三次贝塞尔曲线生成 C++ 代码

void createCurve(point2D *originPoint,int originCount,std::vector<point2D> &curvePoint){
    //控制点收缩系数 ，经调试0.6较好，CvPoint是opencv的，可自行定义结构体(x,y)
    float scale = 0.6;
    point2D midpoints[originCount];
    //生成中点
    for(int i = 0 ;i < originCount ; i++){
        int nexti = (i + 1) % originCount;
        midpoints[i].x = (originPoint[i].x + originPoint[nexti].x)/2.0;
        midpoints[i].y = (originPoint[i].y + originPoint[nexti].y)/2.0;
    }

    //平移中点
    CvPoint extrapoints[2 * originCount];
    for(int i = 0 ;i < originCount ; i++){
         int nexti = (i + 1) % originCount;
         int backi = (i + originCount - 1) % originCount;
         CvPoint midinmid;
         midinmid.x = (midpoints[i].x + midpoints[backi].x)/2.0;
         midinmid.y = (midpoints[i].y + midpoints[backi].y)/2.0;
         int offsetx = originPoint[i].x - midinmid.x;
         int offsety = originPoint[i].y - midinmid.y;
         int extraindex = 2 * i;
         extrapoints[extraindex].x = midpoints[backi].x + offsetx;
         extrapoints[extraindex].y = midpoints[backi].y + offsety;
         //朝 originPoint[i]方向收缩
         int addx = (extrapoints[extraindex].x - originPoint[i].x) * scale;
         int addy = (extrapoints[extraindex].y - originPoint[i].y) * scale;
         extrapoints[extraindex].x = originPoint[i].x + addx;
         extrapoints[extraindex].y = originPoint[i].y + addy;

         int extranexti = (extraindex + 1)%(2 * originCount);
         extrapoints[extranexti].x = midpoints[i].x + offsetx;
         extrapoints[extranexti].y = midpoints[i].y + offsety;
         //朝 originPoint[i]方向收缩
         addx = (extrapoints[extranexti].x - originPoint[i].x) * scale;
         addy = (extrapoints[extranexti].y - originPoint[i].y) * scale;
         extrapoints[extranexti].x = originPoint[i].x + addx;
         extrapoints[extranexti].y = originPoint[i].y + addy;

    }

    CvPoint controlPoint[4];
    //生成4控制点，产生贝塞尔曲线
    for(int i = 0 ;i < originCount ; i++){
           controlPoint[0] = originPoint[i];
           int extraindex = 2 * i;
           controlPoint[1] = extrapoints[extraindex + 1];
           int extranexti = (extraindex + 2) % (2 * originCount);
           controlPoint[2] = extrapoints[extranexti];
           int nexti = (i + 1) % originCount;
           controlPoint[3] = originPoint[nexti];
           float u = 1;
           while(u >= 0){
               int px = bezier3funcX(u,controlPoint);
               int py = bezier3funcY(u,controlPoint);
               //u的步长决定曲线的疏密
               u -= 0.005;
               CvPoint tempP = cvPoint(px,py);
               //存入曲线点
               curvePoint.push_back(tempP);
           }
    }
}
//三次贝塞尔曲线
double CurvePlot::bezier3funcX(double _t,point2D *controlP){ // cal x coor
   double part0 = controlP[0].x * _t * _t * _t;
   double part1 = 3 * controlP[1].x * _t * _t * (1 - _t);
   double part2 = 3 * controlP[2].x * _t * (1 - _t) * (1 - _t);
   double part3 = controlP[3].x * (1 - _t) * (1 - _t) * (1 - _t);
   return part0 + part1 + part2 + part3;
}
double CurvePlot::bezier3funcY(double _t,point2D *controlP){    // cal y coor
   double part0 = controlP[0].y * _t * _t * _t;
   double part1 = 3 * controlP[1].y * _t * _t * (1 - _t);
   double part2 = 3 * controlP[2].y * _t * (1 - _t) * (1 - _t);
   double part3 = controlP[3].y * (1 - _t) * (1 - _t) * (1 - _t);
   return part0 + part1 + part2 + part3;
}
double CurvePlot::cal_angle(double _t, point2D *controlP){ // cal dy / dx angle
    double _dx_1= 3 * controlP[0].x * _t * _t;
    double _dx_2= 3 * controlP[1].x * (_t * 2 - 3 * _t * _t);
    double _dx_3= 3 * controlP[2].x * (1 - 4 * _t + 3 * _t * _t);
    double _dx_4= - 3 * controlP[3].x * (1 - _t) * (1 - _t);
    double _dy_1= 3 * controlP[0].y * _t * _t;
    double _dy_2= 3 * controlP[1].y * (_t * 2 - 3 * _t * _t);
    double _dy_3= 3 * controlP[2].y * (1 - 4 * _t + 3 * _t * _t);
    double _dy_4= - 3 * controlP[3].y * (1 - _t) * (1 - _t);
    return std::atan2(_dy_1 + _dy_2 + _dy_3 + _dy_4 , _dx_1 + _dx_2 + _dx_3 + _dx_4);
}

cal_angle 求分辨率为 _resolution 的时候每一点的切线方向。