Open CASCADE学习|点和曲线的相互转化

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

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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 #include #include #include #include #include #include ​#include #include #include #include #include #include #include ​#include #include ​#include"Viewer.h"​#include #include ​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_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 #include #include #include #include #include #include ​#include #include #include #include #include #include #include ​#include #include ​#include"Viewer.h"​#include #include ​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_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 #include #include #include #include #include #include ​#include #include #include #include #include #include #include ​#include #include ​#include"Viewer.h"​#include #include ​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_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)        {            p=quasiUniDef.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

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#include"Viewer.h"
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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 #include #include #include #include #include #include ​#include #include #include #include #include #include #include ​#include #include ​#include"Viewer.h"​#include #include ​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_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;}

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