---
_id: '5810'
abstract:
- lang: eng
  text: A discrete spherical geodesic path between two voxels s and t lying on a discrete
    sphere is a/the 1-connected shortest path from s to t, comprising voxels of the
    discrete sphere intersected by the real plane passing through s, t, and the center
    of the sphere. We show that the set of sphere voxels intersected by the aforesaid
    real plane always contains a 1-connected cycle passing through s and t, and each
    voxel in this set lies within an isothetic distance of 32 from the concerned plane.
    Hence, to compute the path, the algorithm starts from s, and iteratively computes
    each voxel p of the path from the predecessor of p. A novel number-theoretic property
    and the 48-symmetry of discrete sphere are used for searching the 1-connected
    voxels comprising the path. The algorithm is output-sensitive, having its time
    and space complexities both linear in the length of the path. It can be extended
    for constructing 1-connected discrete 3D circles of arbitrary orientations, specified
    by a few appropriate input parameters. Experimental results and related analysis
    demonstrate its efficiency and versatility.
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 Finding Spherical Geodesic Paths and Circles in ℤ3.
    2014;8668:396-409. doi:<a href="https://doi.org/10.1007/978-3-319-09955-2_33">10.1007/978-3-319-09955-2_33</a>
  apa: 'Biswas, R., &#38; Bhowmick, P. (2014). On Finding Spherical Geodesic Paths
    and Circles in ℤ3. Presented at the DGCI: International Conference on Discrete
    Geometry for Computer Imagery, Berlin, Heidelberg: Springer. <a href="https://doi.org/10.1007/978-3-319-09955-2_33">https://doi.org/10.1007/978-3-319-09955-2_33</a>'
  chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Finding Spherical Geodesic Paths
    and Circles in ℤ3.” Lecture Notes in Computer Science. Berlin, Heidelberg: Springer,
    2014. <a href="https://doi.org/10.1007/978-3-319-09955-2_33">https://doi.org/10.1007/978-3-319-09955-2_33</a>.'
  ieee: R. Biswas and P. Bhowmick, “On Finding Spherical Geodesic Paths and Circles
    in ℤ3,” vol. 8668. Springer, Berlin, Heidelberg, pp. 396–409, 2014.
  ista: Biswas R, Bhowmick P. 2014. On Finding Spherical Geodesic Paths and Circles
    in ℤ3. 8668, 396–409.
  mla: Biswas, Ranita, and Partha Bhowmick. <i>On Finding Spherical Geodesic Paths
    and Circles in ℤ3</i>. Vol. 8668, Springer, 2014, pp. 396–409, doi:<a href="https://doi.org/10.1007/978-3-319-09955-2_33">10.1007/978-3-319-09955-2_33</a>.
  short: R. Biswas, P. Bhowmick, 8668 (2014) 396–409.
conference:
  end_date: 2014-09-12
  location: Siena, Italy
  name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
  start_date: 2014-09-10
date_created: 2019-01-08T20:45:32Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2019-01-24T13:22:49Z
doi: 10.1007/978-3-319-09955-2_33
extern: '1'
intvolume: '      8668'
language:
- iso: eng
oa_version: None
page: 396-409
place: Berlin, Heidelberg
publication_identifier:
  isbn:
  - '9783642387081'
  - '9783642387098'
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer
quality_controlled: '1'
series_title: Lecture Notes in Computer Science
status: public
title: On Finding Spherical Geodesic Paths and Circles in ℤ3
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8668
year: '2014'
...