Z-order Curve
In mathematical analysis and computer science, Z-order, Morton order, or 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 G. M. Morton. The z-value of a point in multidimensions is simply 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 (with low significant bits truncated) hash tables. The resulting ordering can equivalently be described as the order one would get from a depth-first traversal of a quadtree; because of its close connection with quadtrees, the Z-ordering can be used to efficiently construct quadtrees and related higher dimensional data structures.
Read more about Z-order Curve: Coordinate Values, Efficiently Building Quadtrees, Use With One-dimensional Data Structures For Range Searching, Related Structures, Applications in Linear Algebra
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