A fast distance approximation algorithm for encoded quadtree locations

Several distance approximation functions to the Euclidean distance of two points in the two-dimensional Euclidean plane are reviewed. An improved distance function is proposed and compared with previous ones as to their maximum relative errors and their execution times. The improved distance function is then applied for distance calculations in the domain of linear quadtrees using dilated integer arithmetic. The maximum relative error is discussed and execution times are reported.<
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