给别人做网站要问什么问题,wordpress修改文章链接插件,深圳罗湖区网站建设公司,flat movie wordpress旋转体是一个非常重要的概念#xff0c;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#xff0c;实际上是一个连续变化的动态过程#xff0c;但在数学和几何学中#xff0c;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…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#includeViewer.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_SequenceTopoDS_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_SequenceTopoDS_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_SequenceTopoDS_Edge esSplitShapebyaxis(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;
}
