article
From prima quadraginta octant to lattice sphere through primitive integer operations
published
yes
Ranita
Biswas
author 3C2B033E-F248-11E8-B48F-1D18A9856A870000-0002-5372-7890
Partha
Bhowmick
author
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.
Elsevier2015
eng
Theoretical Computer Science
0304-397510.1016/j.tcs.2015.11.018
624456-72
yes
Biswas R, Bhowmick P. 2015. From prima quadraginta octant to lattice sphere through primitive integer operations. Theoretical Computer Science. 624(4), 56–72.
R. Biswas, P. Bhowmick, Theoretical Computer Science 624 (2015) 56–72.
Biswas, Ranita, and Partha Bhowmick. “From Prima Quadraginta Octant to Lattice Sphere through Primitive Integer Operations.” <i>Theoretical Computer Science</i>, vol. 624, no. 4, Elsevier, 2015, pp. 56–72, doi:<a href="https://doi.org/10.1016/j.tcs.2015.11.018">10.1016/j.tcs.2015.11.018</a>.
R. Biswas and P. Bhowmick, “From prima quadraginta octant to lattice sphere through primitive integer operations,” <i>Theoretical Computer Science</i>, vol. 624, no. 4, pp. 56–72, 2015.
Biswas R, Bhowmick P. From prima quadraginta octant to lattice sphere through primitive integer operations. <i>Theoretical Computer Science</i>. 2015;624(4):56-72. doi:<a href="https://doi.org/10.1016/j.tcs.2015.11.018">10.1016/j.tcs.2015.11.018</a>
Biswas, Ranita, and Partha Bhowmick. “From Prima Quadraginta Octant to Lattice Sphere through Primitive Integer Operations.” <i>Theoretical Computer Science</i> 624, no. 4 (2015): 56–72. <a href="https://doi.org/10.1016/j.tcs.2015.11.018">https://doi.org/10.1016/j.tcs.2015.11.018</a>.
Biswas, R., & Bhowmick, P. (2015). From prima quadraginta octant to lattice sphere through primitive integer operations. <i>Theoretical Computer Science</i>, <i>624</i>(4), 56–72. <a href="https://doi.org/10.1016/j.tcs.2015.11.018">https://doi.org/10.1016/j.tcs.2015.11.018</a>
58042019-01-08T20:44:06Z2019-01-24T13:22:46Z