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~ Integer dilation and contraction are functions used in conjunction with quadtree and octree mapping systems. Dilation is the process of inserting a number of zeros before each bit in a word and contraction is the process of removing those zeros. Present methods of dilation and contraction involve lookup tables which consume considerable amounts of memory for mappings of large or high resolution display devices but are very fast under practical limits. A method is proposed which rivals the speed of the tabular methods but eliminates the tables, thereby eliminating the associated memory consumption. The proposed method is applicable to both dilation and contraction for both quadtrees and octrees.

Explicit formulas are presented to generate the coordinates of a point on the two-dimensional Hilbert curve from its location code and vice versa. Execution-time assessments suggest that the proposed algorithms are faster than the ones published previously.

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