Question

For this problem speed is pretty crucial. I’ve drawn a nice image to explain the problem better. The algorithm needs to calculate if edges of a rectangle continue within the confines of the canvas, will the edge intersect another rectangle?

We know:

1. The size of the canvas
2. The size of each rectangle
3. The position of each rectangle

The faster the solution is the better! I’m pretty stuck on this one and don’t really know where to start.

alt text http://www.freeimagehosting.net/uploads/8a457f2925.gif

Cheers

Answer 1

Just create the set of intervals for each of the X and the Y axis. Then for each new rectangle, see if there are intersecting intervals in the X or the Y axis. See here for one way of implementing the interval sets.

In your first example, the interval set on the horizontal axis would be { [0-8], [0-8], [9-10] }, and on the vertical: { [0-3], [4-6], [0-4] }

This is only a sketch, I abstracted many details here (e.g. usually one would ask an interval set/tree “which intervals overlap this one”, instead of “intersect this one”, but nothing not doable).

Edit

Please watch this related MIT lecture (it’s a bit long, but absolutely worths it).
Even if you find simpler solutions (than implementing an augmented red-black tree), it’s good to know the ideas behind these things.