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:
-
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
-
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)
-
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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