在三维空间中，将曲线向曲面投影通常涉及复杂的几何计算。这个过程可以通过多种方法实现，但最常见的是使用数学和几何库，如OpenCASCADE，来处理这些计算。

在OpenCASCADE中，投影曲线到曲面通常涉及以下步骤：

定义曲线（Curve）和曲面（Surface）。

使用适当的算法或类（如BRepProj_Projection）来执行投影。

获取投影后的曲线。

下面是一个简化的例子，展示了如何使用OpenCASCADE的API来将一条曲线投影到一个曲面上：

#include <Geom_BezierCurve.hxx>
#include <BRepBuilderAPI_MakeEdge.hxx>
#include <TopoDS_Edge.hxx>
#include <BRep_Tool.hxx>
#include <BRepLib.hxx>
#include <TopoDS_Face.hxx>
#include <BRepBuilderAPI_MakeFace.hxx>
#include <BRepBuilderAPI_Transform.hxx>
#include <gp_Ax3.hxx> 
#include <gp_Cylinder.hxx> 
#include <Geom_CylindricalSurface.hxx>
#include <BRepProj_Projection.hxx>
​
#include"Viewer.h"
​
int main(int argc, char* argv[])
{
    //Non Rational B-Spline
​
    gp_Pnt points1[8] = {
    gp_Pnt(0.0,-100.0,0.0),
    gp_Pnt(10.0,10.0,0.0),
    gp_Pnt(30.0,-100.0,0.0),
    gp_Pnt(100.0,0.0,0.0),
    gp_Pnt(150.0,50.0,0.0),
    gp_Pnt(200.0,0.0,0.0),
    gp_Pnt(400.0,200.0,0.0),
    gp_Pnt(450.0,0.0,0.0)
    };
​
    NCollection_Array1<gp_Pnt> points(points1[0], 1, 8);//Control points
    Standard_Real realsWeight[8] = { 1.0,1.0,1.0,1.0,1.0,1.0,10.0,1.0 };
    NCollection_Array1<Standard_Real> weight(realsWeight[0], 1, 8);//权系数，倒数第二个点的权系数是其他的10倍。
    Geom_BezierCurve bezier(points); //Non-Rational
​
    Handle(Geom_BezierCurve) bezier1 = &bezier;
    TopoDS_Edge E = BRepBuilderAPI_MakeEdge(bezier1);
​
    Handle(Geom_CylindricalSurface) aCylinder = new Geom_CylindricalSurface(gp::YOZ(), 200);
    TopoDS_Shape Cylinder = BRepBuilderAPI_MakeFace(aCylinder->Cylinder(), 0, 2*M_PI, -200, 500);
​
    BRepProj_Projection prj(E, Cylinder, gp_Dir(0.0, 0.0, 1.0));
    //prj.Current();
    Viewer vout(50, 50, 500, 500);
    vout << E;
    vout << Cylinder;
    vout << prj.Current();
    vout.StartMessageLoop();
    return 0;
}