TY - JOUR
AB - 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.
AU - Biswas, Ranita
AU - Bhowmick, Partha
ID - 5804
IS - 4
JF - Theoretical Computer Science
SN - 0304-3975
TI - From prima quadraginta octant to lattice sphere through primitive integer operations
VL - 624
ER -