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图形学_圆的扫描转换

1.中点画圆算法

(1)P为当前点亮象素,那么,下一个点亮的象素可能是P1Xp+1Yp) 

     或P2Xp +1Yp +1)

2)构造函数:FXY=X2  +  Y2 -  R2 ;则

             FXY=  0  XY)在圆上;

             FXY< 0   XY)在圆内;

             FXY> 0   XY)在圆外。

     设MP1P2间的中点,M=(Xp+1,Yp-0.5)

     有如下结论:

             FM< 0  ->M在圆内->  P1

             FM>= 0 ->M在圆外-> P2

(3)构造判别式

     d = F(M)  =  F(xp + 1, yp - 0.5)

              =  (xp + 1)2 + (yp - 0.5) 2 - R2   

   若d<0, P1 为下一个象素,那么再下一个象素的判别式为:

         d1 = F(xp + 2, yp - 0.5) = (xp + 2)2 + (yp - 0.5) 2 - R2                                                                             

            = d + 2xp +3

         即的增量为 2xp +3.

   若d>=0, P2 为下一个象素,那么再下一个象素的判别式为:

         d1 = F(xp + 2, yp - 1.5)= (xp + 2)2 + (yp - 1.5) 2 - R2

           = d + 2xp + 3+-2 yp + 2

          即的增量为 2 (xp - yp) +5.

   d的初值:d0 = F(1, R-0.5)= 1 + (R-0.5)2 - R2= 1.25 - R

 

 

#include "easyx.h"
#include "math.h"
#include "windows.h"
#include "stdio.h"
#include "stdlib.h"
#include "conio.h"
#include "graphics.h"

int Draw_yuan(int r,int p1,int p2,int color)
{
    int x,y;
    double d;
    x = p1; 
    y = p2 + r; 
    d = 1.25 -r;

    putpixel(x,y,color);
    
    while(x <= y)
    {
         if(d < 0)
         {
             x = x + 1;
             d = (x-p1+1)*(x-p1+1) + (y-p2-0.5)*(y-p2-0.5) - r * r;
         }
         else
         {
             x = x + 1;
             y = y - 1;
             d = (x-p1+1)*(x-p1+1) + (y-p2-0.5)*(y-p2-0.5) - r * r;
         }
            putpixel(x,y,color);
         putpixel(y,x,color);
            putpixel(x,2*p2-y,color);
         putpixel(y,2*p2-x,color);
         
         putpixel(2*p1-x,y,color);
         putpixel(2*p1-y,x,color);
         putpixel(2*p1-x,2*p2-y,color);
         putpixel(2*p1-y,2*p2-x,color);
         
    }
    return 0;
}

int main()
{ 
   //硬件测试,将gd装入图形驱动器,gm置入最大图形模式。 
    int gd=DETECT,gm,p1,p2,r,color;
    printf("绘制圆的中点画圆算法\n");
    printf("请输入半径:");
    scanf("%d",&r);
    printf("请输入圆心坐标:");
    scanf("%d%d",&p1,&p2);
    printf("请输入颜色:");
    scanf("%d",&color);
    
    //图形初始化
    initgraph(&gd,&gm,"c:\\tc");
    //设置兰背景。
    setbkcolor(BLUE);
    cleardevice();
    
    Draw_yuan(r,p1,p2,color);
    
    getch(); 
    closegraph(); 
    
    return 0;
}

 

 

 

2.正负画圆算法

1)设圆的方程为F(x,y)=X2  +  Y2 -  R2=0;

     假设求得Pi的坐标为(xi,yi)

     则当Pi在圆内时-> F(xi,yi)<0 -> 向右-> 向圆外

          Pi在圆外时-> F(xi,yi)>0 -> 向下-> 向圆内

2)即求得Pi点后选择下一个象素点Pi+1的规则为:

     

(3)若F(xi,yi) 已知,计算F(xi+1,yi+1) 可分两种情况

    1. F(xi,yi)0-> xi+1 = xi+1yi+1 = yi;

      F(xi+1,yi+1)= (xi+1 )2 +(yi+1 )2 -R2

       = (xi+1)2+ yi2 -R2 = F(xi,yi) +2xi +1

    2. F(xi,yi)0-> xi+1 = xiyi+1 = yi -1;

      F(xi+1,yi+1)= (xi+1 )2 +(yi+1 )2 -R2

        = xi2+(yi 1)2-R2 = F(xi,yi) - 2yi +1

 

 

//正负画圆算法

#include "easyx.h"
#include "math.h"
#include "windows.h"
#include "stdio.h"
#include "stdlib.h"
#include "conio.h"
#include "graphics.h"

int Draw_yuan(int r,int p1,int p2,int color)
{
    int x0,y0,x,y;    //画圆的起始点
    x0 = p1;
    y0 = p2 + r;  //起始点坐标
    x = x0;
    y = y0;

    int F0 = (x0-p1)*(x0-p1) + (y0-p2)*(y0-p2) - r * r;
    int F1 = F0;
    int F2;
    
    while(x <= y)
    {
         if(F1 <= 0)
         {
             x = x + 1;
             F2 = (x-p1)*(x-p1) + (y-p2)*(y-p2) - r * r;
         }
         else
         {
             y = y - 1;
             F2 = (x-p1)*(x-p1) + (y-p2)*(y-p2) - r * r;
         }
         putpixel(x,y,color);
         putpixel(y,x,color);
         putpixel(x,2*p2-y,color);
         putpixel(y,2*p2-x,color);
         
         putpixel(2*p1-x,y,color);
         putpixel(2*p1-y,x,color);
         putpixel(2*p1-x,2*p2-y,color);
         putpixel(2*p1-y,2*p2-x,color);
         
         F1 = F2;
    }
    return 0;
}




int main()
{ 
   //硬件测试,将gd装入图形驱动器,gm置入最大图形模式。 
    int gd=DETECT,gm,p1,p2,r,color;
    printf("绘制圆的正负画圆算法\n");
    printf("请输入半径:");
    scanf("%d",&r);
    printf("请输入圆心坐标:");
    scanf("%d%d",&p1,&p2);
    printf("请输入颜色:");
    scanf("%d",&color);
    
    //图形初始化
    initgraph(&gd,&gm,"c:\\tc");
    //设置兰背景。
    setbkcolor(BLUE);
    cleardevice();
    
    Draw_yuan(r,p1,p2,color);
    
    getch(); 
    closegraph(); 
    
    return 0;
}