How Do You Rotate a Point Around Another Point in 2D Space?

Rotating a Point around Another Point in Two Dimensions

This article addresses the challenge of calculating the rotation of a point around another point in two dimensions. The task arises in the development of a card game where cards are fanned out. Allegro API's al_draw_rotated_bitmap function facilitates easy card fanning, but it hinders mouse interaction by obscuring the cards underneath. To address this, a polygon collision test is proposed, which requires the rotation of the card's four points.

The solution lies in utilizing a rotation function that performs the following operations:

1. Subtract the pivot point from the point's coordinates.
2. Rotate the point counterclockwise.
3. Add the pivot point back to the point's coordinates.

This function, rotate_point, is implemented as follows:

POINT rotate_point(float cx, float cy, float angleInRads, POINT p)
{
  float s = sin(angleInRads);
  float c = cos(angleInRads);

  // translate point back to origin:
  p.x -= cx;
  p.y -= cy;

  // rotate point
  float xnew = p.x * c - p.y * s;
  float ynew = p.x * s + p.y * c;

  // translate point back:
  p.x = xnew + cx;
  p.y = ynew + cy;

  return p;
}

By implementing this function, the four points of the card can be rotated to determine which card is beneath the mouse, enabling effective mouse interaction in the card game.

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