# include <iostream.h>
 # include <graphics.h>
 # include    <conio.h>
 # include     <math.h>


 void show_screen( );

 void apply_arbitrary_direction_scaling(constint,int [],
                         constfloat,constfloat,float);
 void multiply_matrices(constfloat[3],constfloat[3][3],float[3]);

 void Polygon(constint,constint []);
 void Line(constint,constint,constint,constint);


 int main( )
    {
       int driver=VGA;
       int mode=VGAHI;

       initgraph(&driver,&mode,"..\\Bgi");

       show_screen( );

       int polygon_points[10]={ 270,290, 270,190, 370,190, 370,290, 270,290 };

       setcolor(15);
     Polygon(5,polygon_points);

       setcolor(15);
       settextstyle(0,0,1);
     outtextxy(50,400,"*** 45 is taken as arbitrary direction.");
     outtextxy(50,415,"*** Use '+' and '-' Keys to apply Scaling.");

       int key_code=0;

       char Key=NULL;

       do
      {
         Key=NULL;
         key_code=0;

         Key=getch( );
         key_code=int(Key);

         if(key_code==0)
        {
           Key=getch( );
           key_code=int(Key);
        }

         if(key_code==27)
        break;

         elseif(key_code==43)
        {
           setfillstyle(1,0);
             bar(40,70,600,410);

           apply_arbitrary_direction_scaling(5,polygon_points,
                                 1.2,1.1,45);

           setcolor(10);
             Polygon(5,polygon_points);
        }

         elseif(key_code==45)
        {
           setfillstyle(1,0);
             bar(40,70,600,410);

           apply_arbitrary_direction_scaling(5,polygon_points,
                                 0.8,0.9,45);

           setcolor(12);
             Polygon(5,polygon_points);
        }
      }
       while(1);

       return 0;
    }


 /*************************************************************************///----------------  apply_arbitrary_direction_scaling( )  ---------------///*************************************************************************/void apply_arbitrary_direction_scaling(constint n,int coordinates[],
                       constfloat Sx,constfloat Sy,
                                float angle)
    {
       angle*=(M_PI/180);

       for(int count_1=0;count_1<n;count_1++)
      {
         float matrix_a[3]={coordinates[(count_1*2)],
                         coordinates[((count_1*2)+1)],1};

         float temp_1=((Sx*pow(cos(angle),2))+(Sy*pow(sin(angle),2)));
         float temp_2=((Sy-Sx)*sin(angle*cos(angle)));
         float temp_3=((Sx*pow(sin(angle),2))+(Sy*pow(cos(angle),2)));

         float matrix_b[3][3]={ { temp_1,temp_2,0 } ,
                    { temp_2,temp_3,0 } ,
                         { 0,0,1 } };
         float matrix_c[3]={0};

         multiply_matrices(matrix_a,matrix_b,matrix_c);

         coordinates[(count_1*2)]=(int)(matrix_c[0]+0.5);
         coordinates[((count_1*2)+1)]=(int)(matrix_c[1]+0.5);
      }
    }

 /************************************************************************///----------------------  multiply_matrices( )  ------------------------///************************************************************************/void multiply_matrices(constfloat matrix_1[3],
                   constfloat matrix_2[3][3],float matrix_3[3])
    {
       for(int count_1=0;count_1<3;count_1++)
      {
         for(int count_2=0;count_2<3;count_2++)
        matrix_3[count_1]+=
               (matrix_1[count_2]*matrix_2[count_2][count_1]);
      }
    }

 /*************************************************************************///-----------------------------  Polygon( )  ----------------------------///*************************************************************************/void Polygon(constint n,constint coordinates[])
    {
       if(n>=2)
      {
         Line(coordinates[0],coordinates[1],
                         coordinates[2],coordinates[3]);

         for(int count=1;count<(n-1);count++)
        Line(coordinates[(count*2)],coordinates[((count*2)+1)],
                        coordinates[((count+1)*2)],
                        coordinates[(((count+1)*2)+1)]);
      }
    }

 /*************************************************************************///-------------------------------  Line( )  -----------------------------///*************************************************************************/void Line(constint x_1,constint y_1,constint x_2,constint y_2)
    {
       int color=getcolor( );

       int x1=x_1;
       int y1=y_1;

       int x2=x_2;
       int y2=y_2;

       if(x_1>x_2)
      {
         x1=x_2;
         y1=y_2;

         x2=x_1;
         y2=y_1;
      }

       int dx=abs(x2-x1);
       int dy=abs(y2-y1);
       int inc_dec=((y2>=y1)?1:-1);

       if(dx>dy)
      {
         int two_dy=(2*dy);
         int two_dy_dx=(2*(dy-dx));
         int p=((2*dy)-dx);

         int x=x1;
         int y=y1;

         putpixel(x,y,color);

         while(x<x2)
        {
           x++;

           if(p<0)
              p+=two_dy;

           else
              {
             y+=inc_dec;
             p+=two_dy_dx;
              }

           putpixel(x,y,color);
        }
      }

       else
      {
         int two_dx=(2*dx);
         int two_dx_dy=(2*(dx-dy));
         int p=((2*dx)-dy);

         int x=x1;
         int y=y1;

         putpixel(x,y,color);

         while(y!=y2)
        {
           y+=inc_dec;

           if(p<0)
              p+=two_dx;

           else
              {
             x++;
             p+=two_dx_dy;
              }

           putpixel(x,y,color);
        }
      }
    }

 /*************************************************************************///--------------------------  show_screen( )  ---------------------------///*************************************************************************/void show_screen( )
    {
       setfillstyle(1,1);
     bar(114,26,516,38);

       settextstyle(0,0,1);
     setcolor(15);
       outtextxy(5,5,"******************************************************************************");
       outtextxy(5,17,"*-**************************************************************************-*");
       outtextxy(5,29,"*-----------                                                     ------------*");
       outtextxy(5,41,"*-**************************************************************************-*");
       outtextxy(5,53,"*-**************************************************************************-*");

     setcolor(11);
       outtextxy(122,29,"Scaling Transformation along Arbitrary Direction");

     setcolor(15);

       for(int count=0;count<=30;count++)
          outtextxy(5,(65+(count*12)),"*-*                                                                        *-*");

       outtextxy(5,438,"*-**************************************************************************-*");
       outtextxy(5,450,"*-------------------------                          -------------------------*");
       outtextxy(5,462,"******************************************************************************");

     setcolor(12);
       outtextxy(229,450,"Press any Key to exit.");
    }

 /*************************************************************************//*************************************************************************///-----------------------------  THE END  -------------------------------///*************************************************************************//*************************************************************************/