# 2D Transformations: Rotation

Levels of difficulty: / perform operation:

### Function:

```void rotate( int figure[], int edges, double angle, int cx, int cy ) {
double x, y;
angle = -1 * (angle*3.14/180);
double cos_a = cos(angle);
double sin_a = sin(angle);
for (int i=0; i < edges; i++) {
x = figure[2*i] - cx;
y = figure[2*i+1] - cy;
figure[2*i] = floor( (x * cos_a) - (y * sin_a) + cx + 0.5 );
figure[2*i+1] = floor( (x * sin_a)+(y * cos_a) + cy + 0.5 );
}
}
```

### C Program

```#include<graphics.h>
#include<stdio.h>
#include<conio.h>
#include<math.h>
void rotate( int figure[], int edges, double angle, int cx, int cy ) {
double x, y;
angle = -1 * (angle*3.14/180);
double cos_a = cos(angle);
double sin_a = sin(angle);
for (int i=0; i < edges; i++) {
x = figure[2*i] - cx;
y = figure[2*i+1] - cy;
figure[2*i] = ceil( (x * cos_a) - (y * sin_a) + cx );
figure[2*i+1] = ceil( (x * sin_a)+(y * cos_a) + cy );
}
}
void main() {
int figure[20], edges;
// A Figure with Max 10 edges.
double angle;
int cx=0, cy=0;
int gd = DETECT, gm;
initgraph( &gd, &gm, "" );
int max_y = getmaxy();
clrscr();
cleardevice();
printf( "Number of edges: " );
scanf( "%d", &edges );
for (int i=0; i < edges; i++) {
printf( "Enter edge (x%d,y%d) : ", i , i );
scanf( "%d %d", &figure[2*i], &figure[2*i+1] );
}
figure[2*i] = figure[0];
figure[2*i+1] = figure[1];
edges += 1;
printf( "Enter angle of rotation in degrees: ");
scanf( "%lf", &angle);
printf( "Enter the center of rotation: \n");
printf( "cx: ");
scanf( "%d", &cx);
printf( "cy: ");
scanf( "%d", &cy);
cy = max_y - cy;
cleardevice();
setbkcolor(WHITE);
setcolor(GREEN);
setlinestyle(SOLID_LINE, 0, 3);
drawpoly( edges, figure );
getch();
for (int i=0; i < edges; i++)
figure[2*i+1] = max_y - figure[2*i+1];
rotate(figure,edges,angle,cx,cy);
for (int i=0; i < edges; i++)
figure[2*i+1] = max_y - figure[2*i+1];
setcolor(RED);
drawpoly( edges, figure );
getch();
}
```