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COMPUTER GRAPHICS

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CS2405

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LAB MANUAL

INDEX

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SN

TITLE

PAGE

Line Drawing Using Bresenham Algorithm 1A

Ellipse Drawing Using Bresenham Algorithm

1C 2

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Two Dimensional Transformations

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Cohen Sutherland 2D line clipping and Windowing

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. Three dimensional transformations

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10

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8 9

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. Implementation of Line, Circle and ellipse Attributes

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Circle Drawing Using Bresenham Algorithm

1B

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SYLLABUS COMPUTER GRAPHICS LABORATORY

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CS2405

1. Implementation of Bresenhams Algorithm – Line, Circle, Ellipse. 2. Implementation of Line, Circle and ellipse Attributes Shear. 4. Composite 2D Transformations

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5. Cohen Sutherland 2D line clipping and Windowing

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3. Two Dimensional transformations - Translation, Rotation, Scaling, Reflection,

6. Sutherland – Hodgeman Polygon clipping Algorithm

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7. Three dimensional transformations - Translation, Rotation, Scaling 8. Composite 3D transformations

9. Drawing three dimensional objects and Scenes 10. Generating Fractal images

1) Turbo C

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LIST OF EQUIPMENTS:

TOTAL: 45 PERIODS

2) Visual C++ with OPENGL

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3) Any 3D animation software like 3DSMAX, Maya, Blender

LINE DRAWING USING BRESENHAM ALGORITHM EX.NO: 1A

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DATE:

AIM: To write a C program for Line Drawing Using Bresenham Algorithm.

Step 1 : Start the program. Step 2 : Declare the necessary variables. Step 3 : Initialize the graph using dx, dy, gd, gm. Step 5 : Similarly, absolute values to dx, dy.

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Step 6 : put pixel and set 15 to pixel position.

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Step 4 : Assign the values of x1, y1 to x,y respectively.

Step 7 : Using do-while loop, put e,x,y,I values.

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Step 8 : Stop the program.

PROGRAM: #include #include

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ALGORITHM:

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#include #include #include void main() { float x,y,x1,y1,x2,y2,dx,dy,e; int i,gd=DETECT,gm; printf("\n ENTER THE VALUE OF X1:"); scanf("%f",&x1); scanf("%f",&y1);

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printf("\n ENTER THE VALUES OF Y1:");

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clrscr();

scanf("%f%f",&x2,&y2); initgraph(&gd,&gm," ");

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dx=abs(x2-x1); dy=abs(y2-y1); x=x1; y-y1;

e=2*(dy-dx);

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i=1; do {

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putpixel(x,y,15);

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while(e>=0)

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printf("\n ENTER THE VALUES OF X2 AND Y2:");

{ y=y+1; e=e-(2*dx); } x=x+1; e=e+(2*dy); i=i+1; delay(100);

}while(i<=dx); closegraph();

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getch(); }

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OUTPUT: ENTER THE VALUE OF X1 : 600

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ENTER THE VALUE OF X2 AND Y2 : 300 400

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ENTER THE VALUE OF Y1 : 400

Ex. No : 1B Date AIM:

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CIRCLE DRAWING USING BRESENHAM ALGORITHM

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To write a C program for Circle Drawing Using Bresenham Algorithm. ALGORITHM: Step 1 : Start the program. Step 2 : Declare the necessary variables. Step 3 : Create the function for Circle. Step 5 : Initialize the graph with gd, gm and assign y<-radius. Step 6 : Start the circle function and p<- 1- radius. Step 7 : Check the while loop until the condition is satisfied.

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Step 4 : Enter the radius and center values.

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Step 8 : Check the if –else condition until the condition is satisfied.

PROGRAM: #include #include

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#include

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Step 10 : Stop the Program.

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Step 9 : Assign all operation for circle function and the values.

void circlefun(int xcenter, int ycenter,int x,int y); {

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void main()

int x=0,radius,xcenter,ycenter;

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int y,p,gd=DETECT,gm; clrscr();

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initgraph(&gd,&gm," "); printf("\n ENTER THE XCENTER &YCENTER:"); scanf("%d%d",&xcenter,&ycenter); printf("\n ENTER THE RADIUS:"); scanf("%d",&radius); y=radius; circlefun(xcenter,ycenter,x,y); p=1-radius;

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while(x
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y=y-1; } if(p<0) else p=p+2*(x-y)+1;

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circlefun(xcenter,ycenter,x,y);

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p=p+2*x+1;

}

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getch(); }

void circlefun(int xcenter,int ycenter,int x,int y) {

putpixel(xcenter+x,ycenter+y,1);

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putpixel(xcenter-x,ycenter+y,1); putpixel(xcenter+x,ycenter-y,1); putpixel(xcenter-x,ycenter-y,1);

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putpixel(xcenter+y,ycenter+x,1); putpixel(xcenter-y,ycenter+x,1);

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putpixel(xcenter+y,ycenter-x,1); putpixel(xcenter-y,ycenter-x,1);

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}

OUTPUT: ENTER THE X CENTER AND Y CENTER : 500 250

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ENTER THE RADIUS : 70

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RESULT:

Thus the above program “CIRCLE DRAWING USING BREASENHAM” is executed

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successfully.

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ELLIPSE DRAWING USING BRESENHAM ALGORITHM

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Ex. No : 1C Date

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AIM: To write a C program for Circle Drawing Using Bresenham Algorithm.

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ALGORITHM: Step 1: Start the program. Step 2: Initialize the variables. Step 3: Call the initgraph() function. Step 4: Get the initialize points P1,P2. Step 5: Get the values of Co-Ordinates of the ellipse (x,y).

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Step 6: Enter the coordinates a,b of the ellipse . Step 7: Display the output.

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Step 8: Stop the program

#include #include

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#include

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PROGRAM

#include void disp(); float x,y; int xc,yc; {

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void main()

int gd=DETECT,gm;

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int a,b;

float p1,p2;

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clrscr();

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initgraph(&gd,&gm,""); scanf("%d%d",&xc,&yc); scanf("%d%d",&a,&b); x=0;y=b; disp(); p1=(b*b)-(a*a*b)+(a*a)/4; while((2.0*b*b*x)<=(2.0*a*a*y)) { x++;

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if(p1<=0) p1=p1+(2.0*b*b*x)+(b*b); else { y--; p1=p1+(2.0*b*b*x)+(b*b)-(2.0*a*a*y); }

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disp(); x=-x; disp(); x=-x;

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} y=0; disp();

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p2=(a*a)+2.0*(b*b*a)+(b*b)/4;

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x=a;

while((2.0*b*b*x)>(2.0*a*a*y)) { y++; if(p2>0) else {

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p2=p2+(a*a)-(2.0*a*a*y);

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x--;

p2=p2+(2.0*b*b*x)-(2.0*a*a*y)+(a*a);

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}

disp();

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y=-y;

disp(); y=-y; } getch(); closegraph(); } void disp()

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{ putpixel(xc+x,yc+y,10); putpixel(xc-x,yc+y,10); putpixel(xc+x,yc-y,10); putpixel(xc+x,yc-y,10); }

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INPUT Ellipse Drawing Algorithm Enter the co-ordinates

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Xc = 200 Yc = 200

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A = 100

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B = 70

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OUTPUT

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Result:

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Thus using C++ program implementation of Bresenham’s algorithm for line, circle and

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ellipse drawing is done.

TWO DIMENSIONAL TRANSFORMATIONS

14 Ex. No. :: 3 Date

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AIM:

ALGORITHM: Step 1: Start the program.

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To write a C program for Two Dimensional Transformations.

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Step 2: Declare the necessary variables and initialize the graph, gd, gm. Step 3: Use do-while loop and declare the function clear device. Step 4: Create four cases translation, scaling , rotation and exit. Step 5: In case 1 enter the translation values and print the translation object.

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Step 6: In case 2 enter the scaling values and print the scaling object. Step 7: In case 3 enter the rotaion values and print rotation object. Step 8: Clockwise rotation and counter clockwise rotation use the same

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equation.

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Step 9: Stop the program.

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PROGRAM:

#include #include #include #include #include void main() {

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int x,y,c; float a; int gd=DETECT,gm; initgraph(&gd,&gm," "); do { cleardevice();

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printf("1.TRANSLATION 2.SCALING 3.ROTATION 4.EXIT"); printf("\n ENTER YR CHOICE:"); scanf("%d",&c);

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switch(c) {

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case 1:

rectangle(100,200,300,300);

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printf("\nENTER THE TX AND TY VALUE:"); scanf("%d%d",&x,&y);

outtextxy(130,180," ORIGINAL OBJECT"); rectangle(100+x,200+y,300+x,300+y);

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outtextxy(130+x,180," TRANSLATION OBJECT");

break;

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case 2:

rectangle(50,100,150,150); printf("\n ENTER THE SX AND SY VALUE:"); scanf("%d%d",&x,&y);

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outtextxy(38,85,"ORIGINAL OBJECT"); rectangle(50*x,100*y,150*x,150*y); outtextxy(250,250,"SCALING OBJECT"); break; case 3: printf("\n ENTER THE X AND Y VALUE:"); scanf("%d%d",&x,&y);

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printf("\n ENTER THE ANGLE;"); scanf("%d",&c); a=(3.14*c)/180; cleardevice(); line(100,100,200,100); outtextxy(210,100,"ORIGINAL OBJECT"); line(100*cos(a)-100*sin(a)+x*(1-cos(a))

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+y*sin(a),100*sin(a)+100*cos(a)+y*(1-cos(a)) -x*sin(a),200*cos(a)-100*sin(a)+x*(1-cos(a))

+y*sin(a),200*sin(a)+100*cos(a)+y*(1-cos(a)) -x*sin(a));

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outtextxy(110,75,"COUNTER CLOCKWISE ROTATION");

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line(100*cos(a)+100*sin(a)+x*(1-cos(a)) -y*sin(a),-100*sin(a)+100*cos(a)+y*(1-cos(a))

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+x*sin(a),200*cos(a)+100*sin(a)+x*(1-cos(a))

-y*sin(a),-200*sin(a)+100*cos(a)+y*(1-cos(a)) +x*sin(a));

outtextxy(110,150,"CLOCKWISE ROTATION"); getch();

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break;

case 4:

exit(0);

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}

getch();

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}while(c!=4);

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}

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OUTPUT: 1.TRANSLATION 2. SCALING 3. ROTATION 4. EXIT ENTER YOUR OPTION : 1 ENTER THE TX AND TY VALUE : 150 150 TRANSLATION OBJECT

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ORIGINAL OBJECT

ENTER YOUR OPTION : 2

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ENTER YOUR SX AND SY VALUE : 2 2

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1. TRANSLATION 2.SCALING 3. ROTATION 4. EXIT

1. TRANSLATION 2.SCALING 3. ROTATION 4. EXIT

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ENTER YOUR OPTION : 3

ENTER THE X AND Y VALUE :100 100

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ENTER THE ANGLE :90

ORIGINAL OBJECT

COUNTER CLOCKWISE ROTATION

CLOCKWISE ROTATION

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RESULT: Thus the above program”TWO DIMENSIONAL

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TRANSFORMATIONS” Is executed successfully.

COHEN SUTHERLAND 2D LINE CLIPPING AND WINDOWING Ex. No : 5

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Date

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AIM:

To implement cohen-sutherland 2d clipping and window-view port

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mapping

COHEN-SUTHERLAND 2D LINE CLIPPING

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#include #include

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#include

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#include

float cxl,cxr,cyt,cyb; code(float ,float);

void clip(float ,float,float,float);

void rect(float ,float,float,float); {

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main()

float x1,y1,x2,y2; int g=0,d;

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initgraph(&g,&d,"c:\\tc\\bin");

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settextstyle(1,0,1); outtextxy(40,15,"BEFORE CLIPPING");

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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"); scanf("%f%f%f%f",&x1,&y1,&x2,&y2); line(x1,y1,x2,y2); getch(); cleardevice();

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settextstyle(1,0,1); outtextxy(40,15,"AFTER CLIPPING"); clip(x1,y1,x2,y2); getch(); closegraph(); }

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void clip(float x1,float y1,float x2,float y2) { int c,c1,c2; float x,y;

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c1=code(x1,y1); c2=code(x2,y2);

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getch();

while((c1!=0)||(c2!=0)) {

if((c1&c2)!=0)

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goto out; c=c1;

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if(c==0)

c=c2;

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if((c&1)==1) {

y=y1+(y2-y1)*(cxl-x1); x=cxl; } else if((c&2)==2) { y=y1+(y2-y1)*(cxl-x1)/(x2-x1); x=cxr; }

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else if((c&8)==8) { x=x1+(x2-x1)*(cyb-y1)/(y2-y1); y=cyb; } else { x=x1+(x2-x1)*(cyt-y1)/(y2-y1); y=cyt;

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} if(c==c1)

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{ x1=x;

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y1=y;

c1=code(x,y);

} else {

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x2=x; y2=y;

c2=code(x,y);

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}

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}

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out:

rect(cxl,cyb,cxr,cyt); line(x1,y1,x2,y2);

} code(float x ,float y) { int c=0; if(x
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if((c&4)==4)

c=1;

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else if(x>cxr)

c=2;

if(y
c=c|8;

if(y>cyt)

c=c|4;

else else return c;

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}

void rect(float xl,float yb,float xr,float yt)

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{ line(xr,yb,xr,yt); line(xr,yt,xl,yt);

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line(xl,yt,xl,yb);

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line(xl,yb,xr,yb);

}

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OUTPUT

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SAMPLE INPUT:

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Please Enter Left , Bottom , Right , Top Of The Clip window

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200 200 400 400

Please Enter The Line Coordinates (X1, Y1, X2, Y2) 150 300 400

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450

SAMPLE OUTPUT:

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BEFORE CLIPPING

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AFTER CLIPPING:

Windowing To Viewport Mapping

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#include #include #include #include main() {

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float sx,sy; int w1,w2,w3,w4,x1,x2,x3,x4,y1,y2,y3,y4,v1,v2,v3,v4; int gd=DETECT,gm; initgraph(&gd,&gm,"c:\\tc\\bgi");

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printf("Enter The Coordinate x1,y1,x2,y2,x3,y3\n"); cleardevice(); w2=5; w3=635; w4=465;

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w1=5;

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scanf("%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3);

rectangle(w1,w2,w3,w4); line(x1,y1,x2,y2);

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line(x2,y2,x3,y3); line(x3,y3,x1,y1); getch();

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v1=425; v2=75;

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v3=550;

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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); x2=v1+floor(((float)(x2-w1)*sx)+.5); x3=v1+floor(((float)(x3-w1)*sx)+.5); y1=v2+floor(((float)(y1-w2)*sy)+.5); y2=v2+floor(((float)(y2-w2)*sy)+.5);

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

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}

Enter The Coordinate x1,y1,x2,y2,x3,y3

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100 300 400 500 350

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SAMPLE OUTPUT:

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200

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SAMPLE INPUT:

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Ex. No. :: 07 Date

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TRANSLATION AND SCALING USING 3D

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AIM:

ALGORITHM:

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To write a C program for Translation and Scaling Using 3D Method.

Step 1: Start the program.

Step 2: Declare the necessary variables, with member functions. Step 3: Create the main function, in that function to initialize graph using

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do-while statement.

Step 4: Using Switch statement for translation, scaling, exit. Step 5: Using get function for getting the values.

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Step 6: Similarly, get the draw function for draw the lines.

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Step 7: Stop the program.

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PROGRAM:

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#include #include #include #include

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int n,dep; float x[10],y[10],nx[10],ny[10];

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void translation(); void rotation();

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void scaling(); void draw(float x[],float y[]); void get(); void main() {

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int gd=DETECT,gm,i,ch; initgraph(&gd,&gm," "); get();

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do

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{

cleardevice(); draw(x,y); printf("\n 1.TRANSLATION 2.SCALING 3.EXIT"); printf("\n ENTER UR CHOICE:"); scanf("%d",&ch); switch(ch) { case 1: translation(); break;

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case 2: scaling(); break; case 3: closegraph(); exit(0); }

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getch(); }while(ch!=3); }

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void get() {

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int i;

printf("\n ENTER THE NO.OF SIDES& DEPTH OF THE

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POLYGON:");

scanf("%d%d",&n,&dep);

printf("n ENTER THE CO ORDINATES\n"); for(i=0;i
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printf("\n ENTER THE X%d&Y%d VALUE:"); scanf("%f%f",&x[i],&y[i]);

}

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}

void draw(float x[],float y[])

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{

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int i; for(i=0;i
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} void translation() { int i,ch; float tx,ty; draw(x,y); printf("ENTER THE TRANSLATIONFACTOR TX &TY

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VALUE:"); scanf("%f%f",&tx,&ty); for(i=0; i
ny[i]=y[i]+ty; } } void scaling() { int i,ch; float sx,sy;

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draw(x,y);

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draw(nx,ny);

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nx[i]=x[i]+tx;

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{

printf("ENTER THE SCALING FACTOR SX &SY

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scanf("%f%f",&sx,&sy); for(i=0;i
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{

nx[i]=x[i]*sx; ny[i]=y[i]*sy;

} draw(nx,ny);

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VALUE:");

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OUTPUT: ENTER THE NO OF SIDES & DEPTH OF THE POLYGON : 4 10 ENTER THE CO-ORDINATES : ENTER THE X1 AND Y1 VALUES : 200 10 ENTER THE X2 AND Y2 VALUES : 250 10

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ENTER THE X3 AND Y3 VALUES : 250 60

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1. TRANSLATION 2. SCALING 3. EXIT

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ENTER THE X4 AND Y4 VALUES : 200 60

ENTER YOUR CHOICE : 1

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ENTER THE TRANSLATION FACTORS TX AND TY VALUES : 100 0

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1. TRANSLATION 2. SCALING 3. EXIT ENTER YOUR CHOICE : 2 ENTER THE SCALING FACTORS SX AND SY VALUES : 2 2

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RESULT:

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Thus the above program TRANSLATION AND SCALING USING 3D” Is executed successfully.

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