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

Next TopicHomogeneous Coordinates

2d transformation 3d computer graphics 3d transformation animation techniques cathode ray tube circle generation algorithm color crt monitors computer animation computer graphics tutorial crt curves display processor flat panel display fractals introduction keyframing line generation algorithm polygon filling algorithm random scan display raster scan display surfaces types of curves viewing and clipping

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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