LINE,CIRCLE AND ELLIPSE DRAWING USING BRESENHAM S ALGORITHM

Ex.no :1 Date: LINE,CIRCLE AND ELLIPSE DRAWING USING BRESENHAM S ALGORITHM AIM: To write a program to implement Bresenham s algorithms for line, circle and ellipse drawing. ALGORITHM: Step1: Create a function for line circle and ellipse. Step2: calculate contents Ax, Ay, 2Ay, 2Ay-2Ax and P0=2Ay-Ax to draw the line. Step3: Calculate the initial value parameter as q=q+(4*m)+10,q=q+(4*(m-n))+10 and draw circle using cplot(x,y,m,n). Step4: Calculate putpixel(xc+rx*cos(i*3.14/180),yc+ry*sin(i*3.14/180),15) to draw the ellipse drawing Step5: Display line, circle and ellipse drawing of Bresenham s algorithm. 1

PROGRAM: #include<stdio.h> #include<conio.h> #include<math.h> #include<graphics.h> void lined(int, int, int, int); void circled(int, int, int); void ellipsed(int, int, int, int); void main( ) int x, y, xe, ye, r, rx, ry, n; int gd=detect, gm; initgraph(&gd, &gm, "e:\\tc\\bgi"); do clrscr( ); printf("\n1. Line\n2. Circle\n3. Ellipse\n"); printf("enter the Choice:"); scanf("%d",&n); switch(n) case 1: printf("\nline DRAWING\nEnter the x and y axis:"); scanf("\n%d%d",&x,&y); printf("\nenter the Xend and yend:"); 2

scanf("%d%d",&xe,&ye); lined(x,y,xe,ye); break; case 2: printf("\ncircle DRAWING ); printf( \nenter the x and y axis and also Radius:"); scanf("%d%d%d",&x,&y,&r); circled(x,y,r); break; case 3: printf("\nellipse DRAWING ) printf( \nenter the x,y and rx,ry:"); scanf("%d%d%d%d",&x,&y,&rx,&ry); ellipsed(x,y,rx,ry); break; default: exit(0); break; while(n<=3); getch(); closegraph( ); void lined(int xa,int ya,int xb,int yb) 3

int dx=abs(xa-xb); int dy=abs(ya-yb); int p=2*dy-dx; int xend=2*dy; int yend=2*(dy-dx); int x,y,end; if(xa>xb) x=xb; y=yb; xend=xa; else x=xa; y=ya; yend=xb; while(x<xend) x++; if(p<0) p+=xend; else y++; p+=yend; putpixel(x,y,10); 4

getch( ); void circled(int x,int y,int r) int m=0,n=r, q; void cplot(int,int,int,int); q=3-(2*r); while(m<n) cplot(x,y,m,n); if(q<0) q=q+(4*m)+10; else q=q+(4*(m-n))+10; n--; m++; if(m==n) cplot(x,y,m,n); getch( ); void cplot(int xc,int yc,int x,int y) putpixel(xc+x,yc+y,15); putpixel(xc-x,yc+y,15); 5

putpixel(xc+x,yc-y,15); putpixel(xc-x,yc-y,15); putpixel(xc+y,yc+x,15); putpixel(xc-y,yc+x,15); putpixel(xc+y,yc-x,15); putpixel(xc-y,yc-x,15); void ellipsed(int xc,int yc,int rx,int ry) int i; for(i=0;i<=360;i++) putpixel(xc+rx*cos(i*3.14/180),yc+ry*sin(i*3.14/180),15); getch( ); 6

OUTPUT:- 1.Line 2. Circle 3. Ellipse Enter the Choice:1 LINE DRAWING Enter the x and y axis:10 15 Enter the Xend and yend: 45 60 1.Line 2. Circle 3. Ellipse Enter the Choice:2 CIRCLE DRAWING Enter the x and y axis and also Radius:45 45 45 1.Line 2. Circle 7

3. Ellipse Enter the Choice:3 ELLIPSE DRAWING Enter the x,y and rx,ry:45 45 45 45 RESULT: Thus the program implementation of Bresenham s algorithm for line, circle and ellipse drawing is done successfully. 8

Ex.no :2 Date: 2D-TRANSFORMATION AIM: To create a program to implement the 2D transformation of translation, Rotation, Scaling, Reflection and Shearing. ALGORITHM: Step 1: Start the Program. Step 2: Include the graphics header file Step 3: Initialize graphics using initgraph(). Step 4: Initialize the variable Step 5: Enter the choice for transformation. Step 6: If choice=1 Translation i.e. changing the co-ordinates is performed, x =x+tx y =y+ty Step 7: If choice=2 Rotation i.e. Rotate the object is performed x =x*cosθ-y*sinθ y =x*sinθ+y*cosθ Step 8: If choice=3 Scaling i.e.changing the size of the object is performed x =x*sx y =y*sy Step 9:If choice=4 Reflection i.e to produce the mirror image of the objects. Step 10: If choice=5 Shearing i.e Slanting the objects Step 11: Stop the Program. 9

PROGRAM: #include<stdio.h> #include<conio.h> #include<graphics.h> #include<math.h> #include<alloc.h> #include<stdlib.h> int n,i,p[20],q[20]; int convertx(int x); int converty(int y); void axis(void); void init(void); void share(void); void translate(void); void scaling(void); void rotate(void); void reflect(void); void main( ) int ch, gd=detect,gm; initgraph(&gd,&gm,"e:\\tc\\bgi"); axis( ); printf("\b"); cleardevice( ); printf("enter THE NUMBER OF VERTICES:"); scanf("%d",&n); 10

printf("enterthecoordinate(reenterthefirstvertexattheend )"); for(i=0;i<2*n+2;i++) scanf("%d",&p[i]); clrscr( ); init( ); getch( ); do clrscr( ); cleardevice( ); printf("\n\t\t2d-transformations\n1.translation\n 2. ROTATION\n 3.SCALING\n4.REFLECTION\n5.SHARING\n"); printf("\n\n ENTER UR CHOICE:\n"); scanf("%d",&ch); clrscr( ); cleardevice( ); switch(ch) case 1:axis( ); init( ); translate( ); break; case 2:axis( ); init( ); rotate( ); break; case 3:axis( ); 11

init( ); scaling( ); break; case 4:reflect( ); break; case 5:share( ); break; while(ch!=6); closegraph( ); void axis(void) cleardevice( ); setlinestyle(solid_line,1,1); line(320,0,320,getmaxy( )); line(0,240,getmaxx( ),240); outtextxy(325,245,"0"); line(316,40,324,40); outtextxy(325,41,"400"); line(316,440,324,440); outtextxy(325,441,"-400"); line(20,236,20,244); outtextxy(19,250,"-600"); line(620,236,620,244); outtextxy(608,250,"600"); 12

void init( ) cleardevice( ); axis( ); setcolor(yellow); setlinestyle(solid_line,1,1); for(i=0;i<2*n+2;i+=2) q[i]=convertx(p[i]); for(i=1;i<2*n+2;i+=2) q[i]=converty(p[i]); drawpoly(n+1,q); setcolor(white); int convertx(int x) x=x/2; return(x+=320); int converty(int y) y=y/2; return(y=240-y); void share( ) int sh[20],shr[20]; float shx,shy,c; printf("(1)share RELATIVE TO X-AXIS \n"); 13

printf("(2)share RELATIVE TO Y-AXIS \n"); printf("\n ENTER UR CHOICE:"); scanf("%f",&c); if(c==1) init( ); printf("\n ENTER THE SHARE FACTOR(shx):"); scanf("%f",&shx); for(i=0;i<2*n+2;i+=2) sh[i]=p[i]+(shx*(p[i+1])); for(i=1;i<2*n+2;i+=2) sh[i]=p[i]; else init( ); printf("\n ENTER THE SHARE FACTOR(shy):"); scanf("%f",&shy); for(i=1;i<2*n+2;i+=2) sh[i]=(shy*p[i-1])+p[i]; for(i=0;i<2*n+2;i+=2) sh[i]=p[i]; setlinestyle(dotted_line,1,1); for(i=0;i<2*n+2;i+=2) shr[i]=convertx(sh[i]); for(i=1;i<2*n+2;i+=2) 14

shr[i]=converty(sh[i]); drawpoly(n+1,shr); getch( ); void translate( ) int tr[20],tr1[20],tx,ty; printf("\n ENTER THR X-TRANSLATION VECTOR:"); scanf("%d",&tx); printf("\n ENTER THR Y-TRANSLATION VECTOR:"); scanf("%d",&ty); for(i=0;i<2*n+2;i+=2) tr[i]=p[i]+tx; for(i=1;i<2*n+2;i+=2) tr[i]=p[i]+ty; setlinestyle(dotted_line,1,1); for(i=0;i<2*n+2;i+=2) tr1[i]=convertx(tr[i]); for(i=1;i<2*n+2;i+=2) tr1[i]=converty(tr[i]); drawpoly(n+1,tr1); getch( ); void scaling( ) int sc[20],sc1[20]; float sx,sy; 15

printf("\n ENTER THE X-AXIS SCALING FACTOR:"); scanf("%f",&sx); printf("\n ENTER THE Y-AXIS SCALING FACTOR:"); scanf("%f",&sy); for(i=0;i<2*n+2;i+=2) sc[i]=p[i]*sx; for(i=1;i<2*n+2;i+=2) sc[i]=p[i]*sy; setlinestyle(dotted_line,1,1); for(i=0;i<2*n+2;i+=2) sc1[i]=convertx(sc[i]); for(i=1;i<2*n+2;i+=2) sc1[i]=converty(sc[i]); drawpoly(n+1,sc1); getch( ); void rotate( ) int ro[20],rot[20],xr,yr,v; float ang; printf("\n ENTER THE ANGLE TO ROTATE:"); scanf("%f",&ang); ang=((ang*3.14)/180)*(-1); printf("\n ENTER THE ROTATION VERTEX ("); for(i=1;i<=n;i++) printf("%d)",i); 16

scanf("%d",&v); xr=p[(2*v)-2]; yr=p[((2*v)-2)+1]; for(i=0;i<(2*n+1);i+=2) ro[i]=xr+(p[i]-xr)*cos(ang)-(p[i+1]-yr)*sin(ang); ro[i+1]=yr+(p[i]-xr)*sin(ang)+(p[i+1]-yr)*cos(ang); setlinestyle(dotted_line,1,1); for(i=0;i<2*n+2;i+=2) rot[i]=convertx(ro[i]); for(i=1;i<2*n+2;i+=2) rot[i]=converty(ro[i]); drawpoly(n+1,rot); getch( ); void reflect( ) int j,c,rt[20],rft[20]; printf("\n1.x-axis REFLECTION\n2.y-AXIS REFLECTION"); printf("\n ENTER THE CHOICE:"); scanf("%d",&c); clrscr( ); cleardevice( ); if(c==1) for(i=1;i<2*n+2;i+=2) rt[i]=p[i]*(-1); 17

for(i=0;i<2*n+2;i+=2) rt[i]=p[i]; else for(i=0;i<2*n+2;i+=2) rt[i]=p[i]*(-1); for(i=1;i<2*n+2;i+=2) rt[i]=p[i]; init( ); setlinestyle(dotted_line,1,1); for(i=0;i<2*n+2;i+=2) rft[i]=convertx(rt[i]); for(i=1;i<2*n+2;i+=2) rft[i]=converty(rt[i]); drawpoly(n+1,rft); getch( ); OUTPUT: ENTER THE NUNBER OF VERTICES: 1 ENTER THE COORDINATE (reenter the first vertex at the end) : 100 100 400 400 18

2D-TRANSFORMATIONS 1)TRANSLATION 2)ROTATION 3)SCALING 4)REFLECTION 5)SHEARING ENTER YOUR CHOICE: 1 ENTER THE X-TRANSLATION VECTOR:80 ENTER THE Y-TRANSLATION VECTOR:50 ENTER YOUR CHOICE: 2 ENTER THE ANGLE TO ROTATE:90 ENTER THE ROTATION VERTEX (1) 1 19

ENTER YOUR CHOICE: 3 ENTER THE X-AXIS SCALING FACTOR:100 ENTER THE Y-AXIS SCALING FACTOR:100 ENTER YOUR CHOICE: 4 1. X-AXIS REFLECTION 2. Y-AXIS REFLECTION ENTER YOUR CHOICE:1 20

ENTER YOUR CHOICE: 5 1.SHEAR RELATIVE TO X-AXIS 2.SHEAR RELATIVE TO Y-AXIS ENTER YOUR CHOICE:2 ENTER THE SHEAR FACTOR (shy):100 RESULT: Ex.no :3 Date: ations is executed successfully. 3D Transformation Thu s the above program for Two Dimension al Transform 21

AIM: To create a program to implement the 3D transformation of translation, Rotation, Scaling of objects.. ALGORITHM: 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 do-while statement. Step 4: Using Switch statement for translation, scaling and rotation exit. Step 5: Using get function for getting the values. Step 6: Similarly, get the draw function for draw the lines. Step 7: Stop the program. 22

PROGRAM: #include<graphics.h> #include<process.h> #include<stdlib.h> #include<stdio.h> #include<conio.h> #include<math.h> #include<dos.h> #define X 250 #define Y 100 #define Z 100 int ori[24]; void wtor(int pts3[24]); void cube(int pts1[16]); void main( ) int gd=detect,gm,s,ch; void tran( ); void rot( ); void scale( ); initgraph(&gd,&gm,"e:\\tc\\bgi"); printf("\n\t\t 3D-TRANSFORMATION"); printf("\n\t\t~~~~~~~~~~~~~~~~~~~~\n"); printf("\n ENTER THE SIDE OF THE CUBE:"); scanf("%d",&s); 23

ori[0]=x; ori[1]=y; ori[2]=z; ori[3]=x+s; ori[4]=y; ori[5]=z; ori[6]=x+s; ori[7]=y; ori[8]=z+s; ori[9]=x; ori[10]=y; ori[11]=z+s; ori[12]=x; ori[13]=y-s; ori[14]=z; ori[15]=x+s; ori[16]=y-s; ori[17]=z; ori[18]=x+s; ori[19]=y-s; ori[20]=z+s; ori[21]=x; ori[22]=y-s; ori[23]=z+s; wtor(ori); getch( ); do clearviewport( ); gotoxy(35,5); printf("\n\t\t 3D-TRANSFORMATIONS \n"); printf("\n\t\t 1.TRANSLATION \n"); printf("\n\t\t 2.ROTATION \n"); printf("\n\t\t 3.SCALING\n"); printf("\n\t\t 4.EXIT\n"); printf("\n\n ENTER UR CHOICE:\n"); scanf("%d",&ch); switch(ch) case 1: wtor(ori); 24

tran( ); getch( ); break; case 2: wtor(ori); rot( ); getch( ); break; case 3: wtor(ori); scale( ); getch( ); break; case 4: break; default: printf("\n INVALID ENTRY!!!!!"); getch( ); break; while(ch!=4); closegraph( ); void cube(int pts1[16]) 25

setcolor(15); setlinestyle(dotted_line,1,1); line(pts1[0],pts1[1],pts1[2],pts1[3]); delay(200); line(pts1[2],pts1[3],pts1[4],pts1[5]); delay(200); line(pts1[2],pts1[3],pts1[10],pts1[11]); delay(200); setlinestyle(solid_line,1,1); line(pts1[4],pts1[5],pts1[6],pts1[7]); delay(200); line(pts1[6],pts1[7],pts1[0],pts1[1]); delay(200); line(pts1[0],pts1[1],pts1[8],pts1[9]); delay(200); line(pts1[4],pts1[5],pts1[12],pts1[13]); delay(200); line(pts1[6],pts1[7],pts1[14],pts1[15]); delay(200); line(pts1[8],pts1[9],pts1[10],pts1[11]); delay(200); line(pts1[10],pts1[11],pts1[12],pts1[13]); delay(200); line(pts1[12],pts1[13],pts1[14],pts1[15]); 26

delay(200); line(pts1[8],pts1[9],pts1[14],pts1[15]); delay(200); setcolor(15); void wtor(int pts3[24]) int pts2[16],i,j; float a1=3.14*60/180; float a2=3.14*60/180; for(i=0,j=0;i<24,j<16;i+=3,j+=2) pts2[j]=pts3[i]+pts3[i+2]*1/tan(a1)*cos(a2); pts2[j+1]=pts3[i+1]+pts3[i+2]*1/tan(a1)*sin(a2); cube(pts2); void tran( ) int tr3[24]; int i,tx,ty,tz; printf("\n ENTER THE TRANSLATION VECTORS:"); scanf("%d%d%d",&tx,&ty,&tz); for(i=0;i<24;i+=3) 27

tr3[i]=ori[i]+tx; tr3[i+1]=ori[i+1]+ty; tr3[i+2]=ori[i+2]+tz; wtor(tr3); void rot( ) int r3[24]; float deg,rad; int i,axis; printf("\n ENTER THE ANGLE:"); scanf("%f",&deg); rad=3.14*deg/180; printf("\n ENTER THE AXIS OF ROTATION:"); printf("x=1/y=2/z=3):\n"); scanf("%d",&axis); for(i=0;i<24;i+=3) switch(axis) case 1: r3[i]=ori[i]; r3[i+1]=ori[i+1]*cos(rad)-ori[i+2]*sin(rad); r3[i+2]=ori[i+1]*sin(rad)+ori[i+2]*cos(rad); 28

break; case 2: r3[i]=ori[i+2]*sin(rad)+ori[i]*cos(rad); r3[i+3]=ori[i+1]; r3[i+2]=ori[i+2]*cos(rad)-ori[i+2]*sin(rad); break; case 3: r3[i]=ori[i]*cos(rad)-ori[i+1]*sin(rad); r3[i+1]=ori[i]*sin(rad)+ori[i+1]*cos(rad); break; default: printf("\n INVALID CHOICE!!!!"); getch( ); break; wtor(r3); void scale( ) float sx,sy,sz; int i,s3[24]; printf("\n ENTER THE SCALING FACTOR:"); scanf("%f%f%f",&sx,&sy,&sz); for(i=0;i<24;i+=3) 29

s3[i]=ori[i]*sx; s3[i+1]=ori[i+1]*sy; s3[i+2]=ori[i+2]*sz; wtor(s3); OUTPUT: ENTER THE SIDE OF THE CUBE:50 1. TRANSLATION 2. ROTATION 3. SCALING 4. EXIT ENTER THE CHOICE: 1 ENTER THE TRANSLATION VECTORS: 50 50 50 30

1. TRANSLATION 2. ROTATION 3. SCALING 4. EXIT ENTER THE CHOICE: 2 ENTER THE ANGLE:45 ENTER THE AXIS OF ROTATION:(X=1/Y=2/Z=3):1 ENTER THE CHOICE: 3 ENTER THE SCALING FACTOR: 1 3 1 RESULT: Thus the above program for Three Dimensional Transformation of Translation, Scaling and Rotation is executed successfully. 32

Ex.no :4 Date: Cohen Sutherland 2D clipping and windowing AIM: To write a program to implement Cohen-Sutherland 2D clipping and windowing.. ALGORITHM: Step1: Create a function to get the line co-ordinates and window co-ordinate values. Step2: Check all the co-ordinates of the lines are within the window co-ordinate or not. Step3: Clip the lines which are all outside of the window co-ordinates. Step4: After the clipping draw all the lines along with the window. 33

PROGRAM: #include<graphics.h> #include<stdio.h> #include<conio.h> #include<stdlib.h> #define top 200 #define left 200 #define right 400 #define bottom 400 typedef struct float x,y; wcpt2; int accept(int c1[4],int c2[4]) int k,t; t=1; for(k=0;k<=3;k++) if(c1[k] c2[k]) t=0; return(t); int ptinside(int c[4]) int p; 34

if(c[0] c[2] c[3]) p=0; else p=1; return(p); void main( ) wcpt2 p1,p2,tmp; int code1[4],code2[4],t[4],done=0,draw=0,i,j,k,p,y; int gd=detect,gm; float m; initgraph(&gd,&gm,"e:\\tc\\bgi"); rectangle(left,top,right,bottom); printf("2d-clipping USINGF COHEN SUTHERLAND ALGORITHM \n"); printf("**************************************************\n\n"); printf("enter THE VERTICES OF THE LINE TO BE CLIPPED \n"); scanf("%f%f%f%f",&p1.x,&p1.y,&p2.x,&p2.y); settextstyle(1,0,2); getch(); clrscr( ); cleardevice( ); outtextxy(60,100,"before CLIPPING"); rectangle(left,top,right,bottom); line(p1.x,p1.y,p2.x,p2.y); 35

getch( ); clearviewport( ); rectangle(left,top,right,bottom); while(!done) if(p1.x<left) code1[0]=1; else code1[0]=0; if(p1.x>right) code1[1]=1; else code1[1]=0; if(p1.y>bottom) code1[2]=1; else code1[2]=0; if(p1.y<top) code1[3]=1; else code1[3]=0; if(p2.x<left) code2[0]=1; else code2[0]=0; 36

if(p2.x>right) code2[1]=1; else code2[1]=0; if(p2.y>bottom) code2[2]=1; else code2[2]=0; if(p2.y<top) code2[3]=1; else code2[3]=0; if(accept(code1,code2)) done=1; draw=1; else y=0; for(k=0;k<=3;k++) if(code1[k]&&code2[k]) y=1; if(y==1) done=1; 37

else if(ptinside(code1)) tmp=p1; p1=p2; p2=tmp; for(i=0;i<3;i++) t[i]=code1[i]; for(i=0;i<=3;i++) code2[i]=t[i]; m=(p2.y-p1.y)/(p2.x-p1.x); if(code1[0]) p1.y=p1.y+(left-p1.x)*m; p1.x=left; else if(code1[1]) p1.y=p1.y+(right-p1.x)*m; p1.x=right; else 38

if(code1[2]) p1.y=p1.y+(bottom-p1.y)/m; p1.x=bottom; else if(code1[3]) p1.x=p1.x+(top-p1.y)/m; p1.y=top; if(draw) settextstyle(1,0,2); outtextxy(20,60,"after CLIPPING"); line(abs(p1.x),abs(p1.y),abs(p2.x),abs(p2.y)); getch( ); closegraph( ); 39

OUTPUT: 2D-CLIPPING USING COHEN SUTHERLAND ALGORITHM ************************************************** ENTER THE VERTICES OF THE LINE TO BE CLIPPED: 150 150 300 350 BEFORE CLIPPING: AFTER CLIPPING: RESULT: 41

Thus the above program for Cohen Sutherland 2D clipping and windowing is executed successfully. 5. IMPLEMENTATION OF TWO DIMENSIONAL COMPOSITE TRANSFORMATIONS DESCRIPTION: A transformation is any operation on a point in space (x, y) that maps the point's coordinates into a new set of coordinates (x1, y1).the Two Dimensional Composite transformation represent a sequence of transformations as a single matrix which has the order of operations as Translation, Rotation, Scaling, Shearing, Reflection. CODING: #include <graphics.h> /* include the necessary header files*/ #include <stdlib.h> #include <stdio.h> #include <conio.h> #include <math.h> int xa,xb,xc,ya,yb,yc,y1a,y1b,y1c,x1a,x1b,x1c,x2a,x2b,x2c,y2a,y2b,y2c; int x3a,x3b,x3c,y3a,y3b,y3c,x4a,x4b,x4c,y4a,y4b,y4c,x5a,x5b,x5c,y5a,y5b,y5c; int tx,shx,t,ch,shy; float ang,theta,sx,sy; int main(void) int gdriver = DETECT, gmode, errorcode; initgraph(&gdriver, &gmode,"c:\\tc\\bgi"); /* request for auto detection*/ printf("\n\t\t\t 2D Composite Transformations"); printf("\n\n Enter all coordinates values :"); scanf("%d %d %d %d %d %d",&xa,&ya,&xb,&yb,&xc,&yc); printf("\n\n The original Image"); /* get the coordinates for the original image*/ line(xa,ya,xb,yb); /* draw the original image*/ line(xb,yb,xc,yc); line(xc,yc,xa,ya); 42

printf("\n\n Enter the value tranlsation factor :"); /* get the translation factor*/ scanf("%d",&tx); 43

printf("\n\n After Translation "); x1a=xa+tx; x1b=xb+tx; x1c=xc+tx; y1a=ya; y1b=yb; y1c=yc; line(x1a,y1a,x1b,y1b); /* image after translation*/ line(x1b,y1b,x1c,y1c); line(x1c,y1c,x1a,y1a); delay(1); printf("\n\n Next Operation is Rotation"); printf("\n\n Enter the rotation angle :"); /* get the angle of rotation*/ scanf("%f",&ang); theta=((ang*3.14)/180); /* convert the angle*/ x2a=x1a*cos(theta)-y1a*sin(theta); y2a=x1a*sin(theta)+y1a*cos(theta); x2b=x1b*cos(theta)-y1b*sin(theta); y2b=x1b*sin(theta)+y1b*cos(theta); x2c=x1c*cos(theta)-y1c*sin(theta); y2c=x1c*sin(theta)+y1c*cos(theta); printf("\n\n After Rotation "); /* the rotated object*/ line(x2a,y2a,x2b,y2b); line(x2b,y2b,x2c,y2c); line(x2c,y2c,x2a,y2a); delay(1); printf("\n\n Next Operation is Scaling"); /* get the scale factor*/ printf("\n\n Enter the Scale factor :"); scanf("%f %f",&sx,&sy); x3a=x2a+sx; /* modify the objects coordinates based on the scale factor*/ y3a=y2a+sy; x3b=x2b+sx; 44

y3b=y2b+sy; x3c=x2c+sx; y3c=y2c+sy; printf("\n\n After Scaling "); line(x3a,y3a,x3b,y3b); line(x3b,y3b,x3c,y3c); line(x3c,y3c,x3a,y3a); delay(1); printf("\n\n Next Operation is Shearing"); printf("\n\n Enter 1 for x-axis \n 2 for y-axis: "); /* get the choice of shearing in the x or y axis*/ scanf("%d",&ch); if(ch==1) /* get the shear value*/ printf("\n\n Enter the x-shear (^.^) Value: "); scanf("%d",&shx); else printf("\n\n Enter the y-shear (^.^) Value: "); scanf("%d",&shy); if(ch==1) x3a=x3a+shx*y3a; y4a=y3a; x3b=x3a+shx*y3a; y4b=y3b; x3c=x3a+shx*y3a; y4c=y3c; else 45

x4a=x3a; y3a=y3a+shy*x3a; x4b=x3b; y3b=y3b+shy*x3b; x4c=x3c; y3c=y3c+shy*x3c; printf("\n\n After Shearing "); /* draw the final object after shearing*/ line(x3a,y3a,x3b,y3b); line(x3b,y3b,x3c,y3c); line(x3c,y3c,x3a,y3a); delay(1); printf("\n\n Next Operation is Reflection"); t=abs(y3ay3c); /* calculate the value for reflection*/ x5a=x3a; x5b=x3b; x5c=x3c; y5a=y3a+10+(2*t); y5b=y3b+10; y5c=y3c+10; printf("\n\n After Reflection "); /* the final object after all the transformations*/ line(x5a,y5a,x5b,y5b); line(x5b,y5b,x5c,y5c); line(x5c,y5c,x5a,y5a); getch(); closegraph(); return 0; 47

OUTPUT: 2D Composite Transformations Enter all coordinates values 213 236 253 321 256 214 The original Image Enter the value translation vector 32 After Translation Next Operation is Rotation Enter the rotation angle 20 After Rotation Next Operation is Scaling Enter the scale factor 10 5 49

After Scaling Next Operation is Shearing Enter 0 for x axis and 1 for y axis 0 Enter the x-shear value 1 After Shearing Enter 0 for x axis and 1 for y axis 1 Enter the y-shear value 1 Next Operation is Reflection After Reflection 51

RESULT: Thus the Two dimensional Composite transformations were successfully executed and the output is transformed, drawn and verified. 52

6. IMPLEMENTATION OF LINE, CIRCLE AND ELLIPSE ATTRIBUTES DESCRIPTION: Output primitives have geometric and non-geometric attributes. Geometric attributes, such as the character height, affect the size and shape of a primitive, whereas non-geometric attributes are qualities such as colour, line style, etc. The output primitives Such as Line, Circle and Ellipse are associated with set of attributes such as Line (color and Line Style), Cicrle (Color) and Ellipse (Color and Patterns). CODING: #include<graphics.h> /* include the necessary header files*/ #include<stdlib.h> #include<stdio.h> #include<conio.h> int main(void) /* select a driver and mode that supports */ /* multiple drawing colors.*/ int gdriver=ega,detect,gmode=egahi,errorcode; int color,maxcolor,x,y,s,ch,ch1,ch2,i; int midx,midy; int radius=100; int xradius=100,yradius=50; char msg[80]; char *lname[]="solid Line", "Dotted Line", "Center Line", "Dashed Line", "Usebit Line"; /* initialize graphics and local variables */ initgraph(&gdriver,&gmode,"c:\\tc\\bgi"); /* read result of initialization */ errorcode=graphresult(); if (errorcode!=grok) /* an error occurred */ printf("graphics error: %s\n", grapherrormsg(errorcode)); 53

printf("press any key to halt:"); getch(); exit(1); /* terminate with an error code */ do printf("\n1.line\n2.circle\n3.ellipse\n"); /* get the user choice*/ printf("\nenter Your choice\n"); scanf("%d",&ch); switch(ch) case 1: printf("attribute: 1.Color 2.Style:\n"); scanf("%d",&ch1); switch(ch1) case 1: maxcolor=getmaxcolor(); /* use predefined methods to change the color*/ x=getmaxx()/2; y=getmaxy()/2; for(color=1;color<=maxcolor;color++) cleardevice(); setcolor(color); line(100,100,100,300); sprintf(msg,"color:%d",color); outtextxy(x,y,msg); getch(); closegraph(); break; case 2: 55

initgraph(&gdriver,&gmode,"c:\\tc\\bgi"); 56

for(s=0;s<5;s++) setlinestyle(s,1,1); /* pre defined method for linestyle*/ line(20,20+s*50,120,120+s*50); outtextxy(125,120+s*50,lname[s]); getch(); closegraph(); break; break; case 2: initgraph(&gdriver,&gmode,"c:\\tc\\bgi"); midx=getmaxx()/2; midy=getmaxy()/2; maxcolor=getmaxcolor(); /* draw circles of different colors*/ for(color=1;color<=maxcolor;color++) cleardevice(); setcolor(color); /* draw the circle */ circle(midx,midy,radius); /* clean up */ getch(); closegraph(); break; case 3: printf("\n1.pattern 2.colour\n"); /* get choice for color or style of eclipse*/ printf("\nenter your choice:\n"); scanf("%d",&ch2); 57

switch(ch2) 58

default: case 1: /* initialize graphics and local variables */ initgraph(&gdriver,&gmode,"c:\\tc\\bgi"); midx=getmaxx()/2; midy=getmaxy()/2; /* loop through the fill patterns */ for(i=empty_fill;i<user_fill;i++) /* set fill pattern */ setfillstyle(i,getmaxcolor()); /* draw a filled ellipse */ fillellipse(midx, midy, xradius, yradius); getch(); closegraph(); break; case 2: initgraph(&gdriver,&gmode,"c:\\tc\\bgi"); maxcolor=getmaxcolor(); for(color=1;color<=maxcolor;color++) cleardevice(); setcolor(color); ellipse(100,200,0,360,xradius,yradius); getch(); /* clean up */ closegraph(); break; 59

while(ch==3); return 0; //exit(0); break; OUTPUT: Line Color Line Style 61

Circle Color Ellipse Pattern Ellipse Color 63

RESULT: verified. Thus the attributes were successfully applied to Line, circle and ellipse and the output is drawn and 65

7. IMPLEMENTATION OF SUTHERLAND HODGEMAN POLYGON CLIPPING ALGORITHM DESCRIPTION: The Sutherland Hodgeman Algorithm is used for clipping polygons. It works by extending each line of the convex clip polygon in turn and selecting only vertices from the subject polygon that is on the visible side. This algorithm performs a clipping of a polygon against each window edge in turn. It accepts an ordered sequence of vertices v1, v2, v3... vn and puts out a set of vertices defining the clipped polygon. CODING: #include<stdio.h> /* include the necessary header files*/ #include<graphics.h> #include<conio.h> #include<math.h> #include<process.h> #define TRUE 1 #define FALSE 0 typedef unsigned int outcode; outcode CompOutCode(float x,float y); /* create an user defined function for the output*/ enum TOP=0x1, BOTTOM=0x2, RIGHT=0x4, LEFT=0x8 ; float xmin,xmax,ymin,ymax; void clip(float x0,float y0,float x1,float y1) /* define the clipping function*/ outcode outcode0,outcode1,outcodeout; int accept=false,done=false; outcode0=compoutcode(x0,y0); /* call the user defined function*/ 66

outcode1=compoutcode(x1,y1); do /* assign the values for the condition variables*/ if(!(outcode0 outcode1)) accept=true; done=true; else if(outcode0&outcode1) done=true; else float x,y; outcodeout=outcode0?outcode0:outcode1; /* use the tertiary operator to assign values*/ if(outcodeout&top) /* reassign the value of x and y */ x=x0+(x1-x0)*(ymax-y0)/(y1-y0); y=ymax; else if(outcodeout&bottom) x=x0+(x1-x0)*(ymin-y0)/(y1-y0); y=ymin; else if(outcodeout&right) y=y0+(y1-y0)*(xmax-x0)/(x1-x0); x=xmax; 68

else y=y0+(y1-y0)*(xmin-x0)/(x1-x0); x=xmin; if(outcodeout==outcode0) x0=x; y0=y; outcode0=compoutcode(x0,y0); else x1=x; y1=y; outcode1=compoutcode(x1,y1); while(done==false); if(accept) line(x0,y0,x1,y1); outtextxy(150,20,"polygon AFTER CLIPPING"); rectangle(xmin,ymin,xmax,ymax); /* draw the clipping window*/ outcode CompOutCode(float x,float y) /* define the output function*/ outcode code=0; if(y>ymax) code =TOP; else if(y<ymin) 70

code =BOTTOM; if(x>xmax) code =RIGHT; else if(x<xmin) code =LEFT; return code; void main() float x1,y1,x2,y2; /* request auto detection */ int gdriver=detect,gmode,n,poly[14],i; clrscr( ); printf("enter the no of sides of polygon:"); /* get the sides of the polygon*/ scanf("%d",&n); printf("\nenter the coordinates of polygon\n"); for(i=0;i<2*n;i++) scanf("%d",&poly[i]); poly[2*n]=poly[0]; poly[2*n+1]=poly[1]; printf("enter the rectangular coordinates of clipping window\n"); scanf("%f%f%f%f",&xmin,&ymin,&xmax,&ymax); /* get the coordinates of the clipping window*/ /* initialize graphics and local variables */ initgraph(&gdriver, &gmode, "c:\\tc\\bgi"); outtextxy(150,20,"polygon BEFORE CLIPPING"); drawpoly(n+1,poly); rectangle(xmin,ymin,xmax,ymax); getch(); cleardevice(); 71

for(i=0;i<n;i++) getch(); clip(poly[2*i],poly[(2*i)+1],poly[(2*i)+2],poly[(2*i)+3]); /* call the clipping function*/ restorecrtmode(); OUTPUT: Enter the Sides of the Polygon: 5 Enter the co-ordinates of the Polygon 80 50 200 100 350 350 80 200 40 80 Enter the rectangular co-ordinates 150 150 300 300 RESULT: Thus the Sutherland Hodgeman polygon clipping algorithm was successfully executed and the output is drawn and verified. 72