C语言生成圆弧的Bresenham算法

生成圆弧的Bresenham算法
1. 算法思想
如果我们构造函数F(x,y)=x2+y2-R2，则对于圆上的点有F(x,y)=0，对于圆外的点有F(x,y)>0，对于圆内的点F(x,y)<0 。

与中点画线法一样，构造判别式：
d=F(M)=F(x p+1,y p-0.5)=(x p+1)2+(y p-0.5)2-R2
若d<0，则应取P1为下一象素，而且再下一象素的判别式为：
d=F(x p+2,y p-0.5)=(x p+2)2+(y p-0.5)2-R2=d+2x p+3
若d≥0，则应取P2为下一象素，而且下一象素的判别式为
d=F(x p+2,y p-1.5)=(x p+2)2+(y p-1.5)2-R2=d+2(x p-y p)+5
我们这里讨论的第一个象素是（0,R），判别式d的初始值为：
d0=F(1,R-0.5)=1.25-R
为了进一步提高算法的效率，将上面的算法中的浮点数改写成整数，将乘法运算改成加法运算，即仅用整数实现中点画圆法。

2. C源程序
#include<stdio.h>
#include<graphics.h>
int Center_x,Center_y,radius,color;
/**********显示圆弧的八个对称点**********/
void CirclePoints(int Center_x,int Center_y,int x,int y,int color)
{
putpixel(x+Center_x,y+Center_y,color);
putpixel(x+Center_x,-y+Center_y,color);
putpixel(y+Center_x,x+Center_y,color);
putpixel(y+Center_x,-x+Center_y,color);
putpixel(-x+Center_x,-y+Center_y,color);
putpixel(-x+Center_x,y+Center_y,color);
putpixel(-y+Center_x,-x+Center_y,color);
putpixel(-y+Center_x,x+Center_y,color);
}
/**********消除的乘法的中点算法**********/
void MidPointCircle(int Center_x,int Center_y,int radius,int color) {
int x,y;
int d;
int DeltaE,DeltaSE;
x=0;
y=radius;
d=5-4*radius;
DeltaE=12;
DeltaSE=20-8*radius;
putpixel(Center_x,Center_y,color);
CirclePoints(Center_x,Center_y,x,y,color);
while(y>x)
{
if(d<=0)
{
d+=DeltaE;
DeltaSE+=8;
}
else
{
d+=DeltaSE;
DeltaSE+=16;
y--;
}
DeltaE+=8;
x++;
CirclePoints(Center_x,Center_y,x,y,color);
}
}
/**********主函数**********/
void main( )
{
int graphdriver=DETECT,graphmode;
initgraph(&graphdriver,&graphmode,"\\tc");
printf("************************************************************\n"); printf("* Middle-Point Algorithm for Circling *\n");
printf("* Creator:Zhang Zujin *\n");
printf("* *\n");
printf("* Input: Center and Radius of Circle and Color Index *\n");
printf("* Output: The Circle Related to Input *\n");
printf("************************************************************\n\n"); printf("Please Input Center Coordinate(x,y):");
scanf("%d%d",&Center_x,&Center_y);
printf("Please Input Radius:");
scanf("%d",&radius);
printf("Input Color Index[0,15]:");
scanf("%d",&color);
MidPointCircle(Center_x,Center_y,radius,color); getch( );
closegraph( );
}。