How to Rotate a Point Around Another Point in 2D Space?

Rotation of a Point around Another Point in 2D Space

In a bid to create a card game where cards fan out, an individual encounters a predicament in determining which card lies beneath the cursor. This quandary demands a means of rotating the card's four vertex points to form a polygon for collision detection.

To facilitate this rotation, the Allegro API provides a convenient function:

al_draw_rotated_bitmap(OBJECT_TO_ROTATE, CENTER_X, CENTER_Y, X, Y, DEGREES_TO_ROTATE_IN_RADIANS)

However, to calculate the rotated points manually, it becomes necessary to devise a function:

POINT rotate_point(float cx, float cy, float angle, POINT p)

where (cx, cy) represents the pivot point, angle denotes the counterclockwise rotation angle, and p is the original point to be rotated.

The essence of the solution lies in carrying out the following steps:

1. Translate the point back to the origin, resulting in p.x -= cx and p.y -= cy.

2. Perform the rotation utilizing the equations:

   • xnew = p.x * cos(angle) - p.y * sin(angle)
   • ynew = p.x * sin(angle) p.y * cos(angle)
3. Translate the point back to its original coordinates via p.x = xnew cx and p.y = ynew cy.

By applying this approach, the function can effectively rotate a point around any pivot point on a 2D plane.

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