a simple 2D rectangle collision algorithm that also determines which sides that the rectangles collide?

Question

I initially tried out implementing rectangular intersection, which works well. However, when I have to apply the physics system, such as velocity, acceleration, and directional vectors, I would have to find a way to determine which side of the rectangles collide. Now, in my system, there is no rotated rectangle, so this simplified the problem. However, I couldn't find an easy way to determine which rectangle side collided. I have once deal with this problem before but failed miserably.

What I did in the past is determine the distance between each parallel rectangular sides and check if the distance is close to 0 (use some initially defined distance range) or is 0. However, for floating-point arithmetic, this proves to be unstable because of unknown time elapse. Sometime, the rectangles would actually intersect each other before it meets the defined range.

On the other hand, I was thinking about spawning multiple rectangles, each rectangle for each sides. However, after thinking again, it would be the same thing as having a parallel side with distance range checking, just that that distance range is the width of each mini-rectangle.

Therefore, any suggestion to this problem?

Answer 1

Adapted from my answer to "Which Side Was Hit?":

I suggest computing the Minkowski sum of B and A, which is a new rectangle, and checking where the centre of rectangle A lies relatively to that new rectangle (to know whether a collision is happening) and to its diagonals (to know where the collision is happening):

float w = 0.5 * (A.width() + B.width());
float h = 0.5 * (A.height() + B.height());
float dx = A.centerX() - B.centerX();
float dy = A.centerY() - B.centerY();

if (abs(dx) <= w && abs(dy) <= h)
{
    /* collision! */
    float wy = w * dy;
    float hx = h * dx;

    if (wy > hx)
        if (wy > -hx)
            /* collision at the top */
        else
            /* on the left */
    else
        if (wy > -hx)
            /* on the right */
        else
            /* at the bottom */
}