Hashing 2D, 3D and nD vectors

There's a spatial hash function described in Optimized Spatial Hashing for Collision Detection of Deformable Objects. They use the hash function

hash(x,y,z) = ( x p1 xor y p2 xor z p3) mod n

where p1, p2, p3 are large prime numbers, in our case 73856093, 19349663, 83492791, respectively. The value n is the hash table size.

In the paper, x, y, and z are the discretized coordinates; you could probably also use the binary values of your floats.

I have two suggestions.

• Assume a grid cell of size l and quantize the x, y and z co-ordinates by computing ix = floor(x/l), iy = floor(y/l), and iz = floor(z/l), where ix, iy and iz are integers. Now use the hash function defined in Optimized Spatial Hashing for Collision Detection of Deformable Objects

If you don't do the quantization, it wont be sensitive to closeness(locality).

• Locality Sensitive Hashing has been mentioned for hashing higher dimensional vectors. Why not use them for 3d or 2d vectors as well? A variant of LSH using adapted for Eucledian distance metric (which is what we need for 2d and 3d vectors) is called Locality Sensitive Hashing using p-stable distributions. A very readable tutorial is here.