Question

I have complex polygons which I know the minimum x, minimum y, maximum x and maximum y. I also have another rectangle which I know the top left and bottom right vertices. Knowing this information, how can I know if these 2 bounding boxes are colliding? Thanks

Answer 1

Try something like this:

typedef struct rect {
    int top;     // maximum y-coord
    int bottom;  // minimum y-coord
    int left;    // minimum x-coord
    int right;   // maximum x-coord
} rectangle;

// Returns 1 if the point (x, y) lies within the rectangle, 0 otherwise
int is_point_in_rectangle(rectangle r, int x, int y) {
    if ((r.left   <= x && r.right >= x) &&
        (r.bottom <= y && r.top   >= y))
        return 1;
    return 0;
}

// Returns 1 if the rectangles overlap, 0 otherwise
int do_rectangles_intersect(rectangle a, rectangle b) {
    if ( is_point_in_rectangle(a, b.left , b.top   ) ||
         is_point_in_rectangle(a, b.right, b.top   ) ||
         is_point_in_rectangle(a, b.left , b.bottom) ||
         is_point_in_rectangle(a, b.right, b.bottom))
        return 1;
    if ( is_point_in_rectangle(b, a.left , a.top   ) ||
         is_point_in_rectangle(b, a.right, a.top   ) ||
         is_point_in_rectangle(b, a.left , a.bottom) ||
         is_point_in_rectangle(b, a.right, a.bottom))
        return 1;
    return 0;
}

You can do the same for any polygon, just iterate through all of its points and call is_point_in_rectangle with them. Since you only have a bounding box for the complex polygon, there is a chance that this method gives you a false positive (that is, the rectangle is inside the complex polygon’s bounding box but outside of the polygon itself). However, this restriction applies to any method where a complex shape is simplified to a bounding box.