## Spatial Signatures: Even Faster Collision Detection?

Yes, I'm quite happy with my collision detection engine. But could it be faster? Probably!

Here's an idea I had today. Obviously, I'm obsessed with spatial hashing. It's probably my favorite thing ever. Well, what about this: take a mesh, create a spatial grid of booleans (which can, of course, be represented super-efficiently as a bit vector), then loop over every triangle in the mesh. For any spatial grid that the triangle intersects, the corresponding hash bucket gets set to true. Once this has been done for all triangles, you are left with an array of bits that represents the spatial buckets with which the mesh collides. Purely for the sake of being able to throw around cool and esoteric terminology, I'll call this array the "spatial signature" of the object.

Now, here's the fun part. In my previous technique, I looped over the vertices of one mesh, checking them against the density function of the second. The most expensive part of this check is, without a doubt, evaluating the density function. Well, instead, we could prune the possibilities by first checking the vertex against the spatial signature of the object! It's quite inexpensive to hash the vertex to a bucket in the same space as the one in which the spatial signature was created. Then, we simply check the corresponding index in the bit array. If the array indicates that no triangles intersect that spatial bucket, then there's absolutely no chance that the vertex could be colliding with the mesh. On the other hand, in the event that the bit is turned on, then we continue as before with the full-blown density check.

This is, of course, a completely untested idea, but it seems to me that the speed with which a bit array could be accessed would significantly cut down on the narrow-phase collision check, especially when dealing with complex density functions.