Open CASCADE学习|刚体（ TopoDS_Shape）按某种轨迹运动，停在指定位置上

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今天实现如下功能：刚体做做螺旋运动，轨迹已知，求刚体在每个位置上的所占据的空间，就是把刚体从初始位置变换到该位置。

这里的刚体是一个砂轮截面，螺旋运动轨迹由B样条曲线拟合，通过Frenet标架确定运动轨迹上的局部坐标系，据此计算变换矩阵，将砂轮截面变换到指定位置。

目前可以实现平面刚体的运动，还无法实现三维刚体的运动。

1、起始位置空间的确定

#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 <gp_GTrsf.hxx>
#include <BRepBuilderAPI_Transform.hxx>

#include"Viewer.h"

#include <BRepPrimAPI_MakeCylinder.hxx>
#include <BRepBuilderAPI_MakePolygon.hxx>
#include <BRep_Tool.hxx>
#include <TopoDS.hxx>
#include <BRepAlgoAPI_Cut.hxx>
#include <BRepAlgoAPI_Common.hxx>
#include <BRepAlgoAPI_Section.hxx>
#include <BRepPrimAPI_MakePrism.hxx>
#include <GC_MakeSegment.hxx>
#include <IntAna2d_AnaIntersection.hxx>
#include <ShapeUpgrade_UnifySameDomain.hxx>
#include <BRepTools_WireExplorer.hxx>
#include <GeomFill_TrihedronLaw.hxx>
#include <GeomFill_Frenet.hxx>
#include <GeomFill_CurveAndTrihedron.hxx>
#include <BRepFill_Edge3DLaw.hxx>
#include <BRepFill_SectionPlacement.hxx>
#include <ShapeUpgrade_RemoveLocations.hxx>

TopoDS_Edge createHelix(const Standard_Real HelixRadius, const Standard_Real HelixAngle, const Standard_Real HelixLength)
{
    Standard_Real u0 = 0.0;
    Standard_Real u1 = 2 * M_PI;
    Standard_Real v0 = 0.0;
    Standard_Real v1 = HelixLength;
    double uInter = (u1 - u0) / 1000;
    double vInter = (v1 - v0) / 1000;
    TColgp_HArray1OfPnt Points(1, 1001);
    Handle(Geom_CylindricalSurface) aCylinder = new Geom_CylindricalSurface(gp::XOY(), HelixRadius);
    double u;
    double v;
    //生成点
    for (int i = 0; i < 1001; i++) {
        u = i * vInter * tan(HelixAngle) / HelixRadius;
        v = i * vInter;
        Points[i + 1] = aCylinder->Value(u, v);
    }
    GeomAPI_PointsToBSpline Approx(Points);
    Handle_Geom_BSplineCurve K = Approx.Curve();
    TopoDS_Edge aHelixEdge = BRepBuilderAPI_MakeEdge(K);
    return aHelixEdge;

}
TopoDS_Shape createGrindingwheel()
{
    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);


    TopoDS_Edge anEdge = BRepBuilderAPI_MakeEdge(Line1_p1, Line2_p1);

    TopTools_ListOfShape listEdge;
    listEdge.Append(anEdge);
    listEdge.Append(L1e);
    listEdge.Append(c1ce);
    listEdge.Append(c2ce);
    listEdge.Append(L2e);
    BRepBuilderAPI_MakeWire mw;
    mw.Add(listEdge);
    mw.Build();


    TopoDS_Face out = BRepBuilderAPI_MakeFace(mw);
    gp_Circ  cutcircle(gp_Ax2(gp_Pnt(0, 0, 0), gp_Dir(0, 0, 1)), 0.406 / 2);
    TopoDS_Edge cute = BRepBuilderAPI_MakeEdge(cutcircle);
    TopoDS_Wire cutw = BRepBuilderAPI_MakeWire(cute);
    TopoDS_Face cutf = BRepBuilderAPI_MakeFace(cutw);
    //平移：
    gp_Trsf theTransformation1;
    gp_Vec theVectorOfTranslation1(-c2low.X(), -c2low.Y(), 0.);
    theTransformation1.SetTranslation(theVectorOfTranslation1);

    BRepBuilderAPI_Transform myBRepTransformation1(out, theTransformation1);
    TopoDS_Shape outzero = myBRepTransformation1.Shape();
    TopoDS_Shape theCommonSurface = BRepAlgoAPI_Common(outzero, cutf);

    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(theCommonSurface, 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 = createGrindingwheel();
    //creat a cylinder surface
    Handle(Geom_CylindricalSurface) aCylinder = new Geom_CylindricalSurface(gp::XOY(), 0.306 / 2);
    TopoDS_Shape cF = BRepBuilderAPI_MakeFace(aCylinder->Cylinder(), 0, 2 * M_PI, 0, 3.);

    TopoDS_Solid cys = BRepPrimAPI_MakeCylinder(gp::XOY(), 0.306 / 2, 7);
  
    TopoDS_Edge aE = createHelix(0.306 / 2, M_PI / 4, 6.);
    TopoDS_Wire spine = BRepBuilderAPI_MakeWire(aE);
    
    //crate a sweep surface
    TopoDS_Shape pipe = BRepOffsetAPI_MakePipe(spine, gw, GeomFill_IsFrenet, 1);


    TopoDS_Wire mySpine;
    TopoDS_Shape myProfile;
    TopoDS_Shape myShape;
    gp_Trsf myTrsf;
    Handle(BRepFill_LocationLaw) myLoc;
    Handle(TopTools_HArray2OfShape) mySections;
    Handle(TopTools_HArray2OfShape) myFaces;
    Handle(TopTools_HArray2OfShape) myEdges;
    TopTools_MapOfShape myReversedEdges;
    BRepFill_DataMapOfShapeHArray2OfShape myTapes;
    BRepFill_DataMapOfShapeHArray2OfShape myRails;
    Standard_Integer myCurIndexOfSectionEdge;
    TopoDS_Shape myFirst;
    TopoDS_Shape myLast;
    TopTools_DataMapOfShapeListOfShape myGenMap;
    Standard_Integer myDegmax;
    Standard_Integer mySegmax;
    GeomAbs_Shape myContinuity;
    GeomFill_Trihedron myMode;
    Standard_Boolean myForceApproxC1;
    Standard_Real myErrorOnSurf;

    mySections.Nullify();
    myFaces.Nullify();
    myEdges.Nullify();

    mySpine = spine;
    myProfile = gw;

    TopoDS_Shape TheProf;

    Handle(GeomFill_TrihedronLaw) TLaw;
    TLaw = new GeomFill_Frenet();
    Handle(GeomFill_CurveAndTrihedron) Loc = new (GeomFill_CurveAndTrihedron) (TLaw);
    myLoc = new (BRepFill_Edge3DLaw) (mySpine, Loc);
    if (myLoc->NbLaw() == 0) {
        return 0; // Degenerated case
    }
    myLoc->TransformInG0Law(); // Set into continuity

    BRepFill_SectionPlacement Place(myLoc, gw);
    myTrsf = Place.Transformation();

    TopLoc_Location Loc2(myTrsf), Loc1;
    Loc1 = gw.Location();
    TopoDS_Shape aux;
    TheProf = myProfile;
    TheProf.Location(Loc2.Multiplied(Loc1));

    // Construct First && Last Shape
    Handle(GeomFill_LocationLaw) law;

    gp_Mat M;
    gp_Vec V;
    gp_Trsf fila;
    Standard_Real first,last;
    myLoc->Law(1)->GetDomain(first, last);
    std::cout << "first=" <<first<< std::endl;
    std::cout << "last=" << last << std::endl;
    myLoc->Law(1)->D0(first, M, V);
    fila.SetValues(M(1, 1), M(1, 2), M(1, 3), V.X(),
        M(2, 1), M(2, 2), M(2, 3), V.Y(),
        M(3, 1), M(3, 2), M(3, 3), V.Z());

    fila.Multiply(myTrsf);
    TopLoc_Location LocFirst(fila);
    myFirst = myProfile;
    if (!LocFirst.IsIdentity()) {
        //myFirst.Location( LocFirst.Multiplied(myProfile.Location()) );
        myFirst = BRepBuilderAPI_Transform(myProfile, fila, Standard_True); //copy
    }

    ShapeUpgrade_RemoveLocations RemLoc;
    RemLoc.SetRemoveLevel(TopAbs_COMPOUND);
    RemLoc.Remove(myFirst);
    myFirst = RemLoc.GetResult();

    myLoc->Law(myLoc->NbLaw())->GetDomain(first, last);
    myLoc->Law(myLoc->NbLaw())->D0(last, M, V);
    //    try { // Not good, but there are no other means to test SetValues
    fila.SetValues(M(1, 1), M(1, 2), M(1, 3), V.X(),
        M(2, 1), M(2, 2), M(2, 3), V.Y(),
        M(3, 1), M(3, 2), M(3, 3), V.Z());
    fila.Multiply(myTrsf);
    TopLoc_Location LocLast(fila);
    if (!myLoc->IsClosed() || LocFirst != LocLast) {
        myLast = myProfile;
        if (!LocLast.IsIdentity()) {
            //myLast.Location(LocLast.Multiplied(myProfile.Location()) );
            myLast = BRepBuilderAPI_Transform(myProfile, fila, Standard_True); //copy
        }
    }
    else {
        myLast = myFirst;
    }
    RemLoc.Remove(myLast);
    myLast = RemLoc.GetResult();
   
    Viewer vout(50, 50, 500, 500);
    vout << wbe;
    vout << xline;
    vout << yline;
    vout << zline;
    vout << myProfile;
    vout << myLast;
    vout << spine;
    vout.StartMessageLoop();
    return 0;
}

2、中间任一位置空间的确定

#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 <gp_GTrsf.hxx>
#include <BRepBuilderAPI_Transform.hxx>

#include"Viewer.h"

#include <BRepPrimAPI_MakeCylinder.hxx>
#include <BRepBuilderAPI_MakePolygon.hxx>
#include <BRep_Tool.hxx>
#include <TopoDS.hxx>
#include <BRepAlgoAPI_Cut.hxx>
#include <BRepAlgoAPI_Common.hxx>
#include <BRepAlgoAPI_Section.hxx>
#include <BRepPrimAPI_MakePrism.hxx>
#include <GC_MakeSegment.hxx>
#include <IntAna2d_AnaIntersection.hxx>
#include <ShapeUpgrade_UnifySameDomain.hxx>
#include <BRepTools_WireExplorer.hxx>
#include <GeomFill_TrihedronLaw.hxx>
#include <GeomFill_Frenet.hxx>
#include <GeomFill_CurveAndTrihedron.hxx>
#include <BRepFill_Edge3DLaw.hxx>
#include <BRepFill_SectionPlacement.hxx>
#include <ShapeUpgrade_RemoveLocations.hxx>

TopoDS_Edge createHelix(const Standard_Real HelixRadius, const Standard_Real HelixAngle, const Standard_Real HelixLength)
{
    Standard_Real u0 = 0.0;
    Standard_Real u1 = 2 * M_PI;
    Standard_Real v0 = 0.0;
    Standard_Real v1 = HelixLength;
    double uInter = (u1 - u0) / 1000;
    double vInter = (v1 - v0) / 1000;
    TColgp_HArray1OfPnt Points(1, 1001);
    Handle(Geom_CylindricalSurface) aCylinder = new Geom_CylindricalSurface(gp::XOY(), HelixRadius);
    double u;
    double v;
    //生成点
    for (int i = 0; i < 1001; i++) {
        u = i * vInter * tan(HelixAngle) / HelixRadius;
        v = i * vInter;
        Points[i + 1] = aCylinder->Value(u, v);
    }
    GeomAPI_PointsToBSpline Approx(Points);
    Handle_Geom_BSplineCurve K = Approx.Curve();
    TopoDS_Edge aHelixEdge = BRepBuilderAPI_MakeEdge(K);
    return aHelixEdge;

}
TopoDS_Shape createGrindingwheel()
{
    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);


    TopoDS_Edge anEdge = BRepBuilderAPI_MakeEdge(Line1_p1, Line2_p1);

    TopTools_ListOfShape listEdge;
    listEdge.Append(anEdge);
    listEdge.Append(L1e);
    listEdge.Append(c1ce);
    listEdge.Append(c2ce);
    listEdge.Append(L2e);
    BRepBuilderAPI_MakeWire mw;
    mw.Add(listEdge);
    mw.Build();


    TopoDS_Face out = BRepBuilderAPI_MakeFace(mw);
    gp_Circ  cutcircle(gp_Ax2(gp_Pnt(0, 0, 0), gp_Dir(0, 0, 1)), 0.406 / 2);
    TopoDS_Edge cute = BRepBuilderAPI_MakeEdge(cutcircle);
    TopoDS_Wire cutw = BRepBuilderAPI_MakeWire(cute);
    TopoDS_Face cutf = BRepBuilderAPI_MakeFace(cutw);
    //平移：
    gp_Trsf theTransformation1;
    gp_Vec theVectorOfTranslation1(-c2low.X(), -c2low.Y(), 0.);
    theTransformation1.SetTranslation(theVectorOfTranslation1);

    BRepBuilderAPI_Transform myBRepTransformation1(out, theTransformation1);
    TopoDS_Shape outzero = myBRepTransformation1.Shape();
    TopoDS_Shape theCommonSurface = BRepAlgoAPI_Common(outzero, cutf);

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

    return TransformedShape;
}
TopoDS_Shape getShapeOnPosition(TopoDS_Shape myProfile,Handle(BRepFill_LocationLaw) myLoc,Standard_Real pos, Standard_Real a, Standard_Real b, gp_Trsf myTrsf)
{
    TopoDS_Shape myPos;
    Handle(GeomFill_LocationLaw) law;
    gp_Mat M;
    gp_Vec V;
    gp_Trsf fila;
    Standard_Real first, last;
    myLoc->Law(1)->GetDomain(first, last);
    Standard_Real px = (pos - a) / (b - a);
    myLoc->Law(1)->D0(px, M, V);
    fila.SetValues(M(1, 1), M(1, 2), M(1, 3), V.X(),
        M(2, 1), M(2, 2), M(2, 3), V.Y(),
        M(3, 1), M(3, 2), M(3, 3), V.Z());

    fila.Multiply(myTrsf);
    myPos = myProfile;
    TopLoc_Location LocPos(fila);
    if (!LocPos.IsIdentity()) {
        //myFirst.Location( LocFirst.Multiplied(myProfile.Location()) );
        myPos = BRepBuilderAPI_Transform(myProfile, fila, Standard_True); //copy
    }

    ShapeUpgrade_RemoveLocations RemLoc;
    RemLoc.SetRemoveLevel(TopAbs_COMPOUND);
    RemLoc.Remove(myPos);
    myPos = RemLoc.GetResult();
    return myPos;
}
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 = createGrindingwheel();
    //creat a cylinder surface
    Handle(Geom_CylindricalSurface) aCylinder = new Geom_CylindricalSurface(gp::XOY(), 0.306 / 2);
    TopoDS_Shape cF = BRepBuilderAPI_MakeFace(aCylinder->Cylinder(), 0, 2 * M_PI, 0, 3.);

    TopoDS_Solid cys = BRepPrimAPI_MakeCylinder(gp::XOY(), 0.306 / 2, 7);
  
    TopoDS_Edge aE = createHelix(0.306 / 2, M_PI / 4, 6.);
    TopoDS_Wire spine = BRepBuilderAPI_MakeWire(aE);
    
    //crate a sweep surface
    TopoDS_Shape pipe = BRepOffsetAPI_MakePipe(spine, gw, GeomFill_IsFrenet, 1);


    TopoDS_Wire mySpine;
    TopoDS_Shape myProfile;
    TopoDS_Shape myShape;
    gp_Trsf myTrsf;
    Handle(BRepFill_LocationLaw) myLoc;
    Handle(TopTools_HArray2OfShape) mySections;
    Handle(TopTools_HArray2OfShape) myFaces;
    Handle(TopTools_HArray2OfShape) myEdges;
    TopTools_MapOfShape myReversedEdges;
    BRepFill_DataMapOfShapeHArray2OfShape myTapes;
    BRepFill_DataMapOfShapeHArray2OfShape myRails;
    Standard_Integer myCurIndexOfSectionEdge;
    TopoDS_Shape myFirst;
    TopoDS_Shape myLast;
    TopTools_DataMapOfShapeListOfShape myGenMap;
    Standard_Integer myDegmax;
    Standard_Integer mySegmax;
    GeomAbs_Shape myContinuity;
    GeomFill_Trihedron myMode;
    Standard_Boolean myForceApproxC1;
    Standard_Real myErrorOnSurf;

    mySections.Nullify();
    myFaces.Nullify();
    myEdges.Nullify();

    mySpine = spine;
    myProfile = gw;

    TopoDS_Shape TheProf;

    Handle(GeomFill_TrihedronLaw) TLaw;
    TLaw = new GeomFill_Frenet();
    Handle(GeomFill_CurveAndTrihedron) Loc = new (GeomFill_CurveAndTrihedron) (TLaw);
    myLoc = new (BRepFill_Edge3DLaw) (mySpine, Loc);
    if (myLoc->NbLaw() == 0) {
        return 0; // Degenerated case
    }
    myLoc->TransformInG0Law(); // Set into continuity

    BRepFill_SectionPlacement Place(myLoc, gw);
    myTrsf = Place.Transformation();

    TopLoc_Location Loc2(myTrsf), Loc1;
    Loc1 = gw.Location();
    TopoDS_Shape aux;
    TheProf = myProfile;
    TheProf.Location(Loc2.Multiplied(Loc1));

    // Construct First && Last Shape
    Handle(GeomFill_LocationLaw) law;

    gp_Mat M;
    gp_Vec V;
    gp_Trsf fila;
    Standard_Real first,last;
    myLoc->Law(1)->GetDomain(first, last);
    std::cout << "first=" <<first<< std::endl;
    std::cout << "last=" << last << std::endl;
    std::cout << "myLoc->NbLaw()=" << myLoc->NbLaw() << std::endl;
    myLoc->Law(1)->D0(first, M, V);
    fila.SetValues(M(1, 1), M(1, 2), M(1, 3), V.X(),
        M(2, 1), M(2, 2), M(2, 3), V.Y(),
        M(3, 1), M(3, 2), M(3, 3), V.Z());

    fila.Multiply(myTrsf);
    TopLoc_Location LocFirst(fila);
    myFirst = myProfile;
    if (!LocFirst.IsIdentity()) {
        //myFirst.Location( LocFirst.Multiplied(myProfile.Location()) );
        myFirst = BRepBuilderAPI_Transform(myProfile, fila, Standard_True); //copy
    }

    ShapeUpgrade_RemoveLocations RemLoc;
    RemLoc.SetRemoveLevel(TopAbs_COMPOUND);
    RemLoc.Remove(myFirst);
    myFirst = RemLoc.GetResult();

    myLoc->Law(myLoc->NbLaw())->GetDomain(first, last);
    myLoc->Law(myLoc->NbLaw())->D0(last, M, V);
    //    try { // Not good, but there are no other means to test SetValues
    fila.SetValues(M(1, 1), M(1, 2), M(1, 3), V.X(),
        M(2, 1), M(2, 2), M(2, 3), V.Y(),
        M(3, 1), M(3, 2), M(3, 3), V.Z());
    fila.Multiply(myTrsf);
    TopLoc_Location LocLast(fila);
    if (!myLoc->IsClosed() || LocFirst != LocLast) {
        myLast = myProfile;
        if (!LocLast.IsIdentity()) {
            //myLast.Location(LocLast.Multiplied(myProfile.Location()) );
            myLast = BRepBuilderAPI_Transform(myProfile, fila, Standard_True); //copy
        }
    }
    else {
        myLast = myFirst;
    }
    RemLoc.Remove(myLast);
    myLast = RemLoc.GetResult();

    TopoDS_Shape md1 = getShapeOnPosition(myProfile, myLoc, 0.2, 0., 6., myTrsf);
    TopoDS_Shape md2 = getShapeOnPosition(myProfile, myLoc, 0.4, 0., 6., myTrsf);
    TopoDS_Shape md3 = getShapeOnPosition(myProfile, myLoc, 0.6, 0., 6., myTrsf);
    TopoDS_Shape md4 = getShapeOnPosition(myProfile, myLoc, 0.8, 0., 6., myTrsf);
    TopoDS_Shape md5 = getShapeOnPosition(myProfile, myLoc, 1.0, 0., 6., myTrsf);
   
    Viewer vout(50, 50, 500, 500);
    vout << wbe;
    vout << xline;
    vout << yline;
    vout << zline;
    vout << myProfile;
    vout << myLast;
    vout << spine;
    vout << md1;
    vout << md2;
    vout << md3;
    vout << md4;
    vout << md5;
    vout.StartMessageLoop();
    return 0;
}

3、使用的dll

TKernel.lib

TKMath.lib

TKTopAlgo.lib

TKBRep.lib

TKPrim.lib

TKOpenGl.lib

TKService.lib

TKV3d.lib

kernel32.lib

user32.lib

gdi32.lib

TKBinXCAF.lib

TKSTEP.lib

TKSTEP209.lib

TKSTEPAttr.lib

TKSTEPBase.lib

TKXSBase.lib

TKGeomBase.lib

TKG3d.lib

TKG2d.lib

TKShHealing.lib

TKGeomAlgo.lib

TKOffset.lib

TKBO.lib

TKFeat.lib

TKFillet.lib

TKBool.lib

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