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);
}
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Two-Dimension Transformation In Homogeneous Coordinate

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