How Do I Rotate a Point Around a Fixed Point in 2D?

Rotating Points About a Fixed Point in 2D

In order to create a realistic card-fanning effect in a card game, it is necessary to transform the coordinates of the card points to align with the rotation angle. The Allegro API provides a convenient function for rotating bitmaps, but understanding the underlying mathematical operations is crucial for collision detection purposes.

Rotation Transformation Algorithm

To rotate a point (x, y) about a fixed point (cx, cy) by an angle θ, follow these steps:

1. Subtract the Pivot Point: Subtract the x and y coordinates of the pivot point from the coordinates of the point to be rotated:

   dx = x - cx
   dy = y - cy

2. Apply Rotation Matrix: Apply the rotation matrix to rotate the point by angle θ:

   x_new = dx * cos(θ) - dy * sin(θ)
   y_new = dx * sin(θ) + dy * cos(θ)

3. Add the Pivot Point Back: Add the x and y coordinates of the pivot point back to the transformed coordinates:

   x = x_new + cx
   y = y_new + cy

Implementation

Using this algorithm, here is a C-like function to perform the rotation:

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;
}

Using this function, you can now rotate the points of the card to perform the collision detection for the mouse click events.

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