The coordinate system on the screen is left-handed, i.e. the x coordinate increases from left to right and the y coordinate increases from top to bottom. The origin, O(0, 0) is at the upper left corner of the screen.
A clockwise rotation around the origin of a point with coordinates (x, y) is given by the following equations:
where (x', y') are the coordinates of the point after rotation and angle theta, the angle of rotation (needs to be in radians, i.e. multiplied by: PI / 180).
To perform rotation around a point different from the origin O(0,0), let's say point A(a, b) (pivot point). Firstly we translate the point to be rotated, i.e. (x, y) back to the origin, by subtracting the coordinates of the pivot point, (x - a, y - b). Then we perform the rotation and get the new coordinates (x', y') and finally we translate the point back, by adding the coordinates of the pivot point to the new coordinates (x' + a, y' + b).
Following the above description:
a 2D clockwise theta degrees rotation of point (x, y) around point (a, b) is:
Using your function prototype: (x, y) -> (p.x, p.y); (a, b) -> (cx, cy); theta -> angle:
POINT rotate_point(float cx, float cy, float angle, POINT p){
return POINT(cos(angle) * (p.x - cx) - sin(angle) * (p.y - cy) + cx,
sin(angle) * (p.x - cx) + cos(angle) * (p.y - cy) + cy);
}