How do I Rotate a 2D Point Around Another Point?

Rotating a Point about Another Point (2D)

To determine the points that define a shape for collision detection, it is necessary to rotate the points around a pivot point. In this case, the pivot point is the center of the shape.

To rotate a point p around another point (cx, cy) by an angle angle in radians, follow these steps:

1. Translate the point back to the origin by subtracting (cx, cy):

   p.x -= cx;
   p.y -= cy;

2. Rotate the point counter-clockwise:

   float xnew = p.x * cos(angle) - p.y * sin(angle);
   float ynew = p.x * sin(angle) + p.y * cos(angle);

3. Translate the point back by adding (cx, cy):

   p.x = xnew + cx;
   p.y = ynew + cy;

Using this method, you can rotate any point around any other point and determine the shape of an object for collision detection.

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