BRep_ListIteratorOfListOfPointRepresentation itrp(TV->Points());
 
    while (itrp.More()) {
      const Handle(BRep_PointRepresentation)& PR = itrp.Value();
 
      if (PR->IsPointOnCurve()) {
        myCurves.Add(PR->Curve());
      }
 
      else if (PR->IsPointOnCurveOnSurface()) {
        myCurves2d.Add(PR->PCurve());
        mySurfaces.Add(PR->Surface());
      }
 
      else if (PR->IsPointOnSurface()) {
        mySurfaces.Add(PR->Surface());
      }
 
      ChangeLocations().Add(PR->Location());
      itrp.Next();
    }
 
  }
  else if (S.ShapeType() == TopAbs_EDGE) {
 
    // Add the curve geometry
    Handle(BRep_TEdge) TE = Handle(BRep_TEdge)::DownCast(S.TShape());
    BRep_ListIteratorOfListOfCurveRepresentation itrc(TE->Curves());
 
    while (itrc.More()) {
      const Handle(BRep_CurveRepresentation)& CR = itrc.Value();
      if (CR->IsCurve3D()) {
        if (!CR->Curve3D().IsNull()) {
          myCurves.Add(CR->Curve3D());
          ChangeLocations().Add(CR->Location());
        }
      }
      else if (CR->IsCurveOnSurface()) {
        mySurfaces.Add(CR->Surface());
        myCurves2d.Add(CR->PCurve());
        ChangeLocations().Add(CR->Location());
        if (CR->IsCurveOnClosedSurface())
          myCurves2d.Add(CR->PCurve2());
      }
      else if (CR->IsRegularity()) {
        mySurfaces.Add(CR->Surface());
        ChangeLocations().Add(CR->Location());
        mySurfaces.Add(CR->Surface2());
        ChangeLocations().Add(CR->Location2());
      }
      else if (myWithTriangles) { // for XML Persistence
        if (CR->IsPolygon3D()) {
          if (!CR->Polygon3D().IsNull()) {
            myPolygons3D.Add(CR->Polygon3D());
            ChangeLocations().Add(CR->Location());
          }
        }
        else if (CR->IsPolygonOnTriangulation()) {
          myTriangulations.Add(CR->Triangulation());
          myNodes.Add(CR->PolygonOnTriangulation());
          ChangeLocations().Add(CR->Location());
          if (CR->IsPolygonOnClosedTriangulation())
            myNodes.Add(CR->PolygonOnTriangulation2());
        }
        else if (CR->IsPolygonOnSurface()) {
          mySurfaces.Add(CR->Surface());
          myPolygons2D.Add(CR->Polygon());
          ChangeLocations().Add(CR->Location());
          if (CR->IsPolygonOnClosedSurface())
          myPolygons2D.Add(CR->Polygon2());
        }
      }
      itrc.Next();
    }
  }
 
  else if (S.ShapeType() == TopAbs_FACE) {
 
    // Add the surface geometry
    Handle(BRep_TFace) TF = Handle(BRep_TFace)::DownCast(S.TShape());
    if (!TF->Surface().IsNull())  mySurfaces.Add(TF->Surface());
 
    if (myWithTriangles) { // for XML Persistence
      Handle(Poly_Triangulation) Tr = TF->Triangulation();
      if (!Tr.IsNull()) myTriangulations.Add(Tr);
    }
 
    ChangeLocations().Add(TF->Location());
  }
}

由上述代码可知，Edge中的几何信息较多，Face中的几何信息最少，只是几何曲面或其用于显示的网格数据。在将拓朴数据输出时，拓朴面、边及顶点中包含的几何信息都是前面几何数据的编号，即相当于索引号的形式输出，代码如下所示：

//=======================================================================
//function : WriteGeometry
//purpose  :
//=======================================================================
 
void  BRepTools_ShapeSet::WriteGeometry(const TopoDS_Shape& S,
                                        Standard_OStream&   OS)const
{
  // Write the geometry
 
  if (S.ShapeType() == TopAbs_VERTEX) {
 
    // Write the point geometry
    TopoDS_Vertex V = TopoDS::Vertex(S);
    OS << BRep_Tool::Tolerance(V) << "\n";
    gp_Pnt p = BRep_Tool::Pnt(V);
    OS<<p.X()<<" "<<p.Y()<<" "<<p.Z()<<"\n";
 
    Handle(BRep_TVertex) TV = Handle(BRep_TVertex)::DownCast(S.TShape());
    BRep_ListIteratorOfListOfPointRepresentation itrp(TV->Points());
 
    while (itrp.More()) {
      const Handle(BRep_PointRepresentation)& PR = itrp.Value();
 
      OS << PR->Parameter();
      if (PR->IsPointOnCurve()) {
        OS << " 1 " << myCurves.Index(PR->Curve());
      }
 
      else if (PR->IsPointOnCurveOnSurface()) {
        OS << " 2 " <<  myCurves2d.Index(PR->PCurve());
        OS << " " << mySurfaces.Index(PR->Surface());
      }
 
      else if (PR->IsPointOnSurface()) {
        OS << " 3 " << PR->Parameter2() << " ";
        OS << mySurfaces.Index(PR->Surface());
      }
 
      OS << " " << Locations().Index(PR->Location());
      OS << "\n";
 
      itrp.Next();
    }
 
    OS << "0 0\n"; // end representations
 
  }
 
  else if (S.ShapeType() == TopAbs_EDGE) {
 
    // Write the curve geometry 
 
    Handle(BRep_TEdge) TE = Handle(BRep_TEdge)::DownCast(S.TShape());
 
    OS << " " << TE->Tolerance() << " ";
    OS << ((TE->SameParameter()) ?  : ) << " ";
    OS << ((TE->SameRange())     ?  : ) << " ";
    OS << ((TE->Degenerated())   ?  : ) << "\n";
 
    Standard_Real first, last;
    BRep_ListIteratorOfListOfCurveRepresentation itrc = TE->Curves();
    while (itrc.More()) {
      const Handle(BRep_CurveRepresentation)& CR = itrc.Value();
      if (CR->IsCurve3D()) {
        if (!CR->Curve3D().IsNull()) {
          Handle(BRep_GCurve) GC = Handle(BRep_GCurve)::DownCast(itrc.Value());
          GC->Range(first, last);
          OS << "1 ";                               // -1- Curve 3D
          OS << " "<<myCurves.Index(CR->Curve3D());
          OS << " "<<Locations().Index(CR->Location());
          OS << " "<<first<<" "<<last;
          OS << "\n";
        }
      }
      else if (CR->IsCurveOnSurface()) {
        Handle(BRep_GCurve) GC = Handle(BRep_GCurve)::DownCast(itrc.Value());
        GC->Range(first, last);
        if (!CR->IsCurveOnClosedSurface())
          OS << "2 ";                             // -2- Curve on surf
        else
          OS << "3 ";                             // -3- Curve on closed surf
        OS <<" "<<myCurves2d.Index(CR->PCurve());
        if (CR->IsCurveOnClosedSurface()) {
          OS <<" " << myCurves2d.Index(CR->PCurve2());
          PrintRegularity(CR->Continuity(),OS);
        }
        OS << " " << mySurfaces.Index(CR->Surface());
        OS << " " << Locations().Index(CR->Location());
        OS << " "<<first<<" "<<last;
        OS << "\n";
 
        // Write UV Points // for XML Persistence higher performance
        if (FormatNb() == )
        {
          gp_Pnt2d Pf,Pl;
          if (CR->IsCurveOnClosedSurface()) {
            Handle(BRep_CurveOnClosedSurface) COCS =
              Handle(BRep_CurveOnClosedSurface)::DownCast(CR);
            COCS->UVPoints2(Pf,Pl);
          }
          else {
            Handle(BRep_CurveOnSurface) COS =
              Handle(BRep_CurveOnSurface)::DownCast(CR);
            COS->UVPoints(Pf,Pl);
          }
          OS << Pf.X() << " " << Pf.Y() << " " << Pl.X() << " " << Pl.Y() << "\n";
        }
      }
      else if (CR->IsRegularity()) {
        OS << "4 ";                              // -4- Regularity
        PrintRegularity(CR->Continuity(),OS);
        OS << " "<<mySurfaces.Index(CR->Surface());
        OS << " "<<Locations().Index(CR->Location());
        OS << " "<<mySurfaces.Index(CR->Surface2());
        OS << " "<<Locations().Index(CR->Location2());
        OS << "\n";
      }
 
      else if (myWithTriangles) { // for XML Persistence
        if (CR->IsPolygon3D()) {
          Handle(BRep_Polygon3D) GC = Handle(BRep_Polygon3D)::DownCast(itrc.Value());
          if (!GC->Polygon3D().IsNull()) {
            OS << "5 ";                            // -5- Polygon3D
            OS << " "<<myPolygons3D.FindIndex(CR->Polygon3D());
            OS << " "<<Locations().Index(CR->Location());
            OS << "\n";
          }
        }
        else if (CR->IsPolygonOnTriangulation()) {
          Handle(BRep_PolygonOnTriangulation) PT =
            Handle(BRep_PolygonOnTriangulation)::DownCast(itrc.Value());
          if (!CR->IsPolygonOnClosedTriangulation())
            OS << "6 ";                            // -6- Polygon on triangulation
          else
            OS << "7 ";                            // -7- Polygon on closed triangulation
          OS << " " <<  myNodes.FindIndex(PT->PolygonOnTriangulation());
          if (CR->IsPolygonOnClosedTriangulation()) {
            OS << " " << myNodes.FindIndex(PT->PolygonOnTriangulation2());
          }
          OS << " " << myTriangulations.FindIndex(PT->Triangulation());
          OS << " "<<Locations().Index(CR->Location());
          OS << "\n";
        }
      }
 
      itrc.Next();
    }
    OS << "0\n"; // end of the list of representations
  }
 
  else if (S.ShapeType() == TopAbs_FACE) {
 
    Handle(BRep_TFace) TF = Handle(BRep_TFace)::DownCast(S.TShape());
    const TopoDS_Face& F = TopoDS::Face(S);
 
    if (!(TF->Surface()).IsNull()) {
      OS << ((BRep_Tool::NaturalRestriction(F)) ?  : );
      OS << " ";
      // Write the surface geometry
      OS << " " <<TF->Tolerance();
      OS << " " <<mySurfaces.Index(TF->Surface());
      OS << " " <<Locations().Index(TF->Location());
      OS << "\n";
    }
    else //For correct reading of null face
      {
    OS << ;
    OS << " ";
    OS << " " <<TF->Tolerance();
    OS << " " << ;
    OS << " " << ;
    OS << "\n";
      }
    if (myWithTriangles) { // for XML Persistence
      if (!(TF->Triangulation()).IsNull()) {
        OS << ;
        OS << " ";
        // Write the triangulation
        OS << " " <<myTriangulations.FindIndex(TF->Triangulation());
      }
    }
  }
 
}

通过先将几何数据收集到相应的集合（映射）中，再在拓朴结构对应的地方以索引号的方式输出，这样就便于从文件读取数据时，以类似的方式来重构BRep边界表示的拓朴Shape的结构。即读取文件重构拓朴结构数据是输出的逆过程。

在实现从文件读取BRep表示的数据时，先将几何信息读取到对应的集合中，再读取拓朴结构数据时，若拓朴结构中包含几何信息，则以索引的方式，找到对应的几何数据即可。详细实现可参考源程序。

3. For Debugging

由于BRepTools为Toolkit TKBRep中的类，所以依赖的动态库较少，所以在编程时，若要验证一些算法的正确性时，经常需要将TopoDS_Shape的数据导出，甚至可以直接先在Draw Test Harness中使用相关命令来将导出的数据导入来查看结果。

4. Conclusion

通过BRepTools中对TopoDS_Shape数据的输出及导入的代码分析可知，对于只有组合关系的数据，若想维持这种关系，就需要引入集合映射的类来产生索引，进而在读取数据时，可以根据索引来重构拓朴关系。由于opennurbs中的BRep在内存中本来就是索引的方式，所以在数据存取时，实现要简单很多。

5. References

1. OpenCASCADE Team. BRep Format. 2014.12

2. Shing Liu. Topology and Geometry in OpenCascade-Topology.

http://www.cppblog.com/eryar/archive/2013/09/21/203338.html

3. Shing Liu. Topology and Geometry in OpenCascade-Vertex

http://www.cppblog.com/eryar/archive/2013/08/20/202678.html

4. Shing Liu. Topology and Geometry in OpenCascade-Edge

http://www.cppblog.com/eryar/archive/2013/08/24/202739.html

5. Shing Liu. Topology and Geometry in OpenCascade-Face

http://www.cppblog.com/eryar/archive/2013/09/12/203199.html

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