pymorton

Ordinal hashing of multidimensonal data and geographic coordinates via Morton coding / Z-ordering.

In mathematical analysis and computer science, Z-order, Morton-order, or a Morton-code is a function which maps multidimensional data to one dimension while preserving locality of the data points. It was introduced in 1966 by IBM researcher, G. M. Morton. The z-value of a point in multidimensions is calculated by interleaving the binary representations of its coordinate values. Once the data are sorted into this ordering, any one-dimensional data structure can be used, such as binary search trees, B-trees, skip lists, or hash tables. The resulting ordering can equivalently be described as the order one would achieve from a depth-first traversal of a quadtree, where {x, y, ..., K} are combined into a single ordinal value that is easily compared, searched, and indexed against other Morton numbers.