THREE DIMENSIONAL TRANSFORMATION

THREE DIMENSIONAL TRANSFORMATION

EX.NO:7

AIM

To perform the various 3-dimensional transformations such as translation, scaling, rotation.

Algorithm

Step 1: Input the figure.

Step 2: Display the menu as 1.Translation 2.Scaling 3.Rotation 4.Exit

Step 3: Get the choice from the user.

Step 4: If the choice is 1 a point or an object is translated from position P to position P' with the operation P'=T.P where t_x,t_y and t_z specifying translation distances.

x'=x+ t_x

y'=y+ t_y

z'=z+ t_z

Step 5: If the choice is 2 the scaling transformation of a position P can be written as P'=S.P where scaling parameters s_x,s_y and s_z are assigned any positive values.

x'=x.s_x

y'=y.s_y

z'=z.s_z

Step 6: If the choice is 3 get the rotation angle. Rotate the figure with respect to the axis of rotation.

Step 6a: About z axis rotation

x'=xcosӨ-ysinӨ

y'=xsinӨ+ycosӨ

z'=z

Rotation can be expressed as P'=R_z(Ө).P

Step 6b: About x axis rotation

y'=ycosӨ-zsinӨ

z'=ysinӨ+zcosӨ

x'=x

Rotation can be expressed as P'=R_x(Ө).P

Step 6c: About y axis rotation

z'=zcosӨ-xsinӨ

x'=zsinӨ+xcosӨ

y'=y

Rotation can be expressed as P'=R_y(Ө).P

Step 7: If choice is 4 exit the program.

PROGRAM:

#include<stdio.h>

#include<conio.h>

#include<graphics.h>

#include<math.h>

int maxx,maxy,midx,midy;

void axis()

{

getch();

cleardevice();

line(midx,0,midx,maxy);

line(0,midy,maxx,midy);

}

void main()

{

int gd,gm,x,y,z,o,x1,x2,y1,y2;

detectgraph(&gd,&gm);

initgraph(&gd,&gm," ");

setfillstyle(0,getmaxcolor());

maxx=getmaxx();

maxy=getmaxy();

midx=maxx/2;

midy=maxy/2;

axis();

bar3d(midx+50,midy-100,midx+60,midy-90,5,1);

printf("Enter Translation Factor");

scanf("%d%d%d",&x,&y,&z);

axis();

printf("after translation");

bar3d(midx+(x+50),midy-(y+100),midx+x+60,midy-(y+90),5,1);

axis();

bar3d(midx+50,midy+100,midx+60,midy-90,5,1);

printf("Enter Scaling Factor");

scanf("%d%d%d",&x,&y,&z);

axis();

printf("After Scaling");

bar3d(midx+(x*50),midy-(y*100),midx+(x*60),midy-(y*90),5*z,1);

axis();

bar3d(midx+50,midy-100,midx+60,midy-90,5,1);

printf("Enter Rotating Angle");

scanf("%d",&o);

x1=50*cos(o*3.14/180)-100*sin(o*3.14/180);

y1=50*cos(o*3.14/180)+100*sin(o*3.14/180);

x2=60*sin(o*3.14/180)-90*cos(o*3.14/180);

y2=60*sin(o*3.14/180)+90*cos(o*3.14/180);

axis();

printf("After Rotation about Z Axis");

bar3d(midx+x1,midy-y1,midx+x2,midy-y2,5,1);

axis();

printf("After Rotation about X Axis");

bar3d(midx+50,midy-x1,midx+60,midy-x2,5,1);

axis();

printf("After Rotation about Y Axis");

bar3d(midx+x1,midy-100,midx+x2,midy-90,5,1);

getch();

closegraph();

}

OUTPUT

  Translation

  Enter Translation Factor : 50 60 70