COMPOSITE THREE – DIMENSIONAL TRANSFORMATION

COMPOSITE THREE – DIMENSIONAL TRANSFORMATION

Aim :

To write a C++ program to perform composite 3D transformations such as translation,

rotation, scaling, reflection and shearing.

Algorithm:

Step 1: Start the program.

Step 2: input the points for the cude and size of the Cube.

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

Step 4: Get the choice from the user.

Step 5: 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 tx,ty and tz specifying translation distances.

x'=x+ tx ,y'=y+ ty,z'=z+ tz

Step 6: If the choice is 2 the scaling transformation of a position P can be written as P'=S.P

where scaling parameters sx,sy and sz are assigned any positive values.

x'=x.sx ,y'=y.sy ,z'=z.sz

Step 7: If the choice is 3 get the rotation angle. Rotate the figure with respect to the axis of rotation.

Step 8: About z axis rotation x'=xcosӨ-ysinӨ ,y'=xsinӨ+ycosӨ

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

Step 9: About x axis rotation y'=ycosӨ-zsinӨ z'=ysinӨ+zcosӨ x'=x

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

Step 10: About y axis rotation z'=zcosӨ-xsinӨ x'=zsinӨ+xcosӨ y'=y

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

Step 11: If choice is 4 exit the program.

Step 12: Stop the program.

PROGRAM:

#include<iostream.h>

#include<graphics.h>

#include<math.h>

#include<conio.h>

#include<stdlib.h>

class cube

{

 public:

 void drawcube(int x1[],int y1[])

 {

 int i;

 for(i=0;i<4;i++)

 {

 if(i<3)

 line(x1[i],y1[i],x1[i+1],y1[i+1]);

 line(x1[0],y1[0],x1[3],y1[3]);

 }

 for(i=4;i<8;i++)

 {

 if(i<7)

 line(x1[i],y1[i],x1[i+1],y1[i+1]);

 line(x1[4],y1[4],x1[7],y1[7]);

 }

 for(i=0;i<4;i++)

 {

 line(x1[i],y1[i],x1[i+4],y1[i+4]);

 }

}

};

void main()

{

 int

i,x1[8],y1[8],x2[8],y2[8],z1[8],x3[8],y3[8],z3[8],x4[8],y4[8],theta,op,ch,tx,ty,tz,s

x,sy,sz,xf,yf,zf,x,y,z,size;

 int driver=DETECT;

 int mode;

 initgraph(&driver,&mode,"C:\\tc++\bgi");

 cout<<"enter the points on the cube:";

 cin>>x>>y>>z;

 cout<<"enter the size of the edge:";

 cin>>size;

 x1[0]=x1[3]=x;

 x1[1]=x1[2]=x+size;

 x1[4]=x1[7]=x;

 x1[5]=x1[6]=x+size;

 y1[0]=y1[1]=y;

 y1[2]=y1[3]=y+size;

 y1[4]=y1[5]=y;

 y1[6]=y1[7]=y+size;

 z1[1]=z1[2]=z1[3]=z1[0]=z ;

 z1[4]=z1[5]=z1[6]=z1[7]=z-size;

 for(i=0;i<8;i++)

 {

 x2[i]=x1[i]+z1[i]/2;

 y2[i]=y1[i]+z1[i]/2;

 }

 cube c;

 getch();

 cleardevice();

 do

 {

 cout<<"menu"<<endl;

 cout<<"\n1.translation\n2.rotation\n3.scaling\n4.exit\n";

 cout<<"enter the choice:";

 cin>>ch;

 switch(ch)

 {

 case 1:

 cout<<"enter the translation vector:";

 cin>>tx>>ty>>tz;

 for(i=0;i<8;i++)

 {

 x3[i]=x1[i]+tx;

 y3[i]=y1[i]+ty;

 z3[i]=z1[i]+tz;

 }

 for(i=0;i<8;i++)

 {

 x4[i]=x3[i]+z3[i]/2;

 y4[i]=y3[i]+z3[i]/2;

 }

 cleardevice();

 cout<<"before translation";

 c.drawcube(x2,y2);

 getch();

 cleardevice();

 cout<<"after translation";

 c.drawcube(x4,y4);

 getch();

 cleardevice();

 break;

 case 2:

 cout<<"enter the rotation angle:";

 cin>>theta;

 theta=(theta*3.14)/180;

 cout<<"enter the direction"<<endl;

cout<<"1.rotation about x axis"<<endl<<"2.rotation about y

axis"<<endl<<"3.rotation about z axis"; cin>>op;

 if(op==1)

 {

 for(i=0;i<8;i++)

 {

 x3[i]=x1[i];

 y3[i]=y1[i]*cos(theta)-z1[i]*sin(theta);

 z3[i]=y1[i]*sin(theta)+z1[i]*cos(theta);

 }

 }

 else

 if(op==2)

 {

 for(i=0;i<8;i++)

 {

 y3[i]=y1[i];

 x3[i]=z1[i]*cos(theta)-x1[i]*sin(theta);

 x3[i]=z1[i]*sin(theta)+x1[i]*cos(theta);

 }

 }

 else

 if(op==3)

 {

 for(i=0;i<8;i++)

 {

 z3[i]=z1[i];

 x3[i]=x1[i]*cos(theta)-y1[i]*sin(theta);

 y3[i]=x1[i]*sin(theta)+y1[i]*cos(theta);

 }

 }

 else

 cout<<"enter correct option";

 for(i=0;i<8;i++)

 {

 x4[i]=x3[i]+z3[i]/2;

 y4[i]=y3[i]+z3[i]/2;

 }

 cleardevice();

 cout<<"before rotation";

 c.drawcube(x2,y2);

 getch();

 cleardevice();

 cout<<"after rotation";

 c.drawcube(x4,y4);

 getch();

 cleardevice();

 break;

 case 3:

 cout<<"enter the scaling factor:";

 cin>>sx>>sy>>sz;

 cout<<"enter the reference point:";

 cin>>xf>>yf>>zf;

 for(i=0;i<8;i++)

 {

 x3[i]=xf+(x1[i]*sx)+xf*(1-sx);

 y3[i]=yf+(y1[i]*sy)+yf*(1-sy);

 z3[i]=zf+(z1[i]*sz)+zf*(1-sz);

 }

 for(i=0;i<8;i++)

 {

 x4[i]=x3[i]+z3[i]/2;

 y4[i]=y3[i]+z3[i]/2;

 }

 cleardevice();

 cout<<"before scaling";

 c.drawcube(x2,y2);

 getch();

 cleardevice();

 cout<<"after scaling";

 c.drawcube(x4,y4);

 getch();

 cleardevice();

 break;

 case 4:

 exit(0);

 break;

 }

 }

 while(op!=4);

 getch();

}

OUTPUT :

Enter the points in the cube : 100 100 100

Enter the Size of Edge : 50

MENU

1.Translation

2.Rotation

3.scaling

4.exit

Enter your choice : 1

Enter the Translation Vector 5 10 15