Perfect spatial hashing

Abstract

We explore using hashing to pack sparse data into a compact table while retaining efficient random access. Specifically, we design a perfect multidimensional hash function -- one that is precomputed on static data to have no hash collisions. Because our hash function makes a single reference to a small offset table, queries always involve exactly two memory accesses and are thus ideally suited for parallel SIMD evaluation on graphics hardware. Whereas prior hashing work strives for pseudorandom mappings, we instead design the hash function to preserve spatial coherence and thereby improve runtime locality of reference. We demonstrate numerous graphics applications including vector images, texture sprites, alpha channel compression, 3D-parameterized textures, 3D painting, simulation, and collision detection.

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Index Terms

• Computing methodologies

  • Computer graphics

    • Graphics systems and interfaces

    • Image manipulation

      • Texturing

    • Shape modeling

  • Parallel computing methodologies

• Theory of computation

  • Randomness, geometry and discrete structures