---
_id: '5806'
abstract:
- lang: eng
  text: Although the concept of functional plane for naive plane is studied and reported
    in the literature in great detail, no similar study is yet found for naive sphere.
    This article exposes the first study in this line, opening up further prospects
    of analyzing the topological properties of sphere in the discrete space. We show
    that each quadraginta octant Q of a naive sphere forms a bijection with its projected
    pixel set on a unique coordinate plane, which thereby serves as the functional
    plane of Q, and hence gives rise to merely mono-jumps during back projection.
    The other two coordinate planes serve as para-functional and dia-functional planes
    for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds
    neither of the two. Owing to this, the quadraginta octants form symmetry groups
    and subgroups with equivalent jump conditions. We also show a potential application
    in generating a special class of discrete 3D circles based on back projection
    and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry,
    uniqueness, and bounded distance from the underlying real sphere and real plane.
alternative_title:
- LNCS
article_processing_charge: No
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. On functionality of quadraginta octants of naive sphere
    with application to circle drawing. In: <i>Discrete Geometry for Computer Imagery</i>.
    Vol 9647. Cham: Springer Nature; 2016:256-267. doi:<a href="https://doi.org/10.1007/978-3-319-32360-2_20">10.1007/978-3-319-32360-2_20</a>'
  apa: 'Biswas, R., &#38; Bhowmick, P. (2016). On functionality of quadraginta octants
    of naive sphere with application to circle drawing. In <i>Discrete Geometry for
    Computer Imagery</i> (Vol. 9647, pp. 256–267). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-32360-2_20">https://doi.org/10.1007/978-3-319-32360-2_20</a>'
  chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta
    Octants of Naive Sphere with Application to Circle Drawing.” In <i>Discrete Geometry
    for Computer Imagery</i>, 9647:256–67. Cham: Springer Nature, 2016. <a href="https://doi.org/10.1007/978-3-319-32360-2_20">https://doi.org/10.1007/978-3-319-32360-2_20</a>.'
  ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive
    sphere with application to circle drawing,” in <i>Discrete Geometry for Computer
    Imagery</i>, Nantes, France, 2016, vol. 9647, pp. 256–267.
  ista: 'Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive
    sphere with application to circle drawing. Discrete Geometry for Computer Imagery.
    DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS,
    vol. 9647, 256–267.'
  mla: Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants
    of Naive Sphere with Application to Circle Drawing.” <i>Discrete Geometry for
    Computer Imagery</i>, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:<a href="https://doi.org/10.1007/978-3-319-32360-2_20">10.1007/978-3-319-32360-2_20</a>.
  short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer
    Nature, Cham, 2016, pp. 256–267.
conference:
  end_date: 2016-04-20
  location: Nantes, France
  name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
  start_date: 2016-04-18
date_created: 2019-01-08T20:44:37Z
date_published: 2016-04-09T00:00:00Z
date_updated: 2022-01-28T08:10:11Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/978-3-319-32360-2_20
extern: '1'
intvolume: '      9647'
language:
- iso: eng
month: '04'
oa_version: None
page: 256-267
place: Cham
publication: Discrete Geometry for Computer Imagery
publication_identifier:
  eisbn:
  - 978-3-319-32360-2
  isbn:
  - 978-3-319-32359-6
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On functionality of quadraginta octants of naive sphere with application to
  circle drawing
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9647
year: '2016'
...