OpenCASCADE BRepTools
eryar@163.com
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 0;
myLocations.Add(S.Location());
TopoDS_Shape S2 = S;
S2.Location(TopLoc_Location());
Standard_Integer index = myShapes.FindIndex(S2);
if (index == 0) {
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()) ? 1 : 0) << " ";
OS << ((TE->SameRange()) ? 1 : 0) << " ";
OS << ((TE->Degenerated()) ? 1 : 0) << "\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() == 2)
{
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)) ? 1 : 0);
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 << 0;
OS << " ";
OS << " " <<TF->Tolerance();
OS << " " << 0;
OS << " " << 0;
OS << "\n";
}
if (myWithTriangles) { // for XML Persistence
if (!(TF->Triangulation()).IsNull()) {
OS << 2;
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