DDA, Bresenham and Circle Drawing Algorithms

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DATE:

DDA LINE DRAWING ALGORITHM
EX NO: 1 (a)

AIM:
To implement DDA Line Drawing Algorithm using C.

Functions used:
Line() :- The function line() is used to draw a line from(x1,y1) to (x2,y2)
Syntax :- line (x1,y1,x2,y2)
initgraph() :- This function takes thee arguments and they are
i). The video driver to be used (gd).
ii).The graphics mode (gm).
iii).The path name.
Syntax:- Initgraph(gd,gm,path)

ALGORITHM:
Step 1: Start
Step 2: Get the values of the end points as(x1, y1) &(x2, y2)
Step 3: Assign ax,ab,ya,yb
Step 4: Compute dx=xb-xa
Step 5: Compute dy=yb-ya
Step 6: Assign dx=xb-xa,dsy=yb-ya
Step 7: If dy>dx then interchange the values of dx and dy and assign exch=1
Step 8: Compute xinc=dx/steps & yinc=dy/steps,x=xa,y=ya
Step 9: Put a pixel on(x,y)
Step 14: Stop

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PROGRAM:
#include "stdio.h"
#include "conio.h"
#include "math.h"
#include "graphics.h"
main()
{
int gd=DETECT,gm;
int xa,xb,ya,yb;
int dx,dy,steps,k,xinc,yinc,x,y;
initgraph(&gd,&gm,"c:tcbgi");
printf("Enter the two left end pixel points(xa,ya):n");
scanf("%d%d",&xa,&ya);
printf("Enter the two Right end pixel points(xb,yb):n");
scanf("%d%d",&xb,&yb);
dx=xb-xa;
dy=yb-ya;
if(abs(dx)>abs(dy))
steps=abs(dx);
else
steps=abs(dy);
xinc=dx/steps;
yinc=dy/steps;
x=xa;
y=ya;
putpixel(x,y,6);
for(k=1;k<=steps;k++)
{
x=x+xinc;

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y=y+yinc;
putpixel(x,y,6);
}
getch();
return(0);
}

OUTPUT
Enter The Two Left Endpoints(xa,ya) : 234

124

Enter The Two Right Endpoints(xb,yb) : 578

321

RESULT:
Thus DDA Line Drawing Algorithm was implemented using C .

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DATE:

BRESENHAM’S LINE DRAWING ALGORITHM

EX NO: 1(b)

AIM:
To implement Bresenham’s line drawing Algorithm for drawing lines.
Functions used:
Line() :- The function line() is used to draw a line from(x1,y1)to (x2,y2)
Syntax: line (x1,y1,x2,y2)
initgraph() :- This function takes thee arguments and they are
i).The video driver to be used (gd).
iii).The path name.
Syntax: Initgraph(gd,gm,path)
ALGORITHM:
Step1: Include the graphics header file and obtain graphics mode and driver.
Step2: Get the co-ordinates of two end points of a line (x1,y1) & (x2,y2) and
store left end point in (x1,y1).
Step3: Load (x1,y1) into frame buffer that means plot the first point.
Step4: Calculate constants dx,dy,2dy,2dy-2dx and obtain value for decision
parameter p=2dy-dx.
Step5: At each x along the line perform the test if p<0, next point to plot is
(x+1,y) and p+1=p+2dy otherwise (x+1,y+1) & p+1=p+2dy-2dx
Step6: Repeat steps dx times.
Step7: Display a line.

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PROGRAM:
#include "stdio.h"
#include "conio.h"
#include "math.h"
main()
{
int gd=DETECT,gm;
int xa,xb,ya,yb;
int dx,dy,x,y,xend,p;
printf("Enter The Two Left Endpoints(xa,ya):n");
scanf("%d%d",&xa,&ya);
printf("Enter The Two Right Endpoints(xb,yb):n");
scanf("%d%d",&xb,&yb);
dx=abs(xa-xb);
dy=abs(ya-yb);
p=2*dy-dx;
if(xa>xb)
{
x=xb;
y=yb;
xend=xa;
}
else
{
x=xa;
y=ya;
xend=xb;
}
putpixel(x,y,6);

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while(x<xend)
{
x=x+1;
if(p<0)
{
p=p+2*dy;
}
else
{
y=y+1;
p=p+2*(dy-dx);
}
putpixel(x,y,6);
}
getch();
return(0);
}

OUTPUT:
Enter The Two Left Endpoints(xa,ya):

234

124

Enter The Two Right Endpoints(xb,yb):

578

321

RESULT:
Thus Bresenham’s line drawing Algorithm Algorithm was implemented
using C.

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DATE:

BRESENHAM’S CIRCLE DRAWING ALGORITHM

EX NO: 1(c)

AIM:
To implement Bresenham’s circle drawing algorithm using C.

Functions used:
Circle() :- The function circle() is used to draw a circle using(x,y) as centre point.
Syntax:- circle (x,y,radius)
initgraph():- This function takes thee arguments and they are
iii).the path name.
Syntax:-

Initgraph(gd,gm,path)

Putpixel () :- The function putpixel() is used to place a pixel at particular
coordinate.
Syntax:- Putpixel(x,y,color)

ALGORITHM:

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Step 2: Get the center point (a,b)and radius r of the circle.
Step 3: Initialize the variables and decision parameter as,x=0;y=r;p=1-r;
Step 4: If (p<0)then the next point along the circle is (x+1,y) and p=p+2*x+1;
Else the next point along the circle is (x=1,y-1) and p=p+2*(x-y)+1;
Step 5: Repeat step4 until x<y.
Step 6: Plot the pixel to display the circle using put pixel function.
Step 7: Display the circle

PROGRAM:
#include "stdio.h"
#include "conio.h"
#include "math.h"
main()
{
int gd=DETECT,gm;
int xcenter,ycenter,radius;
int p,x,y;
x=0;
printf("Enter The Radius Value:n");
scanf("%d",&radius);
y=radius;
printf("Enter The xcenter and ycenter Values:n");
scanf("%d%d",&xcenter,&ycenter);
plotpoints(xcenter,ycenter,x,y);
p=1-radius;
while(x<y)
{

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if(p<0)
x=x+1;
else
{
x=x+1;
y=y-1;
}
if(p<0)
p=p+2*x+1;
else
p=p+2*(x-y)+1;
}
getch();
return(0);
}
int plotpoints(int xcenter,int ycenter,int x,int y)
{
putpixel(xcenter+x,ycenter+y,1);
putpixel(xcenter-x,ycenter+y,1);
putpixel(xcenter+x,ycenter-y,1);
putpixel(xcenter-x,ycenter-y,1);
putpixel(xcenter+y,ycenter+x,1);
putpixel(xcenter-y,ycenter+x,1);
putpixel(xcenter+y,ycenter-x,1);
putpixel(xcenter-y,ycenter-x,1);
}

OUTPUT

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Enter the Radius Value: 80
Enter The xcenter and ycenter Values :230 260

RESULT:
Thus Bresenham’s circle drawing Algorithm was implemented using C.

DATE:

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BRESENHAM’S ELLIPSE DRAWING ALGORITHM
EX NO: 1(d)

AIM:
To implement Bresenham’s ellipse drawing algorithm using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:

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Step 2.Input rx,ry and ellipse center(xc,yc) and obtain the first point on an
ellipse centered at origin as (x0,y0)=(0,ry).
Step 3.Calculate the initial value of the decision parameter in region 1 as
p10= ry2- rx2 ry+(1/4)rx2.
Step 4.At each xk position in region 1,starting at k=0,perform the following
text:
a) If p1k<0, the next point along the ellipse centered on (0,0) is
(xk+1,yk) and p1k+1=pk+2 ry2 xk+1+ ry2.
b) Otherwise, the next point along the ellipse is (xk+1,yk-1) and
p1k+1=p1k+2 ry2 xk+1-2 ry2yk+1+ ry2 with 2 ry2 xk+1=2
ry2xk+2ry2,2rx2 yk+1=2rx2yk-2rx2.
Step 5. Calculate the initial value of the decision parameter in region 2
using the last point (x0,y0) calculated in region 1 as
p20=ry2(x0+(1/2))2+ rx2(y0-1)2- rx2 ry2
Step 6. At each yk position in region2, starting at k=0,perform the
following test:
a) If p2k>0, the next point along the ellipse centered on (0,0)
is (xk,yk-1) andp2 k+1=p2 k-2rx2 y k+1+ rx2
b) Otherwise, the next point along the ellipse is (xk+1,yk-1) &
p2k+1=p2 k+2 ry2 xk+1-2 rx2yk+1+ rx2 using the
same incremental calculations for x and y as in region 1.
Step 7. Repeat the steps for region 1 until 2 ry2>=2 rx2y.
Step 8. Plot the pixel to display the ellipse using put pixel function.

PROGRAM:
#include "stdio.h"

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#include "conio.h"
#include "math.h"
main()
{
int gd=DETECT,gm;
int xcenter,ycenter,rx,ry;
int p,x,y,px,py,rx1,ry1,rx2,ry2;
printf("Enter The Radius Value:n");
scanf("%d%d",&rx,&ry);
printf("Enter The xcenter and ycenter Values:n");
scanf("%d%d",&xcenter,&ycenter);
ry1=ry*ry;
rx1=rx*rx;
ry2=2*ry1;
rx2=2*rx1;
/* REGION 1 */
x=0;
y=ry;
p=(ry1-rx1*ry+(0.25*rx1));
px=0;
py=rx2*y;
while(px<py)
{
x=x+1;
px=px+ry2;
if(p>=0)
y=y-1;

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py=py-rx2;
if(p<0)
p=p+ry1+px;
else
p=p+ry1+px-py;
/* REGION 2*/
p=(ry1*(x+0.5)*(x+0.5)+rx1*(y-1)*(y-1)-rx1*ry1);
while(y>0)
{
y=y-1;
py=py-rx2;
if(p<=0)
{
x=x+1;
px=px+ry2;
}
if(p>0)
p=p+rx1-py;
else
p=p+rx1-py+px;
}
}
getch();
return(0);
}
int plotpoints(int xcenter,int ycenter,int x,int y)
{
putpixel(xcenter+x,ycenter+y,6);
putpixel(xcenter-x,ycenter+y,6);
putpixel(xcenter+x,ycenter-y,6);

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putpixel(xcenter-x,ycenter-y,6);

OUTPUT

Enter The Radius Value(Rx,Ry)

:10

30

Enter The xcenter and ycenter Values :300 150

RESULT:
Thus Bresenham’s ellipse drawing Algorithm was implemented using C.

DATE:

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IMPLEMENTATION OF LINE, CIRCLE, ELLIPSE
EX NO: 2

ATTRIBUTES

AIM:
To implement the different attributes of line, circle, ellipse using C.

ALGORITHM:
Step1:-Start the program for line, circle, ellipse type
Step2:-Include the necessary package
Step3:-Declare the line type in lname and fill type in fname character
Step4:-Using setline style and line function to draw the different line function
Step5:-Using ellipse function to draw the different circle, ellipse function
Step6:-Finally terminate the function

PROGRAM:
#include <graphics.h>

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#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <conio.h>
void main()
{
int gd=DETECT,gm;
int s;
char *fname[] = { "EMPTY FILL","SOLID FILL","LINE FILL",
"LTSLASH FILL","SLASH FILL","BKSLASH FILL",
"LTBKSLASH FILL","HATCH FILL",
"XHATCH FILL","INTERLEAVE FILL",
"WIDE DOT FILL","CLOSE DOT FILL","USER FILL"
};
char *lname[]={"SOLID LINE","DOTTED LINE","CENTER LINE","DASHED
LINE","USERBIT LINE"};
initgraph(&gd,&gm," ");
clrscr();
cleardevice();
outtextxy(20,20,"LINE STYLES");
for (s=0;s<5;s++)
{
setlinestyle(s,1,2);
setcolor(s+2);
line(100,30+s*50,250,250+s*50);
outtextxy(255,250+s*50,lname[s]);
}
getch();
cleardevice();
setlinestyle(0,0,0);
for (s=0;s<12;s++)
{

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setfillstyle(s,s+0);
setcolor(15);
outtextxy(20,20,"ELLIPSE WITH VARIOUS FILL ATTRIBUTES");
fillellipse(150,20+s*40,30,15);
outtextxy(275,30+s*40,fname[s]);
outtextxy(360,20,"CIRCLE WITH VARIOUS FILL ATTRIBUTES");
fillellipse(450,20+s*40,18,18);
}
getch();
}

OUTPUT:
LINE STYLES

SOLID LINE
DOTTED LINE
CENTER LINE
DASHED LINE
USER BIT LINE
ELLIPSE & CIRCLE FILL STYLES

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RESULT:
Thus the different attributes of line, circle, ellipse was implemented using C.

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DATE:

2D – BASIC TRANSFORMATIONS

EX NO: 3

AIM:
To perform the 2D transformation such as translation, rotation, scaling using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step1:- Start the program
Step2:-Enter the choice for transformation.
Step 3:-. Perform the translation, rotation, scaling of 2D object.
Step 4:- Get the needed parameters for the transformation from the user.
Step 5:-. In case of rotation, object can be rotated about x or y axis.
Step 6:-. Display the transmitted object in the screen.

PROGRAM:

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#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<dos.h>
#include<math.h>
#include<stdlib.h>
void menu();
void input();
void input1();
void output();
void output1();
void translation();
void rotation();
void scaling();
int a[10][10],b[10][10],b1[10][10],diff,i,j,x,option,temp,angle,tx,ty,fx,fy,sh,k,n,axis,y;
float sx,sy;
void menu()
{
printf("menun");
printf("0.drawn");
printf("1.Translationn");
printf("2.rotationn");
printf("3.scalingn");
printf("4.exitn");
printf("enter the choice:");
scanf("%d",&option);
switch(option)
{
case 0:
input();
menu();
break;

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case 1:
translation();
break;
case 2:
rotation();
break;
case 3:
scaling();
break;
case 4:
exit(0);
break;
}
input();
}
void input()
{
printf("enter the number of vertices:" );
scanf("%d",&n);
for(i=0;i<n;i++)
{
printf("enter the coordinates:");
scanf("%d%d%d%d",&a[i][0],&a[i][1],&a[i+1][0],&a[i+1][1]);
}
}
void output()
{
cleardevice();
for(i=0;i<n;i++)
{
line(a[i][0],a[i][1],a[i+1][0],a[i+1][1]);
}

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for(i=0;i<n;i++)
{
b[i][0]=0;
b[i][1]=0;
}}
void input1()
{
cleardevice();
for(i=0;i<n;i++)
{
line(a[i][0],a[i][1],a[i+1][0],a[i+1][1]);
}
}
void output1()
{
cleardevice();
for(i=0;i<n;i++)
{
line(b[i][0],b[i][1],b[i+1][0],b[i+1][1]);
}
}
void translation()
{
output();
printf("enter the tranformation vertex tx,ty:n");
scanf("%d%d",&tx,&ty);
for(i=0;i<=n;i++)
{
b[i][0]=a[i][0]+tx;
b[i][1]=a[i][1]+ty;
}

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output1();
delay(10);
menu();
}
void rotation()
{
output();
printf("enter the rotating angle:");
scanf("%d",&y);
printf("enter the pivot point:");
scanf("%d%d",&fx,&fy);
k=(y*3.14)/180;

for(i=0;i<=n;i++)
{
b[i][0]=fx+(a[i][0]-fx)*cos(y)+(a[i][1]-fy)*sin(y);
b[i][1]=fy+(a[i][0]-fx)*sin(y)-(a[i][1]-fy)*cos(y);
}
output1();
delay(10);
menu();
}
void scaling()
{
output();
printf("enter the scaling factorn");
scanf("%f%f",&sx,&sy);
printf("enter the fixed point:");
scanf("%d%d",&fx,&fy);
for(i=0;i<=n;i++)

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{
b[i][0]=a[i][0]*sx+fy*(1-sx);
b[i][1]=a[i][1]*sy+fy*(1-sy);
}
output1();
delay(10);
menu();
}

OUTPUT
Menu
0.Draw
1.Translation
2.Rotation
3.Scaling
4.Shearing
5.Reflection
6.Exit
Enter the choice : 0
Enter the number of vertices : 3
Enter the coordinates

:-

30

150

10

200


:-

10

200

60

200


:-

60

200

30

150

TRANSLATION

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Enter the translation factor 30 30

ROTATION
Enter the angle 70
Enter the pivot point 100 200

SCALING

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Enter the scaling factor 0.3

0.3

Enter the fixed point

200

100

RESULT:
Thus the basic 2D transformations was performed successfully using C.

44210205028
DATE:

2D – COMPOSITE TRANSFORMATIONS

EX NO: 4

AIM:
To perform the 2D composite transformation such as translation, rotation, scaling
using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step1:- Start the program
Step2:-Enter the choice for transformation.
Step 3:-. Perform the reflection and shearing of 2D object.
Step 4:- Get the needed parameters for the transformation from the user.
Step 5:-. Incase of rotation, object can be rotated about x or y axis.
Step 6:-. Display the transmitted object in the screen

PROGRAM:

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#include<stdio.h>
#include<conio.h>
#include<dos.h>
#include<math.h>
#include<stdlib.h>
void menu();
void input();
void input1();
void output();
void output1();
void shearing();
void reflection();
inta[10][10],b[10][10],b1[10][10],diff,i,j,x,option,temp,angle,tx,ty,fx,fy,sh,k,n,
axis,y;
float sx,sy;
void menu()
{
printf("menun");
printf("0.drawn");
printf("1.shearingn");
printf("2.reflectionn");
printf("3.exitn");
printf("enter the choice:");
scanf("%d",&option);
switch(option)
{
case 0: input();
menu();
break;
case 1 : shearing();
break;

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case 2:
reflection();
break;
case 3:
exit(0);
break;
}
input();
}
void input()
{
printf("enter the number of vertices:" );
scanf("%d",&n);
for(i=0;i<n;i++)
{
printf("enter the coordinates:");
scanf("%d%d%d%d",&a[i][0],&a[i][1],&a[i+1][0],&a[i+1][1]);
}
}
void output()
{
cleardevice();
for(i=0;i<n;i++)
{
line(a[i][0],a[i][1],a[i+1][0],a[i+1][1]);
}
for(i=0;i<n;i++)
{
b[i][0]=0;
b[i][1]=0;
}
}

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void input1()
{
cleardevice();
for(i=0;i<n;i++)
{
line(a[i][0],a[i][1],a[i+1][0],a[i+1][1]);
}
}
void output1()
{
cleardevice();
for(i=0;i<n;i++)
{
line(b[i][0],b[i][1],b[i+1][0],b[i+1][1]);
}
}
void shearing()
{
output();
printf("enter the shear value:");
scanf("%d",&sh);
printf("enter the axis for shearing if x-axis then 1 if y-axis the 0:");
scanf("%d",&axis);
if(axis==1)
{
for(i=0;i<=n;i++)
{
if(i!=0 && i!=3)
{
b[i][0]=a[i][0]+sh;
b[i][1]=a[i][1];
}

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else
{
b[i][0]=a[i][0];
b[i][1]=a[i][1];
}
}

}

else
{
for(i=0;i<=n;i++)
{
if(i!=1)
{
b[i][1]=a[i][1]+sh;
b[i][0]=a[i][0];
}
else
{
b[i][0]=a[i][0];
b[i][1]=a[i][1];
}
}
}
output1();
delay(10);
menu();
}
void reflection()
{
output();
diff=a[1][1]-a[0][1];
for(i=0;i<=n;i++)
{

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if(i==0||i==3)
{
b[i][0]=a[i][0];
b[i][1]=a[i][1]+(2*diff)+10;
}
else
{
b[i][0]=a[i][0];
b[i][1]=a[i][1]+10;
}
}
for(i=0;i<n;i++)
{
line(b[i][0],b[i][1],b[i+1][0],b[i+1][1]);
}
menu();
}
void main()
{
int gd=DETECT,gm;
menu();
getch();
}

OUTPUT

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Menu
0.Draw
1.Shearing
2.Reflection
3.Exit
Enter the number of vertices : 3
Enter the coordinates :-

30

150

10

200


10

200

60

200


60

200

30

150

SHEARING
Enter the Shear value 50
Enter the axis for shearing if x-axis then 1 if y-axis the 0: 1

Enter the axis for shearing if x-axis then 1 if y-axis the 0: 0

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REFLECTION

RESULT:
Thus the composite 2D transformations was performed successfully using C.

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DATE:

COHEN SUTHERLAND LINE CLIPPING

EX NO: 5(a)

AIM:
To perform Cohen-Sutherland line clipping using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step 1. Create a class with functions drawwindow, drawline, setcode, visibility and
reset endpoint.
Step 2. Using the function line set the parameters to draw window.
Step 3. Using the function defined in class sulc, setcode is used to save the line inside
window and to the line outside the window.
Step 4. Using the function visibility
i).Check the code to know the points inside or outside the window.
ii).If the code value is zero the point is inside the window.

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Step 5. Using the function reset end point
i). if the code value for the line is outside the window.
ii).reset the endpoint to the boundary of the window.
Step 6. Initialize the graphics functions
Step 7. Declare the variables x1, x2, y1, y2 of array type.
Step 8. Get the value of two endpoints x1, y1 and x2, y2 to draw the line.
Step 9. Using the object c, display the window before clipping.
Step 10. Using the function setcode, visibility display the clipped window only with
lines inside the window class was displayed after clipping.

PROGRAM:
#include<stdio.h>
#include<conio.h>
#include<math.h>
float cxl,cxr,cyt,cyb;
code(float ,float);
void clip(float ,float,float,float);
void rect(float ,float,float,float);
main()
{
float x1,y1,x2,y2;
int g=0,d;
initgraph(&g,&d,"c:tcbin");
settextstyle(1,0,1);
outtextxy(40,15,"BEFORE CLIPPING");
printf("n Please Enter Left,Bottom,Right,Top Of Clip Window");
scanf("%f%f%f%f",&cxl,&cyb,&cxr,&cyt);
rect(cxl,cyb,cxr,cyt);
getch();
printf("n Enter The Line Coordinate");

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scanf("%f%f%f%f",&x1,&y1,&x2,&y2);
line(x1,y1,x2,y2);
getch();
cleardevice();
settextstyle(1,0,1);
outtextxy(40,15,"AFTER CLIPPING");
clip(x1,y1,x2,y2);
getch();
closegraph();
}
void clip(float x1,float y1,float x2,float y2)
{
int c,c1,c2;
float x,y;
c1=code(x1,y1);
c2=code(x2,y2);
getch();
while((c1!=0)||(c2!=0))
{
if((c1&c2)!=0)
goto out;
c=c1;
if(c==0)
c=c2;
if((c&1)==1)
{
y=y1+(y2-y1)*(cxl-x1);
x=cxl;
}
else
if((c&2)==2)
{

44210205028
y=y1+(y2-y1)*(cxl-x1)/(x2-x1);
x=cxr;
}
else
if((c&8)==8)
{
x=x1+(x2-x1)*(cyb-y1)/(y2-y1);
y=cyb;
}
else
if((c&4)==4)
{
x=x1+(x2-x1)*(cyt-y1)/(y2-y1);
y=cyt;
}
if(c==c1)
{
x1=x;
y1=y;
c1=code(x,y);
}
else
{
x2=x;
y2=y;
c2=code(x,y);
}
}
out:
rect(cxl,cyb,cxr,cyt);
line(x1,y1,x2,y2);
}

44210205028
code(float x ,float y)
{
int c=0;
if(x<cxl)
c=1;
else
if(x>cxr) c=2;
else
if(y<cyb) c=c|8;
else
if(y>cyt) c=c|4;
return c;
}
void rect(float xl,float yb,float xr,float yt)
{
line(xl,yb,xr,yb);
line(xr,yb,xr,yt);
line(xr,yt,xl,yt);
line(xl,yt,xl,yb);
}

OUTPUT
BEFORE CLIPPING
Please Enter Left , Bottom , Right , Top Of The Clip window
200
200
400
400

Please Enter The Line Coordinates (X1, Y1, X2, Y2)

44210205028
150
300
400
450

AFTER CLIPPING

RESULT:
Thus Cohen-Sutherland clipping was implemented using C.

44210205028
DATE:

WINDOW TO VIEWPORT MAPPING

EX NO: 5(b)

AIM:
To perform window to viewport mapping using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step1: Input the minimum and maximum coordinates of a window.
Step2: Input the minimum and maximum coordinates of a view port.
Step3: Get the coordinates of a point.
Step4: Display a point using set pixel function.

PROGRAM:

44210205028
#include<stdio.h>
#include<conio.h>
#include<math.h>
main()
{
float sx,sy;
int w1,w2,w3,w4,x1,x2,x3,x4,y1,y2,y3,y4,v1,v2,v3,v4;
int gd=DETECT,gm;
printf("Enter The Coordinate x1,y1,x2,y2,x3,y3n");
scanf("%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3);
cleardevice();
w1=5;
w2=5;
w3=635;
w4=465;
rectangle(w1,w2,w3,w4);
line(x1,y1,x2,y2);
line(x2,y2,x3,y3);
line(x3,y3,x1,y1);
getch();
v1=425;
v2=75;
v3=550;
v4=250;
sx=(float)(v3-v1)/(w3-w1);
sy=(float)(v4-v2)/(w4-w2);
rectangle(v1,v2,v3,v4);
x1=v1+floor(((float)(x1-w1)*sx)+.5);

44210205028
y1=v2+floor(((float)(y1-w2)*sy)+.5);
line(x1,y1,x2,y2);
line(x2,y2,x3,y3);
line(x3,y3,x1,y1);
getch();
return 0;
}

OUTPUT
Enter The Coordinate x1,y1,x2,y2,x3,y3
100
200
300
400
500
350

44210205028

RESULT:
Thus the window to view port mapping was implemented using C.

44210205028
DATE:

SUTHERLAND – HODGEMAN POLYGON CLIPPING

EX NO: 6

AIM:
To perform Sutherland – Hodgeman polygon clipping using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step1: Get the minimum and maximum coordinates of both window and view
port.
Step2: Get the number of sides of a polygon and its corresponding
coordinates.
Step3: If the polygon lies within region code window, display it.
Step4. If any one of the polygon side is neither inside nor outside the boundary, find
point of intersection and clip the region that lies outside the
boundary.
Step5:. Display the polygon after clipping.

PROGRAM:

44210205028
#include<stdio.h>
#include<conio.h>
typedef enum { left,right,bottom,top } edge;
#define N_EDGE 4
#define TRUE 1
#define FALSE 0
struct point
{
int x;
int y;
}p,wmin,wmax,p1,p2,ipt,i,pin[50],pout[50],first[50],s[50],i;
int inside(struct point p,int b,struct point wmin,struct point wmax)
{
switch(b)
{
case left:
if(p.x<wmin.x)
return (FALSE);
break;
case right:
if(p.x>wmax.x)
return (FALSE);
break;
case bottom:
if(p.y<wmin.y)
return (FALSE);
break;
case top:
if(p.y>wmax.y)
return (FALSE);

44210205028
break;
}
return (TRUE);
}
int cross(struct point p1,struct point p2,int b,struct point wmin,struct point
wmax)
{
if(inside(p1,b,wmin,wmax)==inside(p2,b,wmin,wmax))
return (FALSE);
else
return (TRUE);
}
struct point intersect(struct point p1,struct point p2,int b,struct point
wmin,struct point wmax)
{
float m;
if(p1.x!=p2.x)
m=(p1.y-p2.y)/(p1.x-p2.x);
switch(b)
{
case left:
ipt.x=wmin.x;
ipt.y=p2.y+(wmin.x-p2.x)*m;
break;
case right:
ipt.x=wmax.x;
ipt.y=p2.y+(wmax.x-p2.x)*m;
break;
case bottom:
ipt.y=wmin.y;
if(p1.x!=p2.x)

44210205028
ipt.x=p2.x+(wmin.y-p2.y)/m;
else
ipt.x=p2.x;
break;
case top:
ipt.y=wmax.y;
if(p1.x!=p2.x)
ipt.x=p2.x+(wmax.y-p2.y)/m;
else
ipt.x=p2.x;
break;
}
return(ipt);}
void clippoint(struct point p,int b,struct point wmin,struct point wmax,struct
point *pout,int *cnt,struct point *first[],struct point *s)
{
if(!first[b])
first[b]=&p;
else
if(cross(p,s[b],b,wmin,wmax))
{
ipt=intersect(p,s[b],b,wmin,wmax);
if(b<top)
clippoint(ipt,b+1,wmin,wmax,pout,cnt,first,s);
else
{
pout[*cnt]=ipt;
(*cnt)++;
}
}
s[b]=p;

44210205028
if(inside(p,b,wmin,wmax))
if(b<top)
clippoint(p,b+1,wmin,wmax,pout,cnt,first,s);
else
{
pout[*cnt]=p;
(*cnt)++;
}
}
void closeclip(struct point wmin,struct point wmax,struct point *pout,int
*cnt,struct point *first[],struct point *s)
{
int b;
for(b=left;b<=top;b++)
{
if(cross(s[b],*first[b],b,wmin,wmax))
{
i=intersect(s[b],*first[b],b,wmin,wmax);
if(b<top)
clippoint(i,b+1,wmin,wmax,pout,cnt,first,s);
else
{
pout[*cnt]=i;
(*cnt)++;
}
}
}
}

int clippolygon(struct point wmin,struct point wmax,int n,struct point

44210205028
*pin,struct point *pout)
{
struct point *first[N_EDGE]={0,0,0,0},s[N_EDGE];
int i,cnt=0;
for(i=0;i<=n;i++)
clippoint(pin[i],left,wmin,wmax,pout,&cnt,first,s);
closeclip(wmin,wmax,pout,&cnt,first,s);
return(cnt);
}
void main()
{
int c,gm,gr,n,j,np;
clrscr();
detectgraph(&gm,&gr);
initgraph(&gm,&gr,"d:tcBGI");
printf("Enter the window minimum coordinates");
scanf("%d%d",&wmin.x,&wmin.y);
printf("Enter the window max coordinates");
scanf("%d%d",&wmax.x,&wmax.y);
rectangle(wmin.x,wmax.y,wmax.x,wmin.y);
printf("Enter the no of sides in polygon:n");
scanf("%d",&n);
printf("Enter the coordinates(x,y)for pin ,pout:n");
for(j=0;j<n;j++)
{
scanf("%d%d",&pin[j].x,&pin[j].y);
scanf("%d%d",&pout[j].x,&pout[j].y);
}
outtextxy(10,10,"BEFORE CLIPPING");
for(j=0;j<n;j++)

44210205028
{
if(j!=n-1)
line(pin[j].x,pin[j].y,pout[j].x,pout[j].y);
else
line(pin[j].x,pin[j].y,pout[j].x,pout[j].y);
}
printf("n1.polygon clipping 2.exit");
scanf("%d",&c);
switch(c)
{
case 1:
np=clippolygon(wmin,wmax,n,pin,pout);
for(j=0;j<np-1;j++)
{
outtextxy(10,10,"AFTER CLIPPING");
line(pout[j].x,pout[j].y,pout[(j+1)].x,pout[(j+1)].y);
}
break;
case 2:
exit(0);
}
getch(); }

OUTPUT

44210205028
Enter the window minimum coordinates : 200 200
Enter the window max coordinates :400 400
Enter the no of sides in polygon :3
Enter the coordinates(x,y)for pin ,pout
150
300
250
175
250
175
350
410
350
410
150
300
BEFORE CLIPPING
1.polygon clipping

Press :- 1

2 Exit

44210205028
AFTER CLIPPING

RESULT:
Thus Sutherland - Hodgeman polygon clipping was implemented using C.

44210205028
DATE:

3D – BASIC TRANSFORMATIONS

EX NO: 7

AIM:
To perform 3D transformations such as Rotation, scaling and Translation using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step1:Enter the choice for transformation.
Step2: Perform the translation, rotation, scaling of 3D object.
Step3: Get the needed parameters for the transformation from the user.
Step4: Increase of rotation, object can be rotated about x or y or z axis.
Step5: Display the transmitted object in the screen

44210205028

PROGRAM:
#include<stdio.h>
#include<math.h>
#include<conio.h>
int gd=DETECT,gm,i,ch,sh,a1,b1,c1;
float temp,theta,temp1;
float a,b,c;
double x1,x2,y1,y2;
void draw_cube(double edge[20][3])
{
initgraph(&gd,&gm,"..bgi");
clearviewport();
for(i=0;i<19;i++)
{
x1=edge[i][0]+edge[i][2]*(cos(2.3562));
y1=edge[i][1]-edge[i][2]*(sin(2.3562));
x2=edge[i+1][0]+edge[i+1][2]*(cos(2.3562));
y2=edge[i+1][1]-edge[i+1][2]*(sin(2.3562));
line(x1+320,240-y1,x2+320,240-y2);
}
line(320,240,320,25);
line(320,240,550,240);
line(320,240,150,410);
getch();
closegraph();
}
void draw_cube1(double edge1[20][3])
{
clearviewport();

44210205028
for(i=0;i<19;i++)
{
x1=edge1[i][0]+edge1[i][2]*(cos(2.3562));
y1=edge1[i][1]-edge1[i][2]*(sin(2.3562));
x2=edge1[i+1][0]+edge1[i+1][2]*(cos(2.3562));
y2=edge1[i+1][1]-edge1[i+1][2]*(sin(2.3562));
line(x1+320,240-y1,x2+320,240-y2);}
line(320,240,320,25);
line(320,240,550,240);
line(320,240,150,410);
getch();
closegraph();
}
void scale(double edge1[20][3],double edge[20][3])
{
printf("Enter The Scaling Factors :=n");
scanf("%f %f %f",&a,&b,&c);
clearviewport();
for(i=0;i<20;i++)
{
edge1[i][0]=edge[i][0]*a;
edge1[i][1]=edge[i][1]*b;
edge1[i][2]=edge[i][2]*c;
}
draw_cube1(edge1);
closegraph();
}
void translate(double edge1[20][3],double edge[20][3])

44210205028
{
printf(" Enter The Translation Factors :=n");
scanf("%d %d %d",&a1,&b1,&c1);
clearviewport();
for(i=0;i<20;i++)
{
edge1[i][0]=edge[i][0]+a1;
edge1[i][1]=edge[i][1]+b1;
edge1[i][2]=edge[i][2]+c1;
}
draw_cube1(edge1);
closegraph();
}
void rotate(double edge1[20][3],double edge[20][3])
{
clrscr();
printf("-=[ Rotate About ]=-n");
printf("1:==> X-Axis n");
printf("2:==> Y-Axis n");
printf("3:==> Z-Axis n");
printf(" Enter Your Choice :=n");
scanf("%d",&ch);
printf("Enter the anglen");
scanf("%f",&theta);
switch(ch)
{
case 1:
theta=(theta*3.14)/180;
for(i=0;i<20;i++)
{
edge1[i][0]=edge[i][0];

44210205028
temp=edge[i][1];
temp1=edge[i][2];
edge1[i][1]=temp*cos(theta)-temp1*sin(theta);
edge1[i][2]=temp*sin(theta)+temp1*cos(theta);
}
draw_cube1(edge1);
break;
case 2:
for(i=0;i<20;i++)
{
temp=edge[i][0];
temp1=edge[i][2];
edge1[i][0]=temp*cos(theta)+temp1*sin(theta);
edge1[i][2]=-temp*sin(theta)+temp1*cos(theta);
}
draw_cube1(edge1);
break;
case 3:
for(i=0;i<20;i++)
{
temp=edge[i][0];
temp1=edge[i][1];
edge1[i][0]=temp*cos(theta)-temp1*sin(theta);
edge1[i][1]=temp*sin(theta)+temp1*cos(theta);
}
draw_cube1(edge1);

44210205028
break;
}
}
void main()
{
int choice;
double edge1[20][3],edge[20][3]=
{
100,0,0,
100,100,0,
0,100,0,
0,100,100,
0,0,100,
0,0,0,
100,0,0,
100,0,100,
100,75,100,
75,100,100,
100,100,75,
100,100,0,
100,100,75,
100,75,100,
75,100,100,
0,100,100,
0,100,0,
0,0,0,
0,0,100,
100,0,100
while(1)
{
clrscr();

};

44210205028
printf("3D BASIC TRANSFORMATIONSn");
printf("1:==> Draw Cuben");
printf("2:==> Translaten");
printf("3:==> Scaling n");
printf("4:==> Rotation n");
printf("5:==> Exit n");
printf("Enter Your Choice :=n");
scanf("%d",&choice);
switch(choice)
{
case 1:
draw_cube(edge);
break;
case 2:
translate(edge1,edge);
break;
case 3:
scale(edge1,edge);
break;
case 4:
rotate(edge1,edge);
break;
case 5:
exit(0);
default:
printf(" Press A Valid Key...!!! ");
getch();

44210205028
break;
}
closegraph();
}}

OUTPUT
3D BASIC TRANSFORMATIONS
1:Draw Circle
2::Translation
3:Scaling
4:Rotaion
5:Exit

44210205028
TRANSLATION
Enter your choice :- 1
Enter the Traanlation Factor :- 50

60

70

0.2

0.3

SCALING
Enter the Scaling Factors :-

0.3

44210205028
ROTATION
Rotate About
1: X-Axis
2:Y-Axis
3:Z-Axis
Enter the angle :- 30



RESULT:

44210205028
Thus 3D Basic transformations was implemented using C.
DATE:

3D – COMPOSITE TRANSFORMATIONS

EX NO: 8

AIM:
To perform 3D composite transformations such as shearing, reflection using C.

Functions used:
iii).the path name.
Syntax:-


coordinate.

ALGORITHM:
Step1:Enter the choice for transformation.
Step2: Perform the translation, rotation, scaling of 3D object.
Step3: Get the needed parameters for the transformation from the user.
Step4: Increase of rotation, object can be rotated about x or y or z axis.
Step5: Display the transmitted object in the screen

44210205028

PROGRAM:
#include<stdio.h>
#include<stdio.h>
#include<math.h>
#include<conio.h>
int gd=DETECT,gm,i,ch,sh;
double x1,x2,y1,y2;
void draw_cube(double edge[20][3])
{
clearviewport();
for(i=0;i<19;i++)
{
x1=edge[i][0]+edge[i][2]*(cos(2.3562));
y1=edge[i][1]-edge[i][2]*(sin(2.3562));
x2=edge[i+1][0]+edge[i+1][2]*(cos(2.3562));
y2=edge[i+1][1]-edge[i+1][2]*(sin(2.3562));
line(x1+320,240-y1,x2+320,240-y2);
}
line(320,240,320,25);
line(320,240,550,240);
line(320,240,150,410);
getch();
closegraph();
}
void draw_cube1(double edge1[20][3])
{

44210205028
clearviewport();
for(i=0;i<19;i++)
{
x1=edge1[i][0]+edge1[i][2]*(cos(2.3562));
y1=edge1[i][1]-edge1[i][2]*(sin(2.3562));
x2=edge1[i+1][0]+edge1[i+1][2]*(cos(2.3562));
y2=edge1[i+1][1]-edge1[i+1][2]*(sin(2.3562));
line(x1+320,240-y1,x2+320,240-y2);
}
line(320,240,320,25);
line(320,240,550,240);
line(320,240,150,410);
getch();
closegraph();
}
void reflect(double edge1[20][3],double edge[20][3])
{
int ch;
int i;
clrscr();
printf("-=[ Reflection About ]=-n");
scanf("%d",&ch);
switch(ch)
{
case 1:
for(i=0;i<20;i++)

44210205028
{
edge1[i][1]=-edge[i][1];
}
draw_cube1(edge1);
break;
case 2:
for(i=0;i<20;i++)
{
}
draw_cube1(edge1);
break;
case 3:
for(i=0;i<20;i++)
{
}
draw_cube1(edge1);
break;
}
}
void shear(double edge1[20][3],double edge[20][3])
{
int ch,sh;
int i;

44210205028
clrscr();
printf("-=[ Shearing About ]=-n");
scanf("%d",&ch);
printf("ENter shear valuen");
scanf("%d",&sh);
switch(ch)
{
case 1:
for(i=0;i<20;i++)
{

if(edge[i][0]==100&&edge[i]

[1]==100&&edge[i][2]==0||edge[i][0]==100&&edge[i][1]==100&&edge[i][2]==100||
edge[i][0]==0&&edge[i][1]==100&&edge[i][2]==100||edge[i][0]==0&&edge[i]
[1]==100&&edge[i][2]==0)
{
edge1[i][0]=edge[i][0]+sh;
}
else
{
}
}
draw_cube1(edge1);
break;
case 2:

44210205028
for(i=0;i<20;i++)
{
if(edge[i][0]==100&&edge[i][1]==100&&edge[i][2]==0||
edge[i][0]==100&&e

dge[i][1]==100&&edge[i][2]==100||edge[i][0]==100&&edge[i]

[1]==0&&edge[i][2]==0||edge[i][0]==100&&edge[i][1]==0&&edge[i][2]==100)
{
edge1[i][1]=edge[i][1]+sh;
}
else
{
}}
draw_cube1(edge1);
break;
case 3:
for(i=0;i<20;i++)
{

if(edge[i][0]==100&&edge[i]

[1]==100&&edge[i][2]==0||edge[i][0]==100&&e
dge[i][1]==100&&edge[i][2]==100)
{
edge1[i][2]=edge[i][2]-sh;
}
else
{

44210205028
}}
draw_cube1(edge1);
break; }}
void main()
{
int choice;
double edge1[20][3],edge[20][3]=
{
100,0,0,
100,100,0,
0,100,0,
0,100,100,
0,0,100,
0,0,0,
100,0,0,
100,0,100,
100,100,100,
100,100,100,
100,100,0,
100,100,0,
100,100,100,
100,100,100,
100,100,100,
0,100,100,
0,100,0,
0,0,0,
0,0,100,
100,0,100 };
while(1)
{
clrscr();

44210205028
printf("3D COMPOSITE ETRANSFORMATIONSn");
printf("1:==>Draw Cuben ");
printf("2:==>Reflectionn ");
printf("3:==>Shearingn");
printf("4:==>Exitn");
printf("Enter Your Choice :=n");
scanf("%d",&choice);
switch(choice)
{
case 1:
draw_cube(edge);
break;
case 2:
reflect(edge1,edge);
break;
case 3:
shear(edge1,edge);;
break;
case 4:
exit(0);
default:
printf(" Press A Valid Key...!!! n");
getch();
break;
}
closegraph();
}
}

44210205028

OUTPUT:
3D COMPOSIITE TRANSFORMATIONS
1:Draw Cube
2:Reflection
3:Shearing
4: Exit

44210205028

REFLECTION
Enter the choice :- 2
REFLECTION IS ABOUT
1:X-AXIS
2:Y-AXIS
3:Z-AXIS



44210205028

SHEARING
Enter the choice :- 3
SHEARING IS ABOUT
1:X-AXIS
2:Y-AXIS
3:Z-AXIS



44210205028

RESULT:
3D Composite transformations was implemented using C.
DATE:

3D MODEL

EX NO: 9

AIM:
To perform the 3D model using Maya or 3d MAX software

DESCRIPTION:
In 3D computer graphics, 3D modeling (also known as meshing) is the
process of developing a mathematical representation of any three-dimensional surface of
object (either inanimate or living) via specialized software. The product is called a 3D
model. It can be displayed as a two-dimensional image through a process called 3D
rendering or used in a computer simulation of physical phenomena. The model can also
be physically created using 3D Printing devices.
Models may be created automatically or manually. The manual modeling process of
preparing geometric data for 3D computer graphics is similar to plastic arts such as
sculpting.
Models
3D models represent a 3D object using a collection of points in 3D space,
connected by various geometric entities such as triangles, lines, curved surfaces, etc.
Being a collection of data (points and other information), 3D models can be created by
hand, algorithmically (procedural modeling), or scanned.
3D models are widely used anywhere in 3D graphics. Actually, their use
predates the widespread use of 3D graphics on personal computers. Many computer
games used pre-rendered images of 3D models as sprites before computers could render
them in real-time.

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3D models are used in a wide variety of fields. The medical industry uses detailed models
of organs. The movie industry uses them as characters and objects for animated and reallife motion pictures. The video game industry uses them as assets for computer and video
games. The science sector uses them as highly detailed models of chemical compounds.
The architecture industry uses them to demonstrate proposed buildings and landscapes
through Software Architectural Models. The engineering community uses them as
designs of new devices, vehicles and structures as well as a host of other uses. In recent
decades the earth science community has started to construct 3D geological models as a
standard practice.
Representation
A modern render of the iconic Utah teapot model developed by Martin Newell (1975).
The Utah teapot is one of the most common models used in 3D graphics education.
Almost all 3D models can be divided into two categories.
•

Solid - These models define the volume of the object they represent (like a
rock). These are more realistic, but more difficult to build. Solid models are
mostly used for nonvisual simulations such as medical and engineering
simulations, for CAD and specialized visual applications such as ray tracing
and constructive solid geometry

•

Shell/boundary - these models represent the surface, e.g. the boundary of the
object, not its volume (like an infinitesimally thin eggshell). These are easier
to work with than solid models. Almost all visual models used in games and
film are shell models.

Because the appearance of an object depends largely on the exterior of the object,
boundary representations are common in computer graphics. Two dimensional surfaces
are a good analogy for the objects used in graphics, though quite often these objects are
non-manifold. Since surfaces are not finite, a discrete digital approximation is required:
polygonal meshes (and to a lesser extent subdivision surfaces) are by far the most
common representation, although point-based representations have been gaining some
popularity in recent years. Level sets are a useful representation for deforming surfaces
which undergo many topological changes such as fluids.

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The process of transforming representations of objects, such as the middle point
coordinate of a sphere and a point on its circumference into a polygon representation of a
sphere, is called tessellation. This step is used in polygon-based rendering, where objects
are broken down from abstract representations ("primitives") such as spheres, cones etc.,
to so-called meshes, which are nets of interconnected triangles. Meshes of triangles
(instead of e.g. squares) are popular as they have proven to be easy to render using
scanline rendering.[1] Polygon representations are not used in all rendering techniques, and
in these cases the tessellation step is not included in the transition from abstract
representation to rendered scene.
Modeling processes
3D computer modeling of the Great mosquee of Kairouan also called the Mosque of Uqba
(in Kairouan, Tunisia)
There are five popular ways to represent a model:
•

Polygonal modeling - Points in 3D space, called vertices, are connected by
line segments to form a polygonal mesh. Used, for example, by Blender. The
vast majority of 3D models today are built as textured polygonal models,
because they are flexible and because computers can render them so quickly.
However, polygons are planar and can only approximate curved surfaces using
many polygons.

•

NURBS modeling - NURBS Surfaces are defined by spline curves, which are
influenced by weighted control points. The curve follows (but does not
necessarily interpolate) the points. Increasing the weight for a point will pull
the curve closer to that point. NURBS are truly smooth surfaces, not
approximations using small flat surfaces, and so are particularly suitable for
organic modeling. Maya, Rhino 3d and solidThinking are the most wellknown commercial programs which use NURBS natively.

•

Splines & Patches modeling - Like NURBS, Splines and Patches depend on
curved lines to define the visible surface. Patches fall somewhere between
NURBS and polygons in terms of flexibility and ease of use.

•

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Primitives modeling - This procedure takes geometric primitives like balls,
cylinders, cones or cubes as building blocks for more complex models.
Benefits are quick and easy construction and that the forms are mathematically
defined and thus absolutely precise, also the definition language can be much
simpler. Primitives modeling is well suited for technical applications and less
for organic shapes. Some 3D software can directly render from primitives (like
POV-Ray), others use primitives only for modeling and convert them to
meshes for further operations and rendering.

•

Sculpt modeling - Still fairly new method of modeling 3D sculpting has
become very popular in the few short years it has been around. There are 2
types of this currently, Displacement which is the most widely used among
applications at this moment, and volumetric. Displacement uses a dense model
(often generated by Subdivision surfaces of a polygon control mesh) and
stores new locations for the vertex positions through use of a 32bit image map
that stores the adjusted locations. Volumetric which is based loosely on
Voxels has similar capabilities as displacement but does not suffer from
polygon stretching when there are not enough polygons in a region to achieve
a deformation.

•

Both of these methods allow for very artistic exploration as the model will
have a new topology created over it once the models form and possibly details
have been sculpted. The new mesh will usually have the original high
resolution mesh information transferred into displacement data or normal map
data if for a game engine.

The modeling stage consists of shaping individual objects that are later used in the scene.
There are a number of modeling techniques, including:
o

constructive solid geometry

o

implicit surfaces

o

subdivision surfaces

Modeling can be performed by means of a dedicated program (e.g., form•Z, Maya, 3DS
Max, Blender, Lightwave, Modo, solidThinking) or an application component (Shaper,

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Lofter in 3DS Max) or some scene description language (as in POV-Ray). In some cases,
there is no strict distinction between these phases; in such cases modeling is just part of
the scene creation process (this is the case, for example, with Caligari trueSpace and
Realsoft 3D).
Complex materials such as blowing sand, clouds, and liquid sprays are modeled with
particle systems, and are a mass of 3D coordinates which have either points, polygons,
texture splats, or sprites assigned to them. Sculpt
Scene setup
• The geometry in 3D modeling is completely described in 3-D space; objects can
be viewed from any angle, revealing the lighting from different angles. Modeled
and ray traced in Cobalt
• Scene setup involves arranging virtual objects, lights, cameras and other entities
on a scene which will later be used to produce a still image or an animation.
• Lighting is an important aspect of scene setup. As is the case in real-world scene
arrangement, lighting is a significant contributing factor to the resulting aesthetic
and visual quality of the finished work. As such, it can be a difficult art to master.
Lighting effects can contribute greatly to the mood and emotional response
effected by a scene, a fact which is well-known to photographers and theatrical
lighting technicians.
It is usually desirable to add color to a model's surface in a user controlled way prior to
rendering. Most 3D modeling software allows the user to color the model's vertices, and
that color is then interpolated across the model's surface during rendering. This is often
how models are colored by the modeling software while the model is being created. The
most common method of adding color information to a 3D model is by applying a 2D
texture image to the model's surface through a process called texture mapping.
Texture images are no different than any other digital image, but during the texture
mapping process, special pieces of information (called texture coordinates or UV
coordinates) are added to the model that indicate which parts of the texture image map to
which parts of the 3D model's surface. Textures allow 3D models to look significantly
more detailed and realistic than they would otherwise.

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Other effects, beyond texturing and lighting, can be done to 3D models to add to their
realism. For example, the surface normals can be tweaked to affect how they are lit,
certain surfaces can have bump mapping applied and any other number of 3D rendering
tricks can be applied.
3D models are often animated for some uses. They can sometimes be
animated from within the 3D modeler that created them or else exported to another
program. If used for animation, this phase usually makes use of a technique called
"keyframing", which facilitates creation of complicated movement in the scene. With the
aid of keyframing, one needs only to choose where an object stops or changes its
direction of movement, rotation, or scale, between which states in every frame are
interpolated. These moments of change are known as keyframes. Often extra data is
added to the model to make it easier to animate. For example, some 3D models of humans
and animals have entire bone systems so they will look realistic when they move and can
be manipulated via joints and bones, in a process known as skeletal animation.
Compared to 2D methods
A fully textured and lit rendering of a 3d model.
3D photorealistic effects are often achieved without wireframe modeling and are
sometimes indistinguishable in the final form. Some graphic art software includes filters
that can be applied to 2D vector graphics or 2D raster graphics on transparent layers.
Advantages of wireframe 3D modeling over exclusively 2D methods include:
•

Flexibility, ability to change angles or animate images with quicker rendering
of the changes;

•

Ease of rendering, automatic calculation and rendering photorealistic effects
rather than mentally visualizing or estimating;

•

Accurate photorealism, less chance of human error in misplacing, overdoing,
or forgetting to include a visual effect.

Disadvantages compare to 2D photorealistic rendering may include a software learning
curve and difficulty achieving certain photorealistic effects. Some photorealistic effects
may be achieved with special rendering filters included in the 3D modeling software. For
the best of both worlds, some artists use a combination of 3D modeling followed by
editing the 2D computer-rendered images from the 3D model.

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3D model market
3CT (3D Catalog Technology) has revolutionized the 3D model market by
offering quality 3D model libraries free of charge for professionals using various CAD
programs. Some believe that this uprising technology is gradually eroding the traditional
"buy and sell" or "object for object exchange" markets although the quality of the
products do not match those sold on specialized 3d marketplaces.
A large market for 3D models (as well as 3D-related content, such as textures, scripts,
etc.) still exists - either for individual models or large collections. Online marketplaces for
3D content allow individual artists to sell content that they have created. Often, the artists'
goal is to get additional value out of assets they have previously created for projects. By
doing so, artists can earn more money out of their old content, and companies can save
money by buying pre-made models instead of paying an employee to create one from
scratch..

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DATE:

GENERATING FRACTAL IMAGE

EX NO: 10

AIM:
To generate fractal images.

DESCRIPTION:
A fractal is "a rough or fragmented geometric shape that can be split into
parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a
property called self-similarity. Roots of the idea of fractals go back to the 17th century,
while mathematically rigorous treatment of fractals can be traced back to functions
studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff a century later in studying
functions that were continuous but not differentiable; however, the term fractal was
coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning
"broken" or "fractured." A mathematical fractal is based on an equation that undergoes
iteration, a form of feedback based on recursion.
There are several examples of fractals, which are defined as portraying exact selfsimilarity, quasi self-similarity, or statistical self-similarity. While fractals are a
mathematical construct, they are found in nature, which has led to their inclusion in
artwork. They are useful in medicine, soil mechanics, seismology, and technical analysis
Characteristics
A fractal often has the following features:
o

It has a fine structure at arbitrarily small scales.

o

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It is too irregular to be easily described in traditional Euclidean geometric
language.

o

It is self-similar (at least approximately or stochastically).

o

It has a Hausdorff dimension which is greater than its topological
dimension (although this requirement is not met by space-filling curves
such as the Hilbert curve).

o

It has a simple and recursive definition.

Because they appear similar at all levels of magnification, fractals are often considered to
be infinitely complex (in informal terms). Natural objects that are approximated by
fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow
flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns.
However, not all self-similar objects are fractals—for example, the real line (a straight
Euclidean line) is formally self-similar but fails to have other fractal characteristics; for
instance, it is regular enough to be described in Euclidean terms.
Images of fractals can be created using fractal-generating software. Images produced by
such software are normally referred to as being fractals even if they do not have the above
characteristics, such as when it is possible to zoom into a region of the fractal that does
not exhibit any fractal properties.
Generation
Four common techniques for generating fractals are:
•

Escape-time fractals – (also known as "orbits" fractals) These are defined by
a formula or recurrence relation at each point in a space (such as the complex
plane). Examples of this type are the Mandelbrot set, Julia set, the Burning
Ship fractal, the Nova fractal and the Lyapunov fractal. The 2d vector fields
that are generated by one or two iterations of escape-time formulae also give
rise to a fractal form when points (or pixel data) are passed through this field
repeatedly.

•

Iterated function systems – These have a fixed geometric replacement rule.
Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake,

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Harter-Highway dragon curve, T-Square, Menger sponge, are some examples
of such fractals.
•

Random fractals – Generated by stochastic rather than deterministic
processes, for example, trajectories of the Brownian motion, Lévy flight,
fractal landscapes and the Brownian tree. The latter yields so-called mass- or
dendritic fractals, for example, diffusion-limited aggregation or reactionlimited aggregation clusters.

•

Strange attractors – Generated by iteration of a map or the solution of a
system of initial-value differential equations that exhibit chaos.

Classification
Fractals can also be classified according to their self-similarity. There are three types of
self-similarity found in fractals
•

Exact self-similarity – This is the strongest type of self-similarity; the fractal
appears identical at different scales. Fractals defined by iterated function
systems often display exact self-similarity. For example, the Sierpinski
triangle and Koch snowflake exhibit exact self-similarity.

•

Quasi-self-similarity – This is a looser form of self-similarity; the fractal
appears approximately (but not exactly) identical at different scales. Quasiself-similar fractals contain small copies of the entire fractal in distorted and
degenerate forms. Fractals defined by recurrence relations are usually quasiself-similar but not exactly self-similar. The Mandelbrot set is quasi-selfsimilar, as the satellites are approximations of the entire set, but not exact
copies.

•

Statistical self-similarity – This is the weakest type of self-similarity; the
fractal has numerical or statistical measures which are preserved across scales.
Most reasonable definitions of "fractal" trivially imply some form of statistical
self-similarity. (Fractal dimension itself is a numerical measure which is
preserved across scales.) Random fractals are examples of fractals which are
statistically self-similar.

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In nature
•

Approximate fractals are easily found in nature. These objects display selfsimilar structure over an extended, but finite, scale range. Examples include
clouds, river networks, fault lines, mountain ranges, craters, snow flakes,
crystals, lightning, cauliflower or broccoli, and systems of blood vessels and
pulmonary vessels, and ocean waves. Coastlines may be loosely considered
fractal in nature.

•

Trees and ferns are fractal in nature and can be modeled on a computer by
using a recursive algorithm. This recursive nature is obvious in these examples
—a branch from a tree or a frond from a fern is a miniature replica of the
whole: not identical, but similar in nature. The connection between fractals
and leaves is currently being used to determine how much carbon is contained
in trees.

•

In 1999, certain self similar fractal shapes were shown to have a property of
"frequency invariance"—the same electromagnetic properties no matter what
the frequency—from Maxwell's equations (see fractal antenna).

In creative works
•

Fractal patterns have been found in the paintings of American artist Jackson
Pollock. While Pollock's paintings appear to be composed of chaotic dripping
and splattering, computer analysis has found fractal patterns in his work.

•

Decalcomania, a technique used by artists such as Max Ernst, can produce
fractal-like patterns. It involves pressing paint between two surfaces and
pulling them apart.

•

Cyberneticist Ron Eglash has suggested that fractal-like structures are
prevalent in African art and architecture. Circular houses appear in circles of
circles, rectangular houses in rectangles of rectangles, and so on. Such scaling

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patterns can also be found in African textiles, sculpture, and even cornrow
hairstyles.
•

In a 1996 interview with Michael Silverblatt, David Foster Wallace admitted
that the structure of the first draft of Infinite Jest he gave to his editor Michael
Pietsch was inspired by fractals, specifically the Sierpinski triangle (aka
Sierpinski gasket) but that the edited novel is "more like a lopsided Sierpinsky
Gasket".

Applications
o Classification of histopathology slides in medicine
o Fractal landscape or Coastline complexity
o Enzyme/enzymology (Michaelis-Menten kinetics)
o Generation of new music
o Signal and image compression
o Creation of digital photographic enlargements
o Seismology
o Fractal in soil mechanics
o Computer and video game design, especially computer graphics for
organic environments and as part of procedural generation
o Fractography and fracture mechanics
o Fractal antennas – Small size antennas using fractal shapes
o Small angle scattering theory of fractally rough systems
o T-shirts and other fashion
o Generation of patterns for camouflage, such as MARPAT
o Digital sundial
o Technical analysis of price series (see Elliott wave principle)

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DATE:

OPENGL TO WORK WITH VISUAL C++

EX NO: 11

INSTALLATION :
1. Install Visual C++ 2008 Express Edition (To support OpenGL).
2. Copy all the .h files into the C:Program FilesMicrosoft
SDKsWindowsv6.1IncludeGL folder.
Header Files (.h files) : Gl.h, glu.h, glut.h, freeglut.h, freeglut_ext.h ,
freeglut_std.h
3. Copy all the .lib files into the C:Program FilesMicrosoft SDKsWindowsv6.1Lib
folder.
Library files (.lib files) : opengl32.lib, glut32.lib, glu32.lib
4. Copy all the .dll files into the C:Windowssystem32 folder.
Dynamic Link Library Files (.dll) : freeglut.dll , glut32.dll
Working with Console Application Program in OpenGL
1. Creating a Project
1. Start Visual C++ and Under the File menu select New → Project
(Ctrl+Shift+N).
2. Select project types as Win32 and Win32 Console Application.
3. Give a User name for the Project.
4. Add a GLUT program to the project in the window.
2. Linking OpenGL Libraries
1. Under the Project menu select Project Properties (Alt+F7) at the bottom.
2. Select Configuration Properties → Select “C/C++” → “Preprocessor” → In
preprocessor definitions additionally include the path where gl/glut.h is
present.
Example : C:Program FilesMicrosoft SDKs Windows v6.0A Include
3. Select "Linker" folder and click "Input" .

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4. Select All Configurations from the Configuration drop-down box at the top of
the dialog. This ensures you are changing the settings for both the Debug and
Release configurations.
5. Select "Additional Dependencies" and type the following contents:
opengl32.lib glut32.lib glu32.lib
3. Compiling the Application
Choose "Build" from the menu options.
Select "Build filename".
4. Run the Application
Choose "Debug" from the menu options.
Select "Start without Debugging".
5. Save the Project
Select “File Menu” → select Save all (Ctrl+Shift+S).
Save all the documents before quitting.

Working with Windows Application Program in OpenGL
1. Creating a Project
1. Start Visual C++ and Under the File menu select New → Project
(Ctrl+Shift+N).
2. Select Win32 Project, enter a Username, and click OK.
3. In the Wizard click Next, then in Additional options check the box of Empty
Project, and click Finish.
4. Under the Project menu select Add New Item (Ctrl+Shift+A).
5. Select C++ File (.cpp), enter a Name, and click OK.
6. Add a GLUT program to the project in the window.
2. Link to the OpenGL libraries:
1. Under the Project menu select Project Properties (Alt+F7) at the bottom.
2. Select Configuration Properties → Linker → Input from the navigation panel
on the left.
3. Select All Configurations from the Configuration drop-down box at the top of
the dialog.
4. Type “opengl32.lib glut32.lib glu32.lib” in Additional Dependencies and
click OK.
1. Compiling the Application
Choose "Build" from the menu options.

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Select "Build filename".
2. Run the Application
Choose "Debug" from the menu options.
Select "Start Without Debugging".
5. Save the Project
Select “File Menu” → select Save all (Ctrl+Shift+S).
Save all the documents before quitting.

PROGRAM
#include "stdafx.h"
#include <gl/glut.h>
#include <stdlib.h>
void init (void)
{
GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 };
GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 };
GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 };
glLightfv (GL_LIGHT0, GL_AMBIENT, light_ambient);
glLightfv (GL_LIGHT0, GL_DIFFUSE, light_diffuse);
glLightfv (GL_LIGHT0, GL_SPECULAR, light_specular);
glLightfv (GL_LIGHT0, GL_POSITION, light_position);
glEnable (GL_LIGHTING);
glEnable (GL_LIGHT0);
glEnable(GL_DEPTH_TEST);
}
void display (void)
{
glClear (GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glPushMatrix ();
glRotatef (20.0, 1.0, 0.0, 0.0);
glPushMatrix ();
glTranslatef (-0.75, 0.5, 0.0);
glRotatef (90.0, 1.0, 0.0, 0.0);
glutSolidTorus (0.275, 0.85, 15, 15);
glPopMatrix ();
glPushMatrix ();
glTranslatef (-0.75, -0.5, 0.0);
glRotatef (270.0, 1.0, 0.0, 0.0);
glutSolidCone (1.0, 2.0, 15, 15);
glPopMatrix ();
glPushMatrix ();

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glTranslatef (0.75, 0.0, -1.0);
glutSolidSphere (1.0, 15, 15);
glPopMatrix (); glPopMatrix ();
glFlush ();
}
void reshape(int w, int h)
{
glViewport (0, 0, (GLsizei) w, (GLsizei) h);
glMatrixMode (GL_PROJECTION);
glLoadIdentity ();
if (w <= h)
glOrtho (-2.5, 2.5, -2.5*(GLfloat)h/(GLfloat)w,
2.5*(GLfloat)h/(GLfloat)w, -10.0, 10.0);
else
glOrtho (-2.5*(GLfloat)w/(GLfloat)h,
2.5*(GLfloat)w/(GLfloat)h, -2.5, 2.5, -10.0, 10.0);
glMatrixMode (GL_MODELVIEW);
glLoadIdentity ();
}
int main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH);
glutInitWindowSize (500, 500);
glutCreateWindow (argv[0]);
init ();
glutReshapeFunc (reshape);
glutDisplayFunc(display);
glutMainLoop();
return 0;
}

OUTPUT:

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RESULT:
Thus OpenGl is used to work with visual C++.

DDA, Bresenham and Circle Drawing Algorithms

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