常用的数学计算C++实现

Posted 2022-05-02 浩瀚之水_csdn

1.  判断三点顺序（顺时针或者逆时针）（模板）

#include <bits/stdc++.h> 
using namespace std;  
int main()  
  
    double x1, y1, x2, y2, x3, y3;  
    while(cin>>x1>>y1>>x2>>y2>>x3>>y3>>x4>>y4)  
    	//分别输入A，B，C三点的坐标 
    	double ans=(x2-x1)*(y3-y1)-(y2-y1)*(x3-x1);//表示向量AB与AC的叉积的结果 
        if(ans>0) 
			cout<<"逆时针"<<endl;  
        if(ans<0) 
			cout<<"顺时针"<<endl;  
		if(ans==0)
			cout<<"共线"<<endl; 
      
    return 0;  
  

判断三点顺序（顺时针或者逆时针）（模板）_Jamence的博客-CSDN博客_判断顺时针 

2. 贝塞尔曲线

void createCurve(CvPoint *originPoint,int originCount,vector<CvPoint> &curvePoint)  
    //控制点收缩系数 ，经调试0.6较好，CvPoint是<a href="http://lib.csdn.net/base/opencv" class='replace_word' title="OpenCV知识库" target='_blank' style='color:#df3434; font-weight:bold;'>OpenCV</a>的，可自行定义结构体(x,y)  
    float scale = 0.6;  
    CvPoint 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  
float bezier3funcX(float uu,CvPoint *controlP)  
   float part0 = controlP[0].x * uu * uu * uu;  
   float part1 = 3 * controlP[1].x * uu * uu * (1 - uu);  
   float part2 = 3 * controlP[2].x * uu * (1 - uu) * (1 - uu);  
   float part3 = controlP[3].x * (1 - uu) * (1 - uu) * (1 - uu);     
   return part0 + part1 + part2 + part3;   
      
float bezier3funcY(float uu,CvPoint *controlP)  
   float part0 = controlP[0].y * uu * uu * uu;  
   float part1 = 3 * controlP[1].y * uu * uu * (1 - uu);  
   float part2 = 3 * controlP[2].y * uu * (1 - uu) * (1 - uu);  
   float part3 = controlP[3].y * (1 - uu) * (1 - uu) * (1 - uu);     
   return part0 + part1 + part2 + part3;   
   

原迹手写之贝赛尔曲线（穿过已知点画平滑曲线（3次贝塞尔曲线）__ArcticOcean的博客-CSDN博客