我去年有一篇帖子，介绍了NURBS曲线生成与显示的实现代码。
https://blog.csdn.net/stonewu/article/details/133387469?spm=1001.2014.3001.5501文章浏览阅读323次，点赞4次，收藏2次。搞3D几何内核算法研究，必须学习NURBS样条曲线曲面。看《非均匀有理B样条 第2版》这本书，学习起来，事半功倍。在《插件化算法研究平台》上，做了一个样条曲线研究功能，可以分析Bezier曲线、BSpline、NURBS曲线的各种性质，有直观的体验，能更好地理解。https://blog.csdn.net/stonewu/article/details/133387469?spm=1001.2014.3001.5501
本贴子介绍如何在OGG几何内核上做个自己NURBS曲线API。
曲线代码框架参考示例如下：（具体实现代码，请参考我去年的帖子自行实现，或联系本人）
namespace stone
{using namespace std;
class Point3
{
public:float x, y, z;Point3(float x = 0, float y = 0, float z = 0) : x(x), y(y), z(z) {}double norm() { return sqrt(x * x + y * y + z * z); }Point3 operator*(double d) { return Point3(x * d, y * d, z * d); }Point3 operator+(const Point3& p) { return Point3(x + p.x, y + p.y, z + p.z); }
};
class BaseCurve
{
public:virtual ~BaseCurve() {}BaseCurve(double precision) { m_precision = precision; }bool finished = false; //完成控制点构成bool m_mousePressed = false;int m_currentControlPointIndex = -1;double m_precision = 0.01; //精度vector<Point3> controlPoints;vector<Point3> curvePoints;//nurbs参数vector<double> weights; //权重vector<double> knots; // 结点向量int degree = 3; // 曲线次数virtual void clear(){//清空curvePoints.clear();//清空controlPoints.clear();finished = false;}virtual void curveInfo() = 0;virtual void createCurve() = 0;virtual void appendControlPoint(Point3 controlPoint) { controlPoints.push_back(controlPoint); }virtual void moveControlPoint(int index, Point3 controlPoint) { controlPoints[index] = controlPoint; }void initKnots(){。。。}void initWeights(){。。。}
};
class BezierCurve : public BaseCurve
{
public:BezierCurve(double precision = 0.01) : BaseCurve(precision){};public:void curveInfo() { debugx("BezierCurve!"); }// 生成N阶贝塞尔曲线点void createCurve(){curveInfo();if (controlPoints.size() <= 1)return;//清空curvePoints.clear();auto size = controlPoints.size();for (double t = 0; t < 1.0000; t += m_precision){ //根据精度绘制点。。。}}
};class BSplineCurve : public BaseCurve
{
public:void curveInfo() { debugx("BSplineCurve!"); }BSplineCurve(int aDegree, double precision) : BaseCurve(precision) { degree = aDegree; }BSplineCurve(vector<Point3> points, int k, double precision) : BaseCurve(precision){controlPoints = points;degree = k;// 初始化结点向量, m = n + 1+ k ,m+1节点数量, n+1控制点数量 ,k 次数。。。}// 计算基函数值double basis(int i, int k, double u){
。。。return a * basis(i, k - 1, u) + b * basis(i + 1, k - 1, u);}// 计算样条曲线上的点virtual Point3 calculatePoint(double u){Point3 result;。。。return result;}void createCurve(){curveInfo();//清空curvePoints.clear();auto size = controlPoints.size();if (size < 2)return;//生成NURBS曲线上所有的点。。。}void moveControlPoint(int index, Point3 controlPoint){controlPoints[index] = controlPoint;if (controlPoints.size() < 2)return;createCurve();}
};class NURBSCurve : public BSplineCurve
{
public:void curveInfo() override { debugx("NURBSCurve!"); }NURBSCurve(int aDegree=3, double precision = 0.01) : BSplineCurve(aDegree, precision) {}// 计算样条曲线上的点Point3 calculatePoint(double u) override{。。。return result;}
};
} //namespace stonenamespace stone
{class CurveUtil
{
public:static BRepBuilderAPI_MakePolygon CreateBezierCurve(TColgp_Array1OfPnt Array1, double precision = 0.01){。。}static BRepBuilderAPI_MakePolygon CreateNURBSCurve(TColgp_Array1OfPnt Array1, int aDegree=3, double precision = 0.01){。。。return makePolygon;}
};} //namespace stone MakeAPI调用代码参考示例：
主要功能Demo:
1、定义5个控制点，并在界面上显示出来。
2、调用自己的曲线算法API，生成BezierCurve，以此线条为路径，生成管道。并显示。
3、调用自己的曲线算法API，生成NURBSCurve，缺省权重为1，degree为3，节点向量自行生成。以此线条为路径，生成管道。并显示。
4、调用 OCCT几何内核的BSpline API。以此线条为路径，生成管道。并显示。
5、调用 OCCT几何内核的BSpline API NUBRS曲线。以此线条为路径，生成管道。并显示。
void myCurveDemo(OccView *view)
{gp_Ax2 ax2;ax2.SetLocation(gp_Pnt(0, 0, 0));TopoDS_Edge circleEdge = BRepBuilderAPI_MakeEdge(gp_Circ(ax2, 0.1));const int pointCount=5;TColgp_HArray1OfPnt points(1, pointCount);points.SetValue(1, gp_Pnt(0.1, 0, 0));points.SetValue(2, gp_Pnt(1.1, 1, 1));points.SetValue(3, gp_Pnt(2.1, 2, 0));points.SetValue(4, gp_Pnt(3.1, 1, -1));points.SetValue(5, gp_Pnt(5.1, 1, -3));// points.SetValue(6, gp_Pnt(5.1, 4, 5));// points.SetValue(7, gp_Pnt(6.1, 5, -3));// points.SetValue(8, gp_Pnt(8.1, 2, -5));//显示控制点for(int i=1;i<=pointCount;i++){auto p=points.Value(i);showPoint(view,p,QString::number(i).toStdString().c_str(),false);}//调用自己的曲线算法API，生成BezierCurveauto curve=stone::CurveUtil::CreateBezierCurve(points);if(curve.IsDone()){Handle(AIS_ColoredShape) ais = new AIS_ColoredShape(curve.Wire());view->Display(ais);}
//调用自己的曲线算法API，生成NURBSCurve，缺省权重为1，degree为3，节点向量自行生成curve=stone::CurveUtil::CreateNURBSCurve(points);if(curve.IsDone()){auto wire=curve.Wire();Handle(AIS_ColoredShape) ais = new AIS_ColoredShape(wire);ais->SetColor(Quantity_NOC_MAROON);view->Display(ais);{//扫掠TopoDS_Shape pipe=BRepOffsetAPI_MakePipe(wire,circleEdge);Handle(AIS_Shape) aisPipe = new AIS_Shape(pipe);aisPipe->SetColor(Quantity_NOC_MAROON);view->Display(aisPipe);}}
//调用 OCCT几何内核的BSpline API{// Make a BSpline curve from the points arrayHandle(Geom_BSplineCurve) aBSplineCurve = GeomAPI_PointsToBSpline(points).Curve();// Make an edge between two point on the BSpline curve.gp_Pnt aPntOnCurve1, aPntOnCurve2;aBSplineCurve->D0(0.75 * aBSplineCurve->FirstParameter()+ 0.25 * aBSplineCurve->LastParameter(),aPntOnCurve1);aBSplineCurve->D0(0.25 * aBSplineCurve->FirstParameter()+ 0.75 * aBSplineCurve->LastParameter(),aPntOnCurve2);TopoDS_Edge anEdgeBSpline = BRepBuilderAPI_MakeEdge(aBSplineCurve);Handle(AIS_ColoredShape) anAisEdgeBSpline = new AIS_ColoredShape(anEdgeBSpline);anAisEdgeBSpline->SetColor(Quantity_Color(Quantity_NOC_MAGENTA));view->Display(anAisEdgeBSpline);{//扫掠auto wire=BRepBuilderAPI_MakeWire(anEdgeBSpline).Wire();TopoDS_Shape pipe=BRepOffsetAPI_MakePipe(wire,circleEdge);Handle(AIS_Shape) aisPipe = new AIS_Shape(pipe);aisPipe->SetColor(Quantity_NOC_MAGENTA);view->Display(aisPipe);}}//调用 OCCT几何内核的BSpline API NUBRS曲线{/// 均匀B样条，节点向量中的节点值成等差排布/// 均匀B样条的基函数呈周期性，即所有的基函数有相同的形状/// 每个后续基函数仅仅市前面基函数在新位置上的重复Standard_Integer degree(2);Standard_Integer KNum = pointCount + degree + 1;TColStd_Array1OfReal knots(1,KNum);for(int i=0; i<KNum; ++i)knots.SetValue(i+1, i);TColStd_Array1OfInteger mults(1,KNum);for(int i=0; i<KNum; ++i)mults.SetValue(i+1, 1);Handle(Geom_BSplineCurve) curve = new Geom_BSplineCurve(points, knots, mults, degree);TopoDS_Edge ed1 = BRepBuilderAPI_MakeEdge(curve);TopoDS_Wire wr1 = BRepBuilderAPI_MakeWire(ed1);Handle(AIS_ColoredShape) ais = new AIS_ColoredShape(wr1);ais->SetColor(Quantity_NOC_SALMON);view->Display(ais);}{/// 准均匀B样条，节点向量中的节点值也是等差排布，但是起点和终点都有k-1的重复度，其中ke为曲线次数。Standard_Integer degree(2);Standard_Integer KNum = pointCount-1;TColStd_Array1OfReal knots(1,KNum);for(int i=0; i<KNum; ++i)knots.SetValue(i+1, i);TColStd_Array1OfInteger mults(1,KNum);for(int i=0; i<KNum; ++i)if(i == 0 || i == KNum-1)mults.SetValue(i+1, degree+1);elsemults.SetValue(i+1, 1);Handle(Geom_BSplineCurve) curve = new Geom_BSplineCurve(points, knots, mults, degree);TopoDS_Edge ed1 = BRepBuilderAPI_MakeEdge(curve);TopoDS_Wire wr1 = BRepBuilderAPI_MakeWire(ed1);Handle(AIS_ColoredShape) ais = new AIS_ColoredShape(wr1);ais->SetColor(Quantity_NOC_SIENNA);view->Display(ais);//扫掠圆，BSpline路径 BRepOffsetAPI_MakePipe{{TopoDS_Shape pipe=BRepOffsetAPI_MakePipe(wr1,circleEdge);Handle(AIS_Shape) aisPipe = new AIS_Shape(pipe);aisPipe->SetColor(Quantity_NOC_BISQUE);view->Display(aisPipe);}}}
}运行效果：
从运行效果上来看，扫掠生成的管道，与曲线形状非常一致。
绿色的管道（粗线）和自定义算法生成的Bezier曲线路径，如下图：
绿色的管道（粗线）和自定义算法生成的NURBS曲线路径，如下图：
绿色的管道（粗线）和OCCT几何内核的NURBS曲线路径，如下图：
以上三个图中，黄色+处，是控制点位置。黄色+的右下边的数字1，2，3，4，5是控制点的顺序号。
 A B C D)
