三次貝塞爾擬合工具

/*
 * 三次貝塞爾擬合java實現
 */
public void createCurve(List<Vector3f> originPoint,int originCount,List<Vector3f>  curvePoint){  
	   
    double scale = 0.6;  
    
    List<Vector3f>  midpoints = new ArrayList<>();
    //生成中點       
    for(int i = 0 ;i +1< originCount ; i++){      
        int nexti = (i + 1) % originCount;  
        Vector3f  v = new Vector3f(0, 0, 0);
        v.setX((originPoint.get(i).getX() + originPoint.get(nexti).getX())/2.0);  
        v.setY((originPoint.get(i).getY() + originPoint.get(nexti).getY())/2.0);  
        midpoints.add(v);
    }      
     
    //平移中點  
    List<Vector3f>  extrapoints = new ArrayList<>();
    for(int i = 0 ;i +1< originCount ; i++){  
         int backi = (i + originCount -2) %( originCount-1);  
         Vector3f midinmid =  new Vector3f(0, 0, 0);  
         midinmid.setX((midpoints.get(i).getX() + midpoints.get(backi).getX())/2.0);  
         midinmid.setY((midpoints.get(i).getY() + midpoints.get(backi).getY())/2.0);  
         double offsetx = originPoint.get(i).getX() - midinmid.getX();  
         double offsety = originPoint.get(i).getY() - midinmid.getY();  
         int extraindex = 2 * i;  
         Vector3f  v = new Vector3f(0, 0, 0);
         v.setX (midpoints.get(backi).getX() + offsetx);  
         v.setY(midpoints.get(backi).getY() + offsety);  
         extrapoints.add(extraindex,v);
         //朝 originPoint[i]方向收縮   
         double addx = (extrapoints.get(extraindex).getX() - originPoint.get(i).getX()) * scale;  
         double addy = (extrapoints.get(extraindex).getY() - originPoint.get(i).getY()) * scale;  
         Vector3f  v1 = new Vector3f(0, 0, 0);
         v1.setX(originPoint.get(i).getX() + addx);
         v1.setY(originPoint.get(i).getY() + addy);
         extrapoints.set(extraindex,v1);         
         int extranexti = (extraindex + 1)%(2 * (originCount-1));  
         Vector3f v2 = new Vector3f(0, 0, 0);
          v2.setX(midpoints.get(i).getX() + offsetx);  
          v2.setY(midpoints.get(i).getY() + offsety);  
          extrapoints.add(extranexti,v2);
         //朝 originPoint[i]方向收縮   
         addx = (extrapoints.get(extranexti).getX() - originPoint.get(i).getX()) * scale;  
         addy = (extrapoints.get(extranexti).getY() - originPoint.get(i).getY()) * scale;  
         Vector3f v3 = new Vector3f(0, 0, 0);
         v3.setX(originPoint.get(i).getX() + addx);  
         v3.setY(originPoint.get(i).getY() + addy); 
         extrapoints.set(extranexti, v3);
    }      
      
    Vector3f[] controlPoint =  new Vector3f[4];  
    //生成4控制點，產生貝塞爾曲線  
    for(int i = 0 ;i+1< originCount ; i++){  
           controlPoint[0] = originPoint.get(i);  
           int extraindex = 2 * i;  
           controlPoint[1] = extrapoints.get(extraindex + 1);  
           int extranexti = (extraindex + 2) % (2 * (originCount-1));  
           controlPoint[2] = extrapoints.get(extraindex + 1);  
           int nexti = (i + 1) % originCount;  
           controlPoint[3] = originPoint.get(nexti);      
           double u = 1;  
           while(u >= 0){  
               double px = bezier3funcX(u,controlPoint);  
               double py = bezier3funcY(u,controlPoint);  
               //u的步長決定曲線的疏密  
               u -= 0.005;  
               Vector3f tempP = new Vector3f(px,py,0);  
               //存入曲線點   
               curvePoint.add(tempP);  
           }      
    }  
}  
//三次貝塞爾曲線  
private double bezier3funcX(double uu, Vector3f[] controlP){  
   double part0 = controlP[0].getX() * uu * uu * uu;  
   double part1 = 3 * controlP[1].getX() * uu * uu * (1 - uu);  
   double part2 = 3 * controlP[2].getX() * uu * (1 - uu) * (1 - uu);  
   double part3 = controlP[3].getX() * (1 - uu) * (1 - uu) * (1 - uu);     
   return part0 + part1 + part2 + part3;   
}      
private double bezier3funcY(double uu, Vector3f[] controlP){  
   double part0 = controlP[0].getY() * uu * uu * uu;  
   double part1 = 3 * controlP[1].getY() * uu * uu * (1 - uu);  
   double part2 = 3 * controlP[2].getY() * uu * (1 - uu) * (1 - uu);  
   double part3 = controlP[3].getY() * (1 - uu) * (1 - uu) * (1 - uu);     
   return part0 + part1 + part2 + part3;   
}