One-dimensional orderings Transformation from d-dimensional grid locations to 1-dimensional points Mostly, from 2-dimensional regular square grid of size Also called space-filling curves Desirable properties   Curve passes through each location once and only once   Both transformation and inverse operations are simple   Stable, i.e., relative ordering is preserved when resolution is changed   Degree of locality is high, i.e., two neighbors in d dimensions are neighbors along the curve and vice versa   Admissible, i.e., one d-dimensional neighbor in each of the directions is already encountered