# Program to illustrate the implementation of Rotation Transformation along a Pivot Point

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

void show_screen( );

void apply_pivot_point_rotation(const int,int [],float,const int,const int);
void multiply_matrices(const float[3],const float[3][3],float[3]);

void Polygon(const int,const int []);
void Line(const int,const int,const int,const int);

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

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

show_screen( );

int polygon_points[8]={ 250,290, 320,190, 390,290, 250,290 };

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

setcolor(15);
settextstyle(0,0,1);
outtextxy(50,400,\"*** (320,240) is taken as Pivot Point.\");
outtextxy(50,415,\"*** Use \'+\' and \'-\' Keys to apply Rotation.\");

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;

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

apply_pivot_point_rotation(4,polygon_points,5,320,240);

setcolor(10);
Polygon(4,polygon_points);
}

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

apply_pivot_point_rotation(4,polygon_points,-5,320,240);

setcolor(12);
Polygon(4,polygon_points);
}
}
while(1);

return 0;
}

//--------------------  apply_pivot_point_rotation( )  ------------------//

void apply_pivot_point_rotation(const int n,int coordinates[],
float angle,const int xr,const int yr)
{
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=(((1-cos(angle))*xr)+(yr*sin(angle)));
float temp_2=(((1-cos(angle))*yr)-(xr*sin(angle)));

float matrix_b[3][3]={ { cos(angle),sin(angle),0 } ,
{ -sin(angle),cos(angle),0 } ,
{ temp_1,temp_2,1 } };
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(const float matrix_1[3],
const float 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(const int n,const int 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(const int x_1,const int y_1,const int x_2,const int 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(140,26,485,38);

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

setcolor(11);
outtextxy(150,29,\"Rotation Transformation along Pivot Point\");

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.\");
}
```