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1、把曲线离散成点
1.1按数量离散
1.2按长度离散
1.3按弦高离散
2、由点合成曲线
2.1B样条插值
2.2B样条近似 1、把曲线离散成点
计算机图形学中绘制曲线#xff0c;无论是绘制参数曲线还是非参数曲线#xff0c;都需要先将参数曲线进行离散化#xff0c;通过离…
目录
1、把曲线离散成点
1.1按数量离散
1.2按长度离散
1.3按弦高离散
2、由点合成曲线
2.1B样条插值
2.2B样条近似 1、把曲线离散成点
计算机图形学中绘制曲线无论是绘制参数曲线还是非参数曲线都需要先将参数曲线进行离散化通过离散化得到一组离散化的点集然后再将点集发送给图形渲染管线进行处理最终生成我们想要的曲线。
OpenCASCADE中提供了GCPnts包。利用GCPnts包中提供的类我们可以很方便的将三维曲线进行离散化。
1.1按数量离散
#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_MakeVertex.hxx#includeViewer.h#include BRepAdaptor_CompCurve.hxx#include GCPnts_UniformAbscissa.hxxint 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_Wire te BRepBuilderAPI_MakeWire(wbe); BRepAdaptor_CompCurve compCurve(te); GCPnts_UniformAbscissa uniAbs(compCurve, 100, -1); gp_Pnt p; Viewer vout(50, 50, 500, 500); vout te; if (uniAbs.IsDone()) { for (Standard_Integer i 1; i uniAbs.NbPoints(); i) { Standard_Real u uniAbs.Parameter(i); compCurve.D0(u, p);//获取每个离散点 TopoDS_Vertex verti BRepBuilderAPI_MakeVertex(p); vout verti; } } vout.StartMessageLoop(); return 0;} 1.2按长度离散
#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_MakeVertex.hxx#includeViewer.h#include BRepAdaptor_CompCurve.hxx#include GCPnts_UniformAbscissa.hxxint 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_Wire te BRepBuilderAPI_MakeWire(wbe); BRepAdaptor_CompCurve compCurve(te); GCPnts_UniformAbscissa uniAbs; uniAbs.Initialize(compCurve, 0.05, -1); gp_Pnt p; Viewer vout(50, 50, 500, 500); vout te; if (uniAbs.IsDone()) { for (Standard_Integer i 1; i uniAbs.NbPoints(); i) { Standard_Real u uniAbs.Parameter(i); compCurve.D0(u, p);//获取每个离散点 TopoDS_Vertex verti BRepBuilderAPI_MakeVertex(p); vout verti; } } vout.StartMessageLoop(); return 0;} 1.3按弦高离散
#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 GCPnts_QuasiUniformDeflection.hxx#include BRepBuilderAPI_MakeVertex.hxx#includeViewer.h#include BRepAdaptor_CompCurve.hxx#include GCPnts_UniformAbscissa.hxxint 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_Wire te BRepBuilderAPI_MakeWire(wbe); BRepAdaptor_CompCurve compCurve(te); GCPnts_QuasiUniformDeflection quasiUniDef; quasiUniDef.Initialize(compCurve, 0.08, GeomAbs_C0); gp_Pnt p; Viewer vout(50, 50, 500, 500); vout te; if (quasiUniDef.IsDone()) { for (Standard_Integer i 1; i quasiUniDef.NbPoints(); i) { pquasiUniDef.Value(i);//获取每个离散点 TopoDS_Vertex verti BRepBuilderAPI_MakeVertex(p); vout verti; } } vout.StartMessageLoop(); return 0;} 2、由点合成曲线
曲线曲面拟合Curve and Surface Fitting的方式可以分为两类插值interpolation和逼近approximation。采用插值的方式时所创建的曲线或曲面必须精确地满足所给的数据条件例如曲线通过所给的插值点。采用逼近的方式时创建的曲线或曲面不必精确地满足所给的数据条件只要在一定的误差范围内接近即可。
2.1B样条插值
#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 GCPnts_QuasiUniformDeflection.hxx
#include BRepBuilderAPI_MakeVertex.hxx
#includeViewer.h
#include BRepAdaptor_CompCurve.hxx
#include GeomTools.hxx
int main(int argc, char* argv[])
{Handle(TColgp_HArray1OfPnt) aPoints new TColgp_HArray1OfPnt(1, 3);Handle(Geom_BSplineCurve) aBSplineCurve;
aPoints-SetValue(1, gp_Pnt(0.0, 0.0, 0.0));aPoints-SetValue(2, gp_Pnt(1.0, 1.0, 0.0));aPoints-SetValue(3, gp_Pnt(2.0, 6.0, 3.0));
GeomAPI_Interpolate aInterpolater(aPoints, Standard_False, Precision::Approximation());aInterpolater.Perform();aBSplineCurve aInterpolater.Curve();//std::cout ok;TopoDS_Edge s BRepBuilderAPI_MakeEdge(aBSplineCurve);Viewer vout(50, 50, 500, 500);vout s;vout BRepBuilderAPI_MakeVertex(aPoints-Value(1));vout BRepBuilderAPI_MakeVertex(aPoints-Value(2));vout BRepBuilderAPI_MakeVertex(aPoints-Value(3));vout.StartMessageLoop();return 0;
} 2.2B样条近似
#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 GCPnts_QuasiUniformDeflection.hxx#include BRepBuilderAPI_MakeVertex.hxx#includeViewer.h#include BRepAdaptor_CompCurve.hxx#include GeomTools.hxxint main(int argc, char* argv[]){ Handle(TColgp_HArray1OfPnt) aPoints new TColgp_HArray1OfPnt(1, 3); Handle(Geom_BSplineCurve) aBSplineCurve; aPoints-SetValue(1, gp_Pnt(0.0, 0.0, 0.0)); aPoints-SetValue(2, gp_Pnt(1.0, 1.0, 0.0)); aPoints-SetValue(3, gp_Pnt(2.0, 6.0, 3.0)); GeomAPI_PointsToBSpline Approx(aPoints-Array1()); Handle(Geom_BSplineCurve) K Approx.Curve(); TopoDS_Edge s BRepBuilderAPI_MakeEdge(K); Viewer vout(50, 50, 500, 500); vout s; vout BRepBuilderAPI_MakeVertex(aPoints-Value(1)); vout BRepBuilderAPI_MakeVertex(aPoints-Value(2)); vout BRepBuilderAPI_MakeVertex(aPoints-Value(3)); vout.StartMessageLoop(); return 0;}
