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
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());
}
}
//
=======================================================================
//
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
