边界表示法（Boundary Representation，简称B-Rep）是几何造型中最成熟、无二义的表示法。它主要用于描述物体的几何信息和拓扑信息。在边界表示法中，一个实体（Solid）由一组封闭的面（Face）组成，而每个面又由其所在的曲面定义加上其边界来表示。面的边界是边的并集，而边又是由点来表示的。

边界表示法中的拓扑信息描述形体上的顶点（Vertex）、边（Edge）、面（Face）的连接关系，形成物体边界表示的“骨架”。拓扑的目的在于描述对象的局限性和连接关系，比如物体的边界以及对象之间的连接（通过公共边界）。例如，相交、相邻、相切、垂直、平行等关系都属于拓扑信息。

TopAbs 包含了 TopAbs_ShapeEnum 枚举类型，列举了不同的拓扑种类，包括COMPOUND（一组任意类型的拓扑物体）、COMPSOLID（复合刚体）、SOLID（由壳限制的空间的一部分）、SHELL（由边相连的面集）、FACE（在2D它是一个平面的一部分；在3D它是一个曲面的一部分）、WIRE（由顶点连接的边的集合）、EDGE（一个与被约束的曲线对应的拓扑元素）以及VERTEX（一个与一个点对应的拓扑元素）。这些拓扑类型形成了一个从复杂到简单的层次结构，因为复杂的物体在其表述中可以包含更简单的物体。

#include <Geom_CylindricalSurface.hxx>
#include <gp_Ax3.hxx>
#include <GeomAPI_Interpolate.hxx>
#include <BRepAdaptor_Curve.hxx>
#include <BRepBuilderAPI_MakeEdge.hxx>
#include <Geom2d_TrimmedCurve.hxx>
#include <GCE2d_MakeSegment.hxx>

#include <GeomAPI_PointsToBSpline.hxx>
#include <BRepBuilderAPI_MakeFace.hxx>
#include <GC_MakeCircle.hxx>
#include <BRepBuilderAPI_MakeWire.hxx>
#include <BRepOffsetAPI_MakePipe.hxx>
#include <GC_MakeArcOfCircle.hxx>
#include <BRepAlgoAPI_Fuse.hxx>
#include <TopExp_Explorer.hxx>
#include <gp_GTrsf.hxx>
#include <BRepBuilderAPI_Transform.hxx>
#include <GC_MakeSegment.hxx>
#include <IntAna2d_AnaIntersection.hxx>
#include <TopoDS.hxx>
#include <BRepPrimAPI_MakeRevol.hxx>

#include"Viewer.h"



TopoDS_Shape createGrindingwheel2()
{
    Standard_Real Line1_angle = 280 * M_PI / 180;
    Standard_Real Line1_length = 0.5031;
    Standard_Real Line2_angle = 236 * M_PI / 180;
    Standard_Real Line2_length = 0.5925;
    Standard_Real Arc1_r = 0.112;
    Standard_Real Arc1_angle = (180 + 10 + 50) * M_PI / 180;
    gp_Pnt Line1_p1(-0.6822 / 2, 0, 0);
    gp_Pnt Line2_p1(0.6822 / 2, 0, 0);
    gp_Lin Line1(Line1_p1, gp_Dir(cos(Line1_angle), sin(Line1_angle), 0.));
    gp_Lin Line2(Line2_p1, gp_Dir(cos(Line2_angle), sin(Line2_angle), 0.));
    Handle(Geom_TrimmedCurve) L1 = GC_MakeSegment(Line1, 0., Line1_length);
    TopoDS_Edge L1e = BRepBuilderAPI_MakeEdge(L1);
    Handle(Geom_TrimmedCurve) L2 = GC_MakeSegment(Line2, 0., Line2_length);
    TopoDS_Edge L2e = BRepBuilderAPI_MakeEdge(L2);
    gp_Pnt l1end = L1->EndPoint();
    gp_Pnt l2end = L2->EndPoint();
    gp_Lin Line1v(l1end, gp_Dir(cos(Line1_angle + M_PI_2), sin(Line1_angle + M_PI_2), 0.));
    gp_Lin2d Line2v(gp_Pnt2d(l2end.X(), l2end.Y()), gp_Dir2d(cos(Line2_angle - M_PI_2), sin(Line2_angle - M_PI_2)));
    gp_Lin Line2v3d(l2end, gp_Dir(cos(Line2_angle - M_PI_2), sin(Line2_angle - M_PI_2), 0.));
    Handle(Geom_TrimmedCurve) L1v = GC_MakeSegment(Line1v, 0., Arc1_r);
    gp_Pnt l1vend = L1v->EndPoint();
    gp_Circ c1(gp_Ax2(l1vend, gp_Dir(0, 0, 1)), Arc1_r);
    Handle(Geom_TrimmedCurve) c1c = GC_MakeArcOfCircle(c1, l1end, Arc1_angle, 1);
    gp_Pnt c1end = c1c->EndPoint();
    gp_Lin2d Line3(gp_Pnt2d(c1end.X(), c1end.Y()), gp_Dir2d(l2end.X() - c1end.X(), l2end.Y() - c1end.Y()));
    gp_Lin2d Line3v = Line3.Normal(gp_Pnt2d((l2end.X() + c1end.X()) / 2, (l2end.Y() + c1end.Y()) / 2));
    IntAna2d_AnaIntersection aIntAna;
    aIntAna.Perform(Line2v, Line3v);
    IntAna2d_IntPoint aIntPoint = aIntAna.Point(1);
    gp_Pnt o2(aIntPoint.Value().X(), aIntPoint.Value().Y(), 0.);
    Handle(Geom_TrimmedCurve) L2v = GC_MakeSegment(Line2v3d, l2end, o2);
    Standard_Real r2 = L2v->LastParameter();
    gp_Circ c2(gp_Ax2(o2, gp_Dir(0, 0, 1)), r2);
    Handle(Geom_TrimmedCurve) c2c = GC_MakeArcOfCircle(c2, c1end, l2end, 0);
    gp_Pnt c2low = c2c->Value(M_PI_2);

    TopoDS_Edge c1ce = BRepBuilderAPI_MakeEdge(c1c);
    TopoDS_Edge L1ev = BRepBuilderAPI_MakeEdge(L1v);
    TopoDS_Edge c2ce = BRepBuilderAPI_MakeEdge(c2c);

    gp_Pnt Line1_up(-0.9832 / 2, 5, 0);
    gp_Pnt Line2_up(0.9832 / 2, 5, 0);
    TopoDS_Edge anEdge1 = BRepBuilderAPI_MakeEdge(Line1_p1, Line1_up);
    TopoDS_Edge anEdge2 = BRepBuilderAPI_MakeEdge(Line1_up, Line2_up);
    TopoDS_Edge anEdge3 = BRepBuilderAPI_MakeEdge(Line2_up, Line2_p1);
    TopTools_ListOfShape listEdge;
    listEdge.Append(anEdge1);
    listEdge.Append(anEdge2);
    listEdge.Append(anEdge3);
    listEdge.Append(L1e);
    listEdge.Append(c1ce);
    listEdge.Append(c2ce);
    listEdge.Append(L2e);
    BRepBuilderAPI_MakeWire mw;
    mw.Add(listEdge);
    mw.Build();

    TopoDS_Shape gwheel = BRepPrimAPI_MakeRevol(mw, gp_Ax1(gp_Pnt(0, 5, 0), gp_Dir(1, 0, 0)), 2 * M_PI);
    //平移：
    gp_Trsf theTransformation1;
    gp_Vec theVectorOfTranslation1(-c2low.X(), -c2low.Y(), 0.);
    theTransformation1.SetTranslation(theVectorOfTranslation1);

    BRepBuilderAPI_Transform myBRepTransformation1(gwheel, theTransformation1);
    TopoDS_Shape outzero = myBRepTransformation1.Shape();


    gp_Trsf theTransformation2;
    gp_Vec theVectorOfTranslation2(0., 0.125 / 2, 0.);
    theTransformation2.SetTranslation(theVectorOfTranslation2);
    //绕一个轴旋转：
    gp_Trsf theTransformation3;
    gp_Ax1 axez = gp_Ax1(gp_Pnt(0, 0, 0), gp_Dir(0., 0., 1.));
    theTransformation3.SetRotation(axez, -90 * M_PI / 180);

    gp_Trsf theTransformation4;
    gp_Ax1 axex = gp_Ax1(gp_Pnt(0, 0, 0), gp_Dir(1., 0., 0.));
    theTransformation4.SetRotation(axex, -50 * M_PI / 180);

    BRepBuilderAPI_Transform myBRepTransformation(outzero, theTransformation4 * theTransformation3 * theTransformation2);
    TopoDS_Shape TransformedShape = myBRepTransformation.Shape();

    return TransformedShape;
}


int main(int argc, char* argv[])
{
    gp_Dir  Z(0.0, 0.0, 1.0);
    gp_Pnt center(0, 0, 0.0);
    gp_Pnt xr(0.5, 0, 0.0);
    gp_Pnt yr(0.0, 1.0, 0.0);
    gp_Pnt zr(0.0, 0.0, 7.0);
    gp_Ax2  wb(center, Z);
    gp_Circ  wbcircle(wb, 0.125 / 2);
    TopoDS_Edge wbe = BRepBuilderAPI_MakeEdge(wbcircle);
    TopoDS_Edge xline = BRepBuilderAPI_MakeEdge(center, xr);
    TopoDS_Edge yline = BRepBuilderAPI_MakeEdge(center, yr);
    TopoDS_Edge zline = BRepBuilderAPI_MakeEdge(center, zr);
    //creat a profile of gringing wheel
    TopoDS_Shape gw = createGrindingwheel2();
    TopExp_Explorer anExp1(gw, TopAbs_SOLID);
    TopExp_Explorer anExp2(gw, TopAbs_SHELL);
    TopExp_Explorer anExp3(gw, TopAbs_FACE);
    TopExp_Explorer anExp4(gw, TopAbs_WIRE);
    TopExp_Explorer anExp5(gw, TopAbs_EDGE);
    int i = 0;
    Viewer vout(50, 50, 500, 500);
    for (; anExp1.More(); anExp1.Next())
    {
        TopoDS_Solid anSolid = TopoDS::Solid(anExp1.Current());
        i++;
    }
    std::cout << "numbers of TopoDS_Solid:" << i << std::endl;
    i = 0;
    for (; anExp2.More(); anExp2.Next())
    {
        TopoDS_Shell anShell = TopoDS::Shell(anExp2.Current());
        i++;
    }
    std::cout << "numbers of TopoDS_Shell:" << i << std::endl;
    i = 0;
    for (; anExp3.More(); anExp3.Next())
    {
        TopoDS_Face anFace = TopoDS::Face(anExp3.Current());
        i++;
    }
    std::cout << "numbers of TopoDS_Face:" <<i<< std::endl;
    i = 0;
    for (; anExp4.More(); anExp4.Next())
    {
        TopoDS_Wire anWire = TopoDS::Wire(anExp4.Current());
        i++;
    }
    std::cout << "numbers of TopoDS_Wire:" << i << std::endl;
    i = 0;
    for (; anExp5.More(); anExp5.Next())
    {
        TopoDS_Edge anEdge = TopoDS::Edge(anExp5.Current());
        i++;
    }
    std::cout << "numbers of TopoDS_Edge:" << i << std::endl;

    vout << wbe;
    vout << xline;
    vout << yline;
    vout << zline;
    vout << gw;
    vout.StartMessageLoop();
    return 0;
}

numbers of TopoDS_Solid:0

numbers of TopoDS_Shell:1

numbers of TopoDS_Face:6

numbers of TopoDS_Wire:6

numbers of TopoDS_Edge:24