---
_id: '5804'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Ranita
  full_name: Biswas, Ranita
  id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
  last_name: Biswas
  orcid: 0000-0002-5372-7890
- first_name: Partha
  full_name: Bhowmick, Partha
  last_name: Bhowmick
citation:
  ama: 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>
  apa: Biswas, R., &#38; Bhowmick, P. (2015). From prima quadraginta octant to lattice
    sphere through primitive integer operations. <i>Theoretical Computer Science</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.tcs.2015.11.018">https://doi.org/10.1016/j.tcs.2015.11.018</a>
  chicago: Biswas, Ranita, and Partha Bhowmick. “From Prima Quadraginta Octant to
    Lattice Sphere through Primitive Integer Operations.” <i>Theoretical Computer
    Science</i>. Elsevier, 2015. <a href="https://doi.org/10.1016/j.tcs.2015.11.018">https://doi.org/10.1016/j.tcs.2015.11.018</a>.
  ieee: 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. Elsevier, pp. 56–72, 2015.
  ista: Biswas R, Bhowmick P. 2015. From prima quadraginta octant to lattice sphere
    through primitive integer operations. Theoretical Computer Science. 624(4), 56–72.
  mla: 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>.
  short: R. Biswas, P. Bhowmick, Theoretical Computer Science 624 (2015) 56–72.
date_created: 2019-01-08T20:44:06Z
date_published: 2015-04-18T00:00:00Z
date_updated: 2021-01-12T08:03:36Z
day: '18'
doi: 10.1016/j.tcs.2015.11.018
extern: '1'
intvolume: '       624'
issue: '4'
language:
- iso: eng
month: '04'
oa_version: None
page: 56-72
publication: Theoretical Computer Science
publication_identifier:
  issn:
  - 0304-3975
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: From prima quadraginta octant to lattice sphere through primitive integer operations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 624
year: '2015'
...