---
_id: '5809'
abstract:
- lang: eng
  text: A discrete spherical circle is a topologically well-connected 3D circle in
    the integer space, which belongs to a discrete sphere as well as a discrete plane.
    It is one of the most important 3D geometric primitives, but has not possibly
    yet been studied up to its merit. This paper is a maiden exposition of some of
    its elementary properties, which indicates a sense of its profound theoretical
    prospects in the framework of digital geometry. We have shown how different types
    of discretization can lead to forbidden and admissible classes, when one attempts
    to define the discretization of a spherical circle in terms of intersection between
    a discrete sphere and a discrete plane. Several fundamental theoretical results
    have been presented, the algorithm for construction of discrete spherical circles
    has been discussed, and some test results have been furnished to demonstrate its
    practicality and usefulness.
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
- first_name: Valentin E.
  full_name: Brimkov, Valentin E.
  last_name: Brimkov
citation:
  ama: 'Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete
    spherical circles. In: <i>Combinatorial Image Analysis</i>. Vol 9448. Cham: Springer
    Nature; 2016:86-100. doi:<a href="https://doi.org/10.1007/978-3-319-26145-4_7">10.1007/978-3-319-26145-4_7</a>'
  apa: 'Biswas, R., Bhowmick, P., &#38; Brimkov, V. E. (2016). On the connectivity
    and smoothness of discrete spherical circles. In <i>Combinatorial image analysis</i>
    (Vol. 9448, pp. 86–100). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-26145-4_7">https://doi.org/10.1007/978-3-319-26145-4_7</a>'
  chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity
    and Smoothness of Discrete Spherical Circles.” In <i>Combinatorial Image Analysis</i>,
    9448:86–100. Cham: Springer Nature, 2016. <a href="https://doi.org/10.1007/978-3-319-26145-4_7">https://doi.org/10.1007/978-3-319-26145-4_7</a>.'
  ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness
    of discrete spherical circles,” in <i>Combinatorial image analysis</i>, vol. 9448,
    Cham: Springer Nature, 2016, pp. 86–100.'
  ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness
    of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.'
  mla: Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical
    Circles.” <i>Combinatorial Image Analysis</i>, vol. 9448, Springer Nature, 2016,
    pp. 86–100, doi:<a href="https://doi.org/10.1007/978-3-319-26145-4_7">10.1007/978-3-319-26145-4_7</a>.
  short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis,
    Springer Nature, Cham, 2016, pp. 86–100.
conference:
  end_date: 2015-11-27
  location: Kolkata, India
  name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
  start_date: 2015-11-24
date_created: 2019-01-08T20:45:19Z
date_published: 2016-01-06T00:00:00Z
date_updated: 2022-01-28T08:13:03Z
day: '06'
department:
- _id: HeEd
doi: 10.1007/978-3-319-26145-4_7
extern: '1'
intvolume: '      9448'
language:
- iso: eng
month: '01'
oa_version: None
page: 86-100
place: Cham
publication: Combinatorial image analysis
publication_identifier:
  eisbn:
  - 978-3-319-26145-4
  eissn:
  - 1611-3349
  isbn:
  - 978-3-319-26144-7
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the connectivity and smoothness of discrete spherical circles
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9448
year: '2016'
...