Open CASCADE学习|按圆离散旋转体

旋转体是一个非常重要的概念，它涉及到三维空间中由二维曲线绕某一轴线旋转形成的立体形状。这种旋转体的形成过程，实际上是一个连续变化的动态过程，但在数学和几何学中，我们往往通过静态的方式来描述和研究它。

旋转体的基本特性包括其形状、大小、表面积和体积等。这些特性不仅取决于原始二维曲线的形状和大小，还受到旋转轴线位置和方向的影响。例如，一个圆绕其直径旋转会形成球体，而绕其切线旋转则会形成圆柱体。

将旋转体离散为一系列的圆（通常称为“截圆”或“横截面”）是一种常用的近似方法，用于在数值计算、计算机图形学以及物理模拟中描述和分析旋转体的性质。这种方法的基本思想是将连续的旋转体划分为一系列离散的、平行的截面，每个截面都是一个圆。

需要注意的是，离散化的精度取决于截面间距的选择。较小的间距可以提高精度，但也会增加计算复杂性和存储需求。因此，在实际应用中，需要根据具体需求和资源限制来选择合适的离散化方案。

#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>
#include <BRepPrimAPI_MakeSphere.hxx>
#include <BRepPrimAPI_MakeRevol.hxx>
#include <BRepAdaptor_CompCurve.hxx>
#include <TopExp_Explorer.hxx>
#include <NCollection_Sequence.hxx>
TopoDS_Edge axis;
NCollection_Sequence<TopoDS_Edge> SplitShapebyaxis(TopoDS_Shape input, TopoDS_Edge cutaxis)
{Standard_Real startParam(0.), endParam(0.);Handle(Geom_Curve) c = BRep_Tool::Curve(cutaxis, startParam, endParam);//得到底层曲线Standard_Real step = (endParam - startParam) / 100;TColgp_HArray1OfPnt Points(1, 101);for (int i = 0; i < 101; i++) {Points[i + 1] = c->Value(startParam + i * step);}gp_Vec dir(Points[1], Points[101]);NCollection_Sequence<TopoDS_Edge> edgeall;for (int i = 2; i < 100; i++){gp_Pln cutplane(Points[i], dir);TopoDS_Face cf = BRepBuilderAPI_MakeFace(cutplane);// 进行布尔运算BRepAlgoAPI_Section section(input, cf, Standard_False);section.ComputePCurveOn1(Standard_True);section.Approximation(Standard_False);section.Build();TopExp_Explorer anExp(section.Shape(), TopAbs_EDGE);int j = 0;for (; anExp.More(); anExp.Next()){TopoDS_Edge anEdge = TopoDS::Edge(anExp.Current());edgeall.Append(anEdge);j++;}//std::cout << "j=" << j << std::endl;}return edgeall;
}
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 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_Edge tmpAxis = BRepBuilderAPI_MakeEdge(gp_Pnt(-0.9832 / 2, 5, 0), gp_Pnt(0.9832 / 2, 5, 0));TopoDS_Shape gwheel = BRepPrimAPI_MakeRevol(mw, gp_Ax1(gp_Pnt(0, 5, 0), gp_Dir(1, 0, 0)), 2 * M_PI);//平移到最低点与原点重合gp_Trsf theTransformation1;gp_Vec theVectorOfTranslation1(-c2low.X(), -c2low.Y(), 0.);theTransformation1.SetTranslation(theVectorOfTranslation1);//往上平移芯厚一半的距离gp_Trsf theTransformation2;gp_Vec theVectorOfTranslation2(0., 0.125 / 2, 0.);theTransformation2.SetTranslation(theVectorOfTranslation2);//顺时针旋转90°，绕z轴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);//顺时针旋转50°，绕x轴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);//实施以上变换：对旋转体、对轴线BRepBuilderAPI_Transform myBRepTransformation(gwheel, theTransformation4 * theTransformation3 * theTransformation2* theTransformation1);TopoDS_Shape TransformedShape = myBRepTransformation.Shape();BRepBuilderAPI_Transform myBRepTransformation2(tmpAxis, theTransformation4 * theTransformation3 * theTransformation2 * theTransformation1);TopoDS_Shape initAxis = myBRepTransformation2.Shape();axis = TopoDS::Edge(initAxis);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()) {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 wheelTopoDS_Shape gw = createGrindingwheel2();//creat a cylinder surfaceStandard_Real R = 0.306 / 2;Handle(Geom_CylindricalSurface) aCylinder = new Geom_CylindricalSurface(gp::XOY(), R);TopoDS_Shape cF = BRepBuilderAPI_MakeFace(aCylinder->Cylinder(), 0, 2 * M_PI, 0, 3.);TopoDS_Solid cys = BRepPrimAPI_MakeCylinder(gp::XOY(), R, 7);TopoDS_Edge aE = createHelix(R, M_PI / 4, 6.);TopoDS_Wire spine = BRepBuilderAPI_MakeWire(aE);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;//myProfile = BRepPrimAPI_MakeSphere(gp_Pnt(0.306/2, 0., 0.),0.306/2);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 continuityBRepFill_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 ShapeHandle(GeomFill_LocationLaw) law;gp_Mat M;gp_Vec V;gp_Trsf fila;Standard_Real first, last;myLoc->Law(1)->GetDomain(first, last);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 SetValuesfila.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();NCollection_Sequence<TopoDS_Edge> es=SplitShapebyaxis(gw, axis);Viewer vout(50, 50, 500, 500);vout << wbe;vout << xline;vout << yline;vout << zline;vout << gw;vout << axis;// 遍历点集合for (int i = 1; i <= es.Length(); ++i) {vout << es.Value(i);}vout.StartMessageLoop();return 0;
}