---
_id: '5801'
abstract:
- lang: eng
  text: Space filling circles and spheres have various applications in mathematical
    imaging and physical modeling. In this paper, we first show how the thinnest (i.e.,
    2-minimal) model of digital sphere can be augmented to a space filling model by
    fixing certain “simple voxels” and “filler voxels” associated with it. Based on
    elementary number-theoretic properties of such voxels, we design an efficient
    incremental algorithm for generation of these space filling spheres with successively
    increasing radius. The novelty of the proposed technique is established further
    through circular space filling on 3D digital plane. As evident from a preliminary
    set of experimental result, this can particularly be useful for parallel computing
    of 3D Voronoi diagrams in the digital space.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Shivam
  full_name: Dwivedi, Shivam
  last_name: Dwivedi
- first_name: Aniket
  full_name: Gupta, Aniket
  last_name: Gupta
- first_name: Siddhant
  full_name: Roy, Siddhant
  last_name: Roy
- 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: 'Dwivedi S, Gupta A, Roy S, Biswas R, Bhowmick P. Fast and Efficient Incremental
    Algorithms for Circular and Spherical Propagation in Integer Space. In: <i>20th
    IAPR International Conference</i>. Vol 10502. Cham: Springer Nature; 2017:347-359.
    doi:<a href="https://doi.org/10.1007/978-3-319-66272-5_28">10.1007/978-3-319-66272-5_28</a>'
  apa: 'Dwivedi, S., Gupta, A., Roy, S., Biswas, R., &#38; Bhowmick, P. (2017). Fast
    and Efficient Incremental Algorithms for Circular and Spherical Propagation in
    Integer Space. In <i>20th IAPR International Conference</i> (Vol. 10502, pp. 347–359).
    Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-66272-5_28">https://doi.org/10.1007/978-3-319-66272-5_28</a>'
  chicago: 'Dwivedi, Shivam, Aniket Gupta, Siddhant Roy, Ranita Biswas, and Partha
    Bhowmick. “Fast and Efficient Incremental Algorithms for Circular and Spherical
    Propagation in Integer Space.” In <i>20th IAPR International Conference</i>, 10502:347–59.
    Cham: Springer Nature, 2017. <a href="https://doi.org/10.1007/978-3-319-66272-5_28">https://doi.org/10.1007/978-3-319-66272-5_28</a>.'
  ieee: S. Dwivedi, A. Gupta, S. Roy, R. Biswas, and P. Bhowmick, “Fast and Efficient
    Incremental Algorithms for Circular and Spherical Propagation in Integer Space,”
    in <i>20th IAPR International Conference</i>, Vienna, Austria, 2017, vol. 10502,
    pp. 347–359.
  ista: 'Dwivedi S, Gupta A, Roy S, Biswas R, Bhowmick P. 2017. Fast and Efficient
    Incremental Algorithms for Circular and Spherical Propagation in Integer Space.
    20th IAPR International Conference. DGCI: International Conference on Discrete
    Geometry for Computer Imagery, LNCS, vol. 10502, 347–359.'
  mla: Dwivedi, Shivam, et al. “Fast and Efficient Incremental Algorithms for Circular
    and Spherical Propagation in Integer Space.” <i>20th IAPR International Conference</i>,
    vol. 10502, Springer Nature, 2017, pp. 347–59, doi:<a href="https://doi.org/10.1007/978-3-319-66272-5_28">10.1007/978-3-319-66272-5_28</a>.
  short: S. Dwivedi, A. Gupta, S. Roy, R. Biswas, P. Bhowmick, in:, 20th IAPR International
    Conference, Springer Nature, Cham, 2017, pp. 347–359.
conference:
  end_date: 2017-09-21
  location: Vienna, Austria
  name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
  start_date: 2017-09-19
date_created: 2019-01-08T20:42:22Z
date_published: 2017-08-22T00:00:00Z
date_updated: 2022-01-27T15:34:25Z
day: '22'
doi: 10.1007/978-3-319-66272-5_28
extern: '1'
intvolume: '     10502'
language:
- iso: eng
month: '08'
oa_version: None
page: 347-359
place: Cham
publication: 20th IAPR International Conference
publication_identifier:
  eisbn:
  - 978-3-319-66272-5
  eissn:
  - 1611-3349
  isbn:
  - 978-3-319-66271-8
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation
  in Integer Space
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10502
year: '2017'
...
---
_id: '5802'
abstract:
- lang: eng
  text: This papers introduces a definition of digital primitives based on focal points
    and weighted distances (with positive weights). The proposed definition is applicable
    to general dimensions and covers in its gamut various regular curves and surfaces
    like circles, ellipses, digital spheres and hyperspheres, ellipsoids and k-ellipsoids,
    Cartesian k-ovals, etc. Several interesting properties are presented for this
    class of digital primitives such as space partitioning, topological separation,
    and connectivity properties. To demonstrate further the potential of this new
    way of defining digital primitives, we propose, as extension, another class of
    digital conics defined by focus-directrix combination.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Eric
  full_name: Andres, Eric
  last_name: Andres
- 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: 'Andres E, Biswas R, Bhowmick P. Digital primitives defined by weighted focal
    set. In: <i>20th IAPR International Conference</i>. Vol 10502. Cham: Springer
    Nature; 2017:388-398. doi:<a href="https://doi.org/10.1007/978-3-319-66272-5_31">10.1007/978-3-319-66272-5_31</a>'
  apa: 'Andres, E., Biswas, R., &#38; Bhowmick, P. (2017). Digital primitives defined
    by weighted focal set. In <i>20th IAPR International Conference</i> (Vol. 10502,
    pp. 388–398). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-66272-5_31">https://doi.org/10.1007/978-3-319-66272-5_31</a>'
  chicago: 'Andres, Eric, Ranita Biswas, and Partha Bhowmick. “Digital Primitives
    Defined by Weighted Focal Set.” In <i>20th IAPR International Conference</i>,
    10502:388–98. Cham: Springer Nature, 2017. <a href="https://doi.org/10.1007/978-3-319-66272-5_31">https://doi.org/10.1007/978-3-319-66272-5_31</a>.'
  ieee: E. Andres, R. Biswas, and P. Bhowmick, “Digital primitives defined by weighted
    focal set,” in <i>20th IAPR International Conference</i>, Vienna, Austria, 2017,
    vol. 10502, pp. 388–398.
  ista: 'Andres E, Biswas R, Bhowmick P. 2017. Digital primitives defined by weighted
    focal set. 20th IAPR International Conference. DGCI: International Conference
    on Discrete Geometry for Computer Imagery, LNCS, vol. 10502, 388–398.'
  mla: Andres, Eric, et al. “Digital Primitives Defined by Weighted Focal Set.” <i>20th
    IAPR International Conference</i>, vol. 10502, Springer Nature, 2017, pp. 388–98,
    doi:<a href="https://doi.org/10.1007/978-3-319-66272-5_31">10.1007/978-3-319-66272-5_31</a>.
  short: E. Andres, R. Biswas, P. Bhowmick, in:, 20th IAPR International Conference,
    Springer Nature, Cham, 2017, pp. 388–398.
conference:
  end_date: 2017-09-21
  location: Vienna, Austria
  name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
  start_date: 2017-09-19
date_created: 2019-01-08T20:42:39Z
date_published: 2017-08-22T00:00:00Z
date_updated: 2022-01-27T15:38:35Z
day: '22'
doi: 10.1007/978-3-319-66272-5_31
extern: '1'
intvolume: '     10502'
language:
- iso: eng
month: '08'
oa_version: None
page: 388-398
place: Cham
publication: 20th IAPR International Conference
publication_identifier:
  eisbn:
  - 978-3-319-66272-5
  eissn:
  - 1611-3349
  isbn:
  - 978-3-319-66271-8
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Digital primitives defined by weighted focal set
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10502
year: '2017'
...