C++ program for Two-Dimension Transformation In Homogeneous Coordinate

Two-Dimension Transformation In Homogeneous Coordinate

This Program Deals With All Two-D Transformation Such As Translation, Scaling, Rotation,

Reflection, Shearing In Homogeneous Coordinates.

Code :

//TwoDimensional Transformations In Homogeneous

#include<graphics.h>

#include<iostream.h>

#include<math.h>

#include<conio.h>

#define MAXSIZE 3

class D_2

{

private:

double Points[MAXSIZE][MAXSIZE];

void Mult(double [MAXSIZE][MAXSIZE]);

void MultTwoMat(double [MAXSIZE][MAXSIZE],double [MAXSIZE][MAXSIZE]);

void Print();

int x,y;

public:

D_2();

void initialize();

void GetPoints();

void Draw(int);

void DrawCord();

void Translate();

void Rotate();

void Reflect();

void Display(double[MAXSIZE][MAXSIZE]);

void Shear();

void Scale_Fixed();

void Scale_Dir();

};

D_2::D_2()

{

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i == (MAXSIZE-1))

Points[i][j] = 1;

else

Points[i][j] = 0;

}

}

initialize();

x = getmaxx();

y = getmaxy();

}

void D_2::initialize()

{

int gdrive = DETECT,gmode;

initgraph(&gdrive,&gmode,"c: c gi");

}

void D_2::GetPoints()

{

closegraph();

cout<<"Enter The Points Of The Triangle.

";

for(int j=0;j<MAXSIZE;j++)

{

cout<<"Enter Point "<<j+1<<":-";

for(int i=0;i<MAXSIZE-1;i++)

{

cout<<"

Enter "<<char(i+'X')<<": ";

cin>>Points[i][j];

}

}

initialize();

}

void D_2::Mult(double temp[MAXSIZE][MAXSIZE])

{

int i,j,k;

double z[MAXSIZE][MAXSIZE];

for(i=0;i<MAXSIZE;i++)

{

for(j=0;j<MAXSIZE;j++)

z[i][j]=0;

}

for(i=0;i<MAXSIZE;i++)

{

for(j=0;j<MAXSIZE;j++)

{

for(k=0;k<MAXSIZE;k++)

z[i][j]=z[i][j]+(temp[i][k] * Points[k][j]);

}

}

for(i=0;i<MAXSIZE;i++)

{

for(j=0;j<MAXSIZE;j++)

{

Points[i][j] = z[i][j];

}

}

}

void D_2::Draw(int color)

{

int Poly[2*MAXSIZE+2];

int k = 0;

if(color == GREEN)

DrawCord();

for(int j=0;j<MAXSIZE;j++)

{

for(int i=0;i<MAXSIZE-1;i++)

{

if(i==0)

Poly[k++] = x/2+Points[i][j];

else

Poly[k++] = y/2-Points[i][j];

}

}

Poly[k++] = Poly[0];

Poly[k] = Poly[1];

setcolor(color);

drawpoly(4,Poly);

}

void D_2::Display(double Mat[MAXSIZE][MAXSIZE])

{

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

cout<<Mat[i][j]<<" ";

}

cout<<"

";

}

}

void D_2::Print()

{

setcolor(GREEN);

setfillstyle(SOLID_FILL,GREEN);

fillellipse(19,36,2,2);

outtextxy(23,34," Original Triangle");

setcolor(MAGENTA);

setfillstyle(SOLID_FILL,MAGENTA);

fillellipse(x-178,y-32,2,2);

outtextxy(x-175,y-34," Tranformed Triangle");

}

void D_2::DrawCord()

{

setcolor(12);

line(x/2,0,x/2,y);

line(0,y/2,x,y/2);

setcolor(10);

setfillstyle(SOLID_FILL,10);

fillellipse(x/2,y/2,2,2);

for(int i=(x/2+50),j=(x/2-50);i<=x,j>=0;i=i+50,j=j-50)

{

fillellipse(i,y/2,2,2);

fillellipse(j,y/2,2,2);

}

for(i=(y/2+50),j=(y/2-50);i<=x,j>=0;i=i+50,j=j-50)

{

fillellipse(x/2,i,2,2);

fillellipse(x/2,j,2,2);

}

outtextxy(x/2+3,y/2+4,"0");

outtextxy(x/2+45,y/2+5,"50");

outtextxy(x/2+95,y/2+5,"100");

outtextxy(x/2+145,y/2+5,"150");

outtextxy(x/2+195,y/2+5,"200");

outtextxy(x/2+245,y/2+5,"250");

outtextxy(x/2+295,y/2+5,"300");

outtextxy(x/2-65,y/2+5,"-50");

outtextxy(x/2-115,y/2+5,"-100");

outtextxy(x/2-165,y/2+5,"-150");

outtextxy(x/2-215,y/2+5,"-200");

outtextxy(x/2-265,y/2+5,"-250");

outtextxy(x/2-315,y/2+5,"-300");

outtextxy(x/2+5,y/2+45,"-50");

outtextxy(x/2+5,y/2+95,"-100");

outtextxy(x/2+5,y/2+145,"-150");

outtextxy(x/2+5,y/2+195,"-200");

outtextxy(x/2+5,y/2-50,"50");

outtextxy(x/2+5,y/2-100,"100");

outtextxy(x/2+5,y/2-150,"150");

outtextxy(x/2+5,y/2-200,"200");

}

void D_2::MultTwoMat(double temp[MAXSIZE][MAXSIZE],double

temp1[MAXSIZE][MAXSIZE])

{

int i,j,k;

double z[MAXSIZE][MAXSIZE];

for(i=0;i<MAXSIZE;i++)

{

for(j=0;j<MAXSIZE;j++)

z[i][j]=0;

}

for(i=0;i<MAXSIZE;i++)

{

for(j=0;j<MAXSIZE;j++)

{

for(k=0;k<MAXSIZE;k++)

z[i][j]=z[i][j]+(temp[i][k] * temp1[k][j]);

}

}

for(i=0;i<MAXSIZE;i++)

{

for(j=0;j<MAXSIZE;j++)

{

temp1[i][j] = z[i][j];

}

}

}

void D_2::Translate()

{

int Tx,Ty;

double Trans[MAXSIZE][MAXSIZE];

closegraph();

cout<<"Enter Translation Factor Along X-Axis: ";

cin>>Tx;

cout<<"Enter Translation Factor Along Y-Axis: ";

cin>>Ty;

initialize();

for(int j=0;j<MAXSIZE;j++)

{

for(int i=0;i<MAXSIZE;i++)

{

if(i==j)

Trans[i][j] = 1;

else

Trans[i][j] = 0;

}

}

Trans[0][MAXSIZE-1] = Tx;

Trans[1][MAXSIZE-1] = Ty;

Draw(GREEN);

Mult(Trans);

Draw(MAGENTA);

Print();

}

void D_2::Rotate()

{

double ang;

const double PI = 22.0/7;

double xr,yr;

double TransMat[MAXSIZE][MAXSIZE];

double RotMat[MAXSIZE][MAXSIZE];

double InvTransMat[MAXSIZE][MAXSIZE];

closegraph();

cout<<"Enter Angle Of Rotation: ";

cin>>ang;

cout<<"Enter Point Of Rotation:

X: ";

cin>>xr;

cout<<"

Y: ";

cin>>yr;

initialize();

ang = (PI * ang)/180.0;

setcolor(YELLOW);

setfillstyle(SOLID_FILL,YELLOW);

fillellipse(x/2+xr,y/2-yr,2,2);

outtextxy(x/2+xr,y/2-yr-2," Point Of Rotation");

//Transformation Matrix

//Translate arbitrary point to origin then rotate then translate back.

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i == j)

{

TransMat[i][j] = 1;

InvTransMat[i][j] = 1;

RotMat[i][j] = 1;

}

else

{

TransMat[i][j] = 0;

InvTransMat[i][j] = 0;

RotMat[i][j] = 0;

}

}

}

TransMat[0][2] = -xr;

TransMat[1][2] = -yr;

InvTransMat[0][2] = xr;

InvTransMat[1][2] = yr;

RotMat[0][0] = cos(ang);

RotMat[0][1] = -sin(ang);

RotMat[1][0] = sin(ang);

RotMat[1][1] = cos(ang);

Draw(GREEN);

Print();

MultTwoMat(InvTransMat,RotMat);

MultTwoMat(RotMat,TransMat);

Mult(TransMat);

Draw(MAGENTA);

}

void D_2::Reflect()

{

double ang;

double a,b,c;

double xr,yr;

double TransMat[MAXSIZE][MAXSIZE];

double RotMat[MAXSIZE][MAXSIZE];

double InvTransMat[MAXSIZE][MAXSIZE];

double InvRotMat[MAXSIZE][MAXSIZE];

double RefMat[MAXSIZE][MAXSIZE];

closegraph();

cout<<"Enter The Line (ax+by+c=0): ";

cout<<"

a: ";

cin>>a;

cout<<"

b: ";

cin>>b;

cout<<"

c: ";

cin>>c;

if(b!=0)

{

yr = (-c/b);

xr = 0;

double m = -a/b;

ang = atan(m);

}

else

{

yr = 0;

xr = (-c/a);

ang = 22.0/14.0; // Angle = PI/2

}

initialize();

//Transformation Matrix

//Translate arbitrary point to origin then rotate then translate back.

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i == j)

{

TransMat[i][j] = 1;

InvTransMat[i][j] = 1;

RotMat[i][j] = 1;

InvRotMat[i][j] = 1;

RefMat[i][j] = 1;

}

else

{

TransMat[i][j] = 0;

InvTransMat[i][j] = 0;

RotMat[i][j] = 0;

InvRotMat[i][j] = 0;

RefMat[i][j] = 0;

}

}

}

TransMat[0][2] = -xr;

TransMat[1][2] = -yr;

InvTransMat[0][2] = xr;

InvTransMat[1][2] = yr;

RotMat[0][0] = cos(ang);

RotMat[0][1] = sin(ang);

RotMat[1][0] = -sin(ang);

RotMat[1][1] = cos(ang);

InvRotMat[0][0] = cos(ang);

InvRotMat[0][1] = -sin(ang);

InvRotMat[1][0] = sin(ang);

InvRotMat[1][1] = cos(ang);

for(i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i==j)

RefMat[i][j] = pow(-1,i)*1;

else

RefMat[i][j] = 0;

}

}

Print();

Draw(GREEN);

MultTwoMat(InvTransMat,InvRotMat);

MultTwoMat(InvRotMat,RefMat);

MultTwoMat(RefMat,RotMat);

MultTwoMat(RotMat,TransMat);

Mult(TransMat);

Draw(MAGENTA);

}

void D_2::Shear()

{

double ang;

double a,b,c;

double xr,yr,shx;

double TransMat[MAXSIZE][MAXSIZE];

double RotMat[MAXSIZE][MAXSIZE];

double InvTransMat[MAXSIZE][MAXSIZE];

double InvRotMat[MAXSIZE][MAXSIZE];

double ShearMat[MAXSIZE][MAXSIZE];

closegraph();

cout<<"Enter The Line (ax+by+c=0): ";

cout<<"

a: ";

cin>>a;

cout<<"

b: ";

cin>>b;

cout<<"

c: ";

cin>>c;

cout<<"Enter Shearing Factor Along X-Axis: ";

cin>>shx;

if(b!=0)

{

yr = (-c/b);

xr = 0;

double m = -a/b;

ang = atan(m);

}

else

{

yr = 0;

xr = (-c/a);

ang = 22.0/14.0; // Angle = PI/2

}

initialize();

//Transformation Matrix

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i == j)

{

TransMat[i][j] = 1;

InvTransMat[i][j] = 1;

RotMat[i][j] = 1;

InvRotMat[i][j] = 1;

ShearMat[i][j] = 1;

}

else

{

TransMat[i][j] = 0;

InvTransMat[i][j] = 0;

RotMat[i][j] = 0;

InvRotMat[i][j] = 0;

ShearMat[i][j] = 0;

}

}

}

TransMat[0][2] = -xr;

TransMat[1][2] = -yr;

InvTransMat[0][2] = xr;

InvTransMat[1][2] = yr;

RotMat[0][0] = cos(ang);

RotMat[0][1] = sin(ang);

RotMat[1][0] = -sin(ang);

RotMat[1][1] = cos(ang);

InvRotMat[0][0] = cos(ang);

InvRotMat[0][1] = -sin(ang);

InvRotMat[1][0] = sin(ang);

InvRotMat[1][1] = cos(ang);

ShearMat[0][1] = shx;

Print();

Draw(GREEN);

MultTwoMat(InvTransMat,InvRotMat);

MultTwoMat(InvRotMat,ShearMat);

MultTwoMat(ShearMat,RotMat);

MultTwoMat(RotMat,TransMat);

Mult(TransMat);

Draw(MAGENTA);

}

void D_2::Scale_Fixed()

{

double sx,sy;

double xr,yr;

double TransMat[MAXSIZE][MAXSIZE];

double ScaleMat[MAXSIZE][MAXSIZE];

double InvTransMat[MAXSIZE][MAXSIZE];

closegraph();

cout<<"Enter The Scaling Factor Along X-Axis: ";

cin>>sx;

cout<<"Enter The Scaling Factor Along Y-Axis: ";

cin>>sy;

cout<<"Enter Point Of Scaling:

X: ";

cin>>xr;

cout<<"

Y: ";

cin>>yr;

initialize();

//Transformation Matrix

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i == j)

{

TransMat[i][j] = 1;

InvTransMat[i][j] = 1;

ScaleMat[i][j] = 1;

}

else

{

TransMat[i][j] = 0;

InvTransMat[i][j] = 0;

ScaleMat[i][j] = 0;

}

}

}

TransMat[0][2] = -xr;

TransMat[1][2] = -yr;

InvTransMat[0][2] = xr;

InvTransMat[1][2] = yr;

ScaleMat[0][0] = sx;

ScaleMat[1][1] = sy;

Draw(GREEN);

Print();

MultTwoMat(InvTransMat,ScaleMat);

MultTwoMat(ScaleMat,TransMat);

Mult(TransMat);

Draw(MAGENTA);

}

void D_2::Scale_Dir()

{

double sx,sy;

double ang;

const double PI = 22.0/7;

double RotMat[MAXSIZE][MAXSIZE];

double ScaleMat[MAXSIZE][MAXSIZE];

double InvRotMat[MAXSIZE][MAXSIZE];

closegraph();

cout<<"Enter The Scaling Factor Along X-Axis: ";

cin>>sx;

cout<<"Enter The Scaling Factor Along Y-Axis: ";

cin>>sy;

cout<<"Enter The Direction Of Scaling: ";

cin>>ang;

ang = (PI * ang)/180.0;

initialize();

//Transformation Matrix

for(int i=0;i<MAXSIZE;i++)

{

for(int j=0;j<MAXSIZE;j++)

{

if(i == j)

{

RotMat[i][j] = 1;

InvRotMat[i][j] = 1;

ScaleMat[i][j] = 1;

}

else

{

RotMat[i][j] = 0;

InvRotMat[i][j] = 0;

ScaleMat[i][j] = 0;

}

}

}

RotMat[0][0] = cos(ang);

RotMat[0][1] = sin(ang);

RotMat[1][0] = -sin(ang);

RotMat[1][1] = cos(ang);

InvRotMat[0][0] = cos(ang);

InvRotMat[0][1] = -sin(ang);

InvRotMat[1][0] = sin(ang);

InvRotMat[1][1] = cos(ang);

ScaleMat[0][0] = sx;

ScaleMat[1][1] = sy;

Draw(GREEN);

Print();

MultTwoMat(RotMat,ScaleMat);

MultTwoMat(ScaleMat,InvRotMat);

Mult(InvRotMat);

Draw(MAGENTA);

}

void main()

{

D_2 D1;

D1.DrawCord();

getch();

int ch;

D1.GetPoints();

D1.Draw(GREEN);

getch();

do

{

closegraph();

clrscr();

cout<<"1.To ReDraw The Triangle.

";

cout<<"2.Translate The Triangle.

";

cout<<"3.Scaling The Triangle About Fixed Point.

";

cout<<"4.Scaling The Triangle In A Direction.

";

cout<<"5.Rotating The Triangle About Arbitrary Point.

";

cout<<"6.Reflecting The Triangle About Arbitrary Line.

";

cout<<"7.Shearing Of The Triangle.

";

cout<<"8.Exit.

";

cout<<"Enter The Choice: ";

cin>>ch;

D1.initialize();

switch(ch)

{

case 1:

D1.GetPoints();

D1.Draw(GREEN);

getch();

break;

case 2:

cleardevice();

D1.Translate();

getch();

closegraph();

break;

case 3:

cleardevice();

D1.Scale_Fixed();

getch();

closegraph();

break;

case 4:

cleardevice();

D1.Scale_Dir();

getch();

closegraph();

break;

case 5:

cleardevice();

D1.Rotate();

getch();

closegraph();

break;

case 6:

cleardevice();

D1.Reflect();

getch();

closegraph();

break;

case 7:

cleardevice();

D1.Shear();

getch();

closegraph();

break;

case 8:

return;

default:

cout<<"

WRONG CHOICE.

";

getch();

break;

}

}while(1);

}