clamped b_spline

#ifndef B_SPLINE_H
#define B_SPLINE_H#include <vector>//节点个数 m + 1
//最大次数 p = m
//定义基函数class BaseFunction {public:BaseFunction(){};~BaseFunction(){};void setKnots(std::vector<double> knots_) {knots = knots_;m = knots.size() - 1;max_p = m - 1;};// i_:  0 -- m-1// p_:  0 -- max_p// u_:  knots.front()  --  knots.back()// i_ + p_ <= max_pdouble baseN(int i_, int p_, double u_) {if (p_ == 0) {if (u_ >= knots[i_] && u_ < knots[i_ + 1])return 1;elsereturn 0;} else {double a = 0;if ((knots[i_ + p_] - knots[i_]) != 0)a = (u_ - knots[i_]) / (knots[i_ + p_] - knots[i_]);double b = 0;if ((knots[i_ + p_ + 1] - knots[i_ + 1]) != 0)b = (knots[i_ + p_ + 1] - u_) / (knots[i_ + p_ + 1] - knots[i_ + 1]);return a * baseN(i_, p_ - 1, u_) + b * baseN(i_ + 1, p_ - 1, u_);}}private:std::vector<double> knots;int m = 1;int max_p = 1;
};//对一组数据计算BSpline
class BSpline {public:BSpline(){};~BSpline(){};void setP(int p_) {p = p_;m = n + p + 1;generateKnots();};void addControlPoints(std::vector<double> control_points_) {control_points = control_points_;n = control_points.size() - 1;m = n + p + 1;generateKnots();};void setPointsNum(int points_num_) {points_num = points_num_;u.clear();for (int i = 0; i < points_num; i++) {u.emplace_back((double)i / (double)(points_num - 1));}};bool bSplineCal() {if (n < 2) {return false;}data_out.clear();BaseFunction bf;bf.setKnots(knots);for (int j = 0; j < u.size(); j++) {double c_u = 0;for (int i = 0; i <= n; i++) {if (j == u.size() - 1 && i == n)c_u += control_points[i];elsec_u += (bf.baseN(i, p, u[j]) * control_points[i]);}data_out.emplace_back(c_u);}return true;}public:std::vector<double> getDataOut() const { return data_out; };private:std::vector<double> control_points;  //控制点int n = 1;                           //控制点n+1个std::vector<double> knots;           //节点0-1范围内int m = 1;                           //节点数量m+1个int p = 3;                           //曲线阶数int points_num = 10;std::vector<double> u;         //根据points_num计算采样点的std::vector<double> data_out;  //计算完成后的数据//生成knotsvoid generateKnots() {knots.clear();for (size_t i = 0; i < m + 1; i++) {if (i <= p)knots.emplace_back(0);else if (i >= m - p)knots.emplace_back(1);else {// p+1 --- m-p-1区间范围内int num = m - p - p;if (num < 2) return;double step = 1.0 / (double)num;knots.emplace_back(step * (i - p));}}}
};class BSpline2D {public:BSpline2D(){};~BSpline2D(){};std::vector<double> getXOut() const { return x_out; };std::vector<double> getYOut() const { return y_out; };void setP(int p_) { p = p_; };void setPointsNum(int points_num_) { points_num = points_num_; };void addXControlData(std::vector<double> x_control_data_) {x_control_data = x_control_data_;};void addYControlData(std::vector<double> y_control_data_) {y_control_data = y_control_data_;};bool bSpline2DCal() {BSpline bs;bs.setP(p);bs.setPointsNum(points_num);// x方向bs.addControlPoints(x_control_data);if (!bs.bSplineCal()) {return false;}x_out = bs.getDataOut();// y方向bs.addControlPoints(y_control_data);if (!bs.bSplineCal()) {return false;}y_out = bs.getDataOut();return true;};private:std::vector<double> x_control_data, y_control_data;std::vector<double> x_out, y_out;int p = 3;int points_num = 30;
};#endif

使用方法：

BSpline2D bs2d;

bs2d.setPointsNum(point_num);//设置点数量（默认30个点）

bs2d.setP(3);//设置曲线阶数（默认3阶数）

bs2d.addXControlData(x_control_data);//设置控制点

bs2d.addYControlData(y_control_data);

//进行计算

if (!bs2d.bSpline2DCal()) {

return false;

}

//提取插值点数据

std::vector<double> x_out = bs2d.getXOut();

std::vector<double> y_out = bs2d.getYOut();

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