Matrix Representation of 2D Transformation

Program to implement 2-D Transformations:

  #include<iostream.h>  #include<conio.h>  #include<math.h>  #include<stdlib.h>  #include<conio.h>  class trans  {  float x[20],y[20],xm,ym,ref[2][2],shx,shy;  int i,j,k,n;  float sx,sy,tx,ty,ang;  int gd,gm;  float xtmp [20],ytmp[20];  public:  void takeinput();  void menu();  void graphmode();  void mapgraph();  void plotint();  void translate();  void scale();  void rotate();  void reflect();  void shear();  void plotfinal();  };  int ch;  void trans::takeinput()  {  cout<<“ENTER THE NO OF VERTICESn”;  cin>>n;  for (i=0;i<n;i++)  {  cout<<“ENTER THE “<<i+1<<“COORDINATES n”;  cin>>x[i]>>y[i];  }  clrscr();  }  void trans::menu()  {  int kk;  cout<<“n1:TRANSLATION”;  cout<<“n2:SCALING”;  cout<<“n3:ROTATION”;  cout<<“n4:REFLECTION”;  cout<<“n5:SHEARING”;  cout<<“n6:EXIT”;  cin>>ch;  switch (ch)  {  case1:  cout<<“n ENTER TX AND TY”;  cin>>tx>>ty;  break;  case2:  cout<<“n ENTER SX AND SY”;  cin>>sx>>sy;  break;  case3:  cout<<“n ENTER ANGLE OF ROTATION”;  cin>>ang;  break;  case4:  cout<<“n REFLECTION MENU”;  cout<<“n 1:X-PLANE”;  cout<<“n 2: Y-PLANE”;  cout<<“n 3: ORIGIN”;  cout<<“n 4: Y=X PLANE”;  cout<<“n 5: Y=-X PLANE”;  cout<<“n ENTER YOUR CHOICE”;  cin>>kk;  switch (kk)  {  case1:           ref [0][0] =1;  ref [0][1]=0;  ref [1][0]=0;  ref [1][1]=1;  break;  case2:  ref [0][0]= -1;  ref [0][1]=0;  ref [1][0]=0;  ref [1][1]=1;  break;  case3:  ref [0][0]=-1;  ref [0][1]=0;  ref [1][0]=0;  ref [1][1]=1;  break;  case4:  ref [0][0]=0;  ref [0][1]=1;  ref [1][0] =1;  ref [1][1]=0;  break;  case5:  ref [0][0]=0;  ref [0][1]=1;  ref [1][0]=1;  ref [1][1]=0;  break;  case5:  cout<< “n SHEARING MENU”;  cout<<“n 1:X-DIRn 2: Y-DIR n 3: X-Y DIRn ENTER YOUR CHOICE”;  cin>>kk;  switch (kk)  {  case1:  cout<<“n ENTER SHX”;  cin>> shx;  ref[0][0] =1;  ref [0][1]=0;  ref [1][0]=shx;  ref [1][1]=1;  break;  case2:  cout<< “n ENTER SHY”;  cin>>shy;  ref [0][0]=1;  ref [0][1]=shy;  ref [1][0]=0;  ref [1][1] =1;  break;  case3:  cout<<“n ENTER SHX”;  cin >> shx;  cout<<“n ENTER SHY”;  cin>> shy;  ref [0][0] =1;  ref [0][1] =shy;  ref [1][0] =shx;  ref [1][1] =1;  break;  }  break;  }  }  void trans::graphmode()  {  gd=DETECT;  initgraph (&gd, &gm, “”);  }  void trans::mapgraph()  {  xm=getmaxx ()/2;  ym=getmaxy ()/2;  line (xm,0,xm,2*ym);  line (0,ym,2 * xm,ym);  }  void trans::plotint()  {  for(i=0;i<n-1;i++)  {  circle (x[i] +xm,-y[i]+ym,2)  circle x [n-1]+xm,(-y[n-1]+ym),2;  line (x[i]+xm,(-y[i]+ym),x[i+1]+xm,(-y[i+1]+ym));  }  line (x[n-1]+xm,(-y[n-1]+ym,)x[0]+xm,(-y[0]+ym));  }  void trans::translate()  {  for(i=0;i<n;i++)  {  xtmp[i]=x[i]+tx;  ytmp[i]=y[i]+ty;  }  }  void trans::plotfinal()  {  for (i=0;i<n-1;i++)  {  circle (xtmp[i]+xm, (-ytmp[i]+ym,2);  circle (xtmp[n-1]+xm,(-ytmp[n-1]+ym),2);  line (xtmp[i]+xm,(-ytmp[i]+ym),xtmp[i+1]+xm,(-ytmp[i+1]+ym));  }  line (xtmp[n-1]+xm,(-ytmp[n-1]+ym),xtmp[0]+xm,(-ytmp[0]+ym));  }  void trans::scale()  {  float s [2][2],mxy[7][2],rxy[7][2];  s [0][0]=sx;  s [0][1]=0;  s [1][0]=0;  s [1][1]=sy;  tx=-x[0];  ty=-y[0];  translate ();  k=0;  for(i=0;i<n;i++)  {  j=0;  mxy[i][j]=xtmp[k];  mxy[i][j+1]=ytmp[k];  k++;  }  for (i=0;i<n;i++)  {  for(j=0;j<2;j++)  {  rxy[i][j]=0;  for(k=0;k<2;k++)  {  rxy[i][j]+=mxy[i][k]*s[k][j];  }  }  }  j=0;  k=0;  for(i=0;i<n;i++)  {  j=0;  x[k]=rxy[i][j];  y[k]=rxy[i][j+1];  k++;  }  tx=-tx;  ty=-ty;  translate();  }  void trans::rotate()  {  float r[2][2],mxy[7][2],rxy[7][2],tmp;  tmp=22/7;  tmp=(tmp*ang)/180;  r[0][0]=cos(tmp);  r[0][1]=sin(tmp);  r[1][0]=cos(tmp);  r[1][1]=sy;  tx=-x[0];  ty=-y[0];  translate ();  k=0;  for (i=0;i<n;i++)        {  j=0;  mxy[i][j]=xtmp[k];  mxy[i][j+1]=ytmp[k];  k++;        }  for (i=0;i<n;i++)  {  for (j=0;j<2;j++)  {  rxy[i][j]=0;  for (k=0;k<2;k++)  {  rxy[i][j]+=mxy[i][k]*r[k][j];  }  }  }  j=0;  k=0;  for(i=0;i<n;i++)  {  j=0;  x[k]=rxy[i][j];  y[k]=rxy[i][j+1];  k++;  }  tx=-tx;  ty=-ty;  translate();  }  void trans::reflect()  {  float mxy[7][2],rxy[7][2],tmp;  tx=0;  ty=0;  translate();  k=0;  for(i=0;i<n;i++)  {  j=0;  mxy[i][j]=xtmp[k];  mxy[i][j+1]=ytmp[k];  k++;  }  for(i=0;i<n;i++)  {  for(j=0;j<2;j++)  {  rxy[i][j]=0;  for(k=0;k<2;k++)  {  rxy[i][j]|+=mxy[i][k]*r[k][j];  }  }  }  j=0;  k=0;  for(i=0;i<n;i++)  {  j=0;  x[k]=rxy[i][j];  y[k]=rxy[i][j+1];  k++;  }  tx=-tx;  ty=-ty;  translate();  }  void trans::shear()  {  float mxy[7][2],rxy[7][2],tmp;  tx=0;  ty=0;  translate ();  k=0;  for(i=0;i<n;i++)  {  j=0;  mxy[i][j]=xtmp[k];  mxy[i][j+1]=ytmp[k];  k++;  }  for(i=0;i<n;i++)  {  for(j=0;j<2;j++)  {  rxy[i][j]=0;  for (k=0;k<2;k++)  {  rxy[i][j]|+=mxy[i][k]*r[k][j];  }  }  }  j=0;  k=0;  for(i=0;i<n;i++)  {  j=0;  x[k]=rxy[i][j];  y[k]=rxy[i][j+1];  k++;  }  tx=-tx;  ty=-ty;  translate ();  }  void main()  {  clrscr ();  trans t1;  t1.takeinput ();  t1.menu ();  t1.graphmode ();  t1.mapgraph ();  t1.plotint ();  switch (ch)  {  case1:  t1.translate ();  break;  case2:  t1.scale ();  break ();  case3:  t1.rotate ();  break;  case4:  t1.reflect ();  break;  case5:  t1.shear ();  break;  case6:  exit ();  }  getch ();  t1.plotfinal ();  getch ();  closegraph ();  }  

Output:

Translate

1: TRANSLATION
2: SCALING
3: ROTATION
4: REFLECTION
5: SHEARING
6: EXIT
ENTER YOUR CHOICE 4
REFLECTION MENU
1: X-PLANE
2: Y-PLANE
3: ORIGIN
4: Y=X PLANE
5: Y=-X PLANE
ENTER YOUR CHOICE 4
1: TRANSLATION
2: SCALING
3: ROTATION
4: REFLECTION
5: SHEARING
6: EXIT
ENTER YOUR CHOICE 5
SHEARING MENU
1: X-DIR
2: Y-DIR
ENTER YOUR CHOICE 3

ENTER SHX 5
ENTER SHY 5
ENTER THE NO OF VERTICES
5
ENTER THE 1 COORDINATES
10 10
ENTER THE 2 COORDINATES
30 10
ENTER THE 3 COORDINATES
40 20
ENTER THE 4 COORDINATES
35 30
ENTER THE 5 COORDINATES
15 20
1: TRANSLATION
2: SCALING
3: ROTATION
4: REFLECTION
5: SHEARING
6: EXIT
ENTER YOUR CHOICE 1
ENTER TX AND TY 10 10

Matrix Representation of 2D Transformation

Next TopicHomogeneous Coordinates

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Matrix Representation of 2D Transformation

Matrix Representation of 2D Transformation

Program to implement 2-D Transformations:

Application of Computer Graphics

FTP Commands

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