clamped b_spline

你的名字 2023-01-08 08:26 65阅读 0赞

#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_p
      double baseN(int i_, int p_, double u_) {
        if (p_ == 0) {
          if (u_ >= knots[i_] && u_ < knots[i_ + 1])
            return 1;
          else
            return 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];
            else
              c_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knots
    
      void 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();