How can you calculate the percentage overlap of two rectangles?

Question

I wrote a drawing function that draws various on-screen sprites. These sprites can only overlap up to a point. If they have to much overlap, they become too obscured. As a result I need to detect when these sprites are too much overlapped. Luckily, the problem is simplified in that the sprites can be treated as orthogonal rectangles. I'd like to know by how much these rectangles overlap. Right now, I just brute force it by testing each pixel in one rectangle to see if the other contains it. I count these and calculate the percentage overlap. I think there's probably a better, less brute force approach. What algorithm can I use to determine this?

I'm using wxwidgets.

Answer 1

The results depends on how you define overlapping percentage, to keep it symmetric, I would code it like this:

double CalculatePercentOverlap(const wxRect& rect1, const wxRect& rect2)
{
  wxRect inter = rect1.Intersect(rect2);
  if (inter.IsEmpty())
    return 0;
  return (double)(inter.GetWidth()*inter.GetHeight()) * 2.0 /
    (double)(rect1.GetWidth()*rect1.GetHeight() + 
             rect2.GetWidth()*rect2.GetHeight());
}