计算机图形学试验
班级：应数0301
学号：1301030106
姓名：张祖锦
指导老师：陈明
目录
实验1 生成直线段的DDA算法·············································· 1
实验2 生成直线段的中点算法················································ 3
实验3 生成圆弧的中点算法···················································· 7
实验4 生成椭圆弧的中点算法·············································· 10
实验5 三点确定一圆····························································· 13
2005-12-29 18:56
实验1 生成直线段的DDA算法
一． 算法思想
设过端点P1(x1 ,y1)、P1(x2 ,y2)的直线段为L(P1 ,P2)，则直线段L的斜率为
二． C源程序
#include<graphics.h>
#include<stdio.h>
/**********生成直线段的DDA算法**********/
void LineDDA(int x1,int y1,int x2,int y2,int color)
{
float x,y,dx,dy,k;
dx=x2-x1;
dy=y2-y1;
k=dy/dx;
if(k>=-1 && k<=1)
{
y=y1;
for(x=x1;x<=x2;x++)
{
putpixel((int)x,(int)(y+0.5),color);
y+=k;
}
}
else
{
k=1.0/k;
x=x1;
for(y=y1;y<=y2;y++)
{
putpixel((int)(x+0.5),(int)y,color);
x+=k;
}
}
}
/**********主函数**********/
void main( )
{
int graphdriver=DETECT,graphmode;
int x1,y1,x2,y2,color;
initgraph(&graphdriver,&graphmode,"\\tc");
printf("****************************************\n");
printf("* DDA Algorithm for Lining *\n");
printf("* Creator:Zhang Zujin *\n");
printf("* *\n");
printf("* Input:Two Pixels and Color Index *\n");
printf("* Output: The Line Related to Input*\n");
printf("****************************************\n\n");
printf("Please Input Two Pixels(x1,y1),(x2,y2):");
scanf("%d%d%d%d", &x1,&y1,&x2,&y2);
printf("Input Color Index[0,15]:");
scanf("%d",&color);
LineDDA(x1,y1,x2,y2,color);
outtextxy(x1,y1,"Start Point");
outtextxy(x2,y2,"End Point");
getch( );
closegraph( );
}
2005-12-29 18:58
实验2 生成直线段的中点算法
一．算法思想
假定直线斜率k在0~1之间(k的其它取值可以类似处理)，当前象素点为（xp,yp），则下一个象素点有两种可选择点P1（xp+1,yp）或P2（xp+1,yp+1）。若P1与P2的中点（xp+1,yp+0.5）称为M，Q为理想直线与x=xp+1垂线的交点。当M在Q的下方时，则取P2应为下一个象素点；当M在Q的上方时，则取P1为下一个象素点。这就是中点画线法的基本原理。
图1 中点画线法每步迭代涉及的象素和中点示意图
下面讨论中点画线法的实现。过点(x0,y0)、(x1, y1)的直线段L的方程式为F(x, y)=ax+by+c=0，其中，a=y0-y1, b=x1-x0, c=x0y1-x1y0，欲判断中点M在Q点的上方还是下方，只要把M代入F（x，y），并判断它的符号即可。为此，我们构造判别式:
d=F(M)=F(xp+1, yp+0.5)=a(xp+1)+b(yp+0.5)+c
当d<0时，M在L(Q点)下方，取P2为下一个象素；
当d>0时，M在L(Q点)上方，取P1为下一个象素；
当d=0时，选P1或P2均可，约定取P1为下一个象素；
注意到d是xp, yp的线性函数，可采用增量计算，提高运算效率。
若当前象素处于d³0情况，则取正右方象素P1(xp+1, yp),要判下一个象素位置，应计算 d1=F(xp+2, yp+0.5)=a(xp+2)+b(yp+0.5)=d+a，增量为a。
若d<0时，则取右上方象素P2(xp+1, yp+1)。要判断再下一象素，则要计算d2= F(xp+2, yp+1.5)=a(xp+2)+b(yp+1.5)+c=d+a+b ，增量为a＋b。画线从(x0, y0)开始，d的初值 d0=F(x0+1, y0+0.5)=F(x0, y0)+a+0.5b，因 F(x0, y0)=0，所以d0=a+0.5b。
由于我们使用的只是d的符号，而且d的增量都是整数，只是初始值包含小数。因此，我们可以用2d代替d来摆脱小数，写出仅包含整数运算的算法程序。
二．C源程序
#include<graphics.h>
#include<stdio.h>
/**********生成直线段的中点算法**********/
void MidPointLine(int x1,int y1,int x2,int y2,int color)
{
float x,y,dx,dy;
float k,d;
float IncrE,IncrNE;
dx=x2-x1;
dy=y2-y1;
k=dy/dx;
if(k>=-1 && k<=1)
{
d=dx-2*dy;
IncrE=-2*dy;
IncrNE=2*(dx-dy);
x=x1;y=y1;
putpixel(x,y,color);
while(x<x2)
{
if(d>0)
d+=IncrE;
else
{
d+=IncrNE;
y++;
}
x++;
putpixel((int)x,(int)y,color);
}
}
else
{
d=dy-2*dx;
IncrE=-2*dx;
IncrNE=2*(dy-dx);
x=x1;y=y1;
putpixel(x,y,color);
while(y<y2)
{
if(d>0)
d+=IncrE;
else
{
d+=IncrNE;
x++;
}
y++;
putpixel((int)x,(int)y,color);
}
}
}
/**********主函数**********/
void main( )
{
int graphdriver=DETECT,graphmode;
int x1,y1,x2,y2,color;
initgraph(&graphdriver,&graphmode,"\\tc");
printf("*************************************************\n");
printf("* Middle-Point Algorithm for Lining *\n");
printf("* Creator:Zhang Zujin *\n");
printf("* *\n");
printf("* Input:Two Pixels and Color Index *\n");
printf("* Output: The Line Related to Input *\n");
printf("*************************************************\n\n");
printf("Please Input Two Pixels(x1,y1),(x2,y2):");
scanf("%d%d%d%d", &x1,&y1,&x2,&y2);
printf("Input Color Index[0,15]:");
scanf("%d",&color);
MidPointLine(x1,y1,x2,y2,color);
outtextxy(x1,y1,"Start Point");
outtextxy(x2,y2,"End Point");
getch( );
closegraph( );
}
2005-12-29 18:59
实验3 生成圆弧的中点算法
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(xp+1,yp-0.5)=(xp+1)2+(yp-0.5)2-R2
d=F(xp+2,yp-0.5)=(xp+2)2+(yp-0.5)2-R2=d+2xp+3
d=F(xp+2,yp-1.5)=(xp+2)2+(yp-1.5)2-R2=d+2(xp-yp)+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
图2 当前象素与下一象素的候选者
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( );
}
2005-12-29 18:59
实验4 生成椭圆弧的中点算法
1. 算法思想
不敢多写，注意到圆弧是椭圆弧的特殊情况，故而可以很好的利用实验3的知识。只不过要注意到椭圆弧是四对称的，并且在画第一象限时要注意分情况，具体实现方法见C源程序。
2. C源程序
#include<stdio.h>
#include<math.h>
#include<graphics.h>
long a,b;
long color;
long Center_x,Center_y;
/**********绘椭圆弧上对称的四个要素**********/
void EllipsePoints(long Center_x,long Center_y,long x,long y,long color)
{
putpixel(Center_x+x,Center_y+y,color);
putpixel(Center_x+x,Center_y-y,color);
putpixel(Center_x-x,Center_y+y,color);
putpixel(Center_x-x,Center_y-y,color);
}
/**********绘椭圆弧主要程序**********/
void MidPointEllipse(longCenter_x,longCenter_y,longa,longb,longcolor)
/* 椭圆中心在(Center_x,Center_y),长半轴为a，短半轴为b */
{
long x,y,d,P_x,P_y,Square_a,Square_b;
Square_a=a*a;
Square_b=b*b;
P_x=(int)(0.5+(float)Square_a/sqrt((float)(Square_a+Square_b)));
P_y=(int)(0.5+(float)Square_b/sqrt((float)(Square_a+Square_b)));
/* 生成第一象限内的上半部分椭圆弧 */
x=0;
y=b;
d=4*(Square_b-b*Square_a)+Square_a;
EllipsePoints(Center_x,Center_y,x,y,color);
while(x<=P_x)
{
if(d<=0)
d+=4*Square_b*(2*x+3);
else
{
d+=4*Square_b*(2*x+3)-8*Square_a*(y-1);
y--;
}
x++;
EllipsePoints(Center_x,Center_y,x,y,color);
}
/* 生成第一象限内的上半部分椭圆弧 */
x=a;
y=0;
d=4*(Square_a-a*Square_b)+Square_b;
EllipsePoints(Center_x,Center_y,x,y,color);
while(y<P_y)
{
if(d<=0)
d+=4*Square_a*(2*y+3);
else
{
d+=4*Square_a*(2*y+3)-8*Square_b*(x-1);
x--;
}
y++;
EllipsePoints(Center_x,Center_y,x,y,color);
}
}
2005-12-29 19:00
/**********主函数**********/
void main( )
{
int graphdriver=DETECT,graphmode;
initgraph(&graphdriver,&graphmode,"\\tc");
printf("*************************************************\n");
printf("* Mid-PolongAlgorithm for Ellipse *\n");
printf("* Creator:Zhang Zujin *\n");
printf("* *\n");
printf("* Input:Center Coordinate , and Color Index *\n");
printf("* Output: The Ellipse Related to Input *\n");
printf("*************************************************\n\n");
while(1)
{
printf("\n");
printf("Please Input Center Coordinate(x,y):");
scanf("%d%d",&Center_x,&Center_y);
printf("Input half major axis(a),half major axis(b):");
scanf("%d%d",&a,&b);
printf("Inpute Color Index(0,15):");
scanf("%d",&color);
MidPointEllipse(Center_x,Center_y,a,b,color);
}
getch( );
closegraph( );
}
2005-12-29 19:00
2005-12-29 19:03
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