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

#include

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( );

}