10.1016/j.tcs.2015.11.018
Biswas, Ranita
Ranita
Biswas0000-0002-5372-7890
Bhowmick, Partha
Partha
Bhowmick
From prima quadraginta octant to lattice sphere through primitive integer operations
Elsevier
2015
2019-01-08T20:44:06Z
2019-01-24T13:22:46Z
journal_article
https://research-explorer.app.ist.ac.at/record/5804
https://research-explorer.app.ist.ac.at/record/5804.json
0304-3975
We present here the first integer-based algorithm for constructing a well-defined lattice sphere specified by integer radius and integer center. The algorithm evolves from a unique correspondence between the lattice points comprising the sphere and the distribution of sum of three square numbers in integer intervals. We characterize these intervals to derive a useful set of recurrences, which, in turn, aids in efficient computation. Each point of the lattice sphere is determined by resorting to only a few primitive operations in the integer domain. The symmetry of its quadraginta octants provides an added advantage by confining the computation to its prima quadraginta octant. Detailed theoretical analysis and experimental results have been furnished to demonstrate its simplicity and elegance.