---
_id: '13134'
abstract:
- lang: eng
text: We propose a characterization of discrete analytical spheres, planes and lines
in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently
proposed alternative compact coordinate system, in which each integer triplet
addresses some voxel in the grid. We define spheres and planes through double
Diophantine inequalities and investigate their relevant topological features,
such as functionality or the interrelation between the thickness of the objects
and their connectivity and separation properties. We define lines as the intersection
of planes. The number of the planes (up to six) is equal to the number of the
pairs of faces of a BCC voxel that are parallel to the line.
acknowledgement: The first author has been partially supported by the Ministry of
Science, Technological Development and Innovation of the Republic of Serbia through
the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG
Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’,
Austrian Science Fund (FWF), grant no. I 02979-N35.
article_number: '109693'
article_processing_charge: No
article_type: original
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical
objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10).
doi:10.1016/j.patcog.2023.109693
apa: Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023).
Discrete analytical objects in the body-centered cubic grid. Pattern Recognition.
Elsevier. https://doi.org/10.1016/j.patcog.2023.109693
chicago: Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and
Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern
Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693.
ieee: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete
analytical objects in the body-centered cubic grid,” Pattern Recognition,
vol. 142, no. 10. Elsevier, 2023.
ista: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical
objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693.
mla: Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic
Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693.
short: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition
142 (2023).
date_created: 2023-06-18T22:00:45Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2023-10-10T07:37:16Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.patcog.2023.109693
external_id:
isi:
- '001013526000001'
intvolume: ' 142'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa_version: None
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Pattern Recognition
publication_identifier:
issn:
- 0031-3203
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete analytical objects in the body-centered cubic grid
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 142
year: '2023'
...
---
_id: '13182'
abstract:
- lang: eng
text: "We characterize critical points of 1-dimensional maps paired in persistent
homology\r\ngeometrically and this way get elementary proofs of theorems about
the symmetry\r\nof persistence diagrams and the variation of such maps. In particular,
we identify\r\nbranching points and endpoints of networks as the sole source of
asymmetry and\r\nrelate the cycle basis in persistent homology with a version
of the stable marriage\r\nproblem. Our analysis provides the foundations of fast
algorithms for maintaining a\r\ncollection of sorted lists together with its persistence
diagram."
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This
project has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme, grant no. 788183,
from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and
from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of
this paper thank anonymous reviewers for their constructive criticism and Monika
Henzinger for detailed comments on an earlier version of this paper.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera Di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera Di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization
of the persistence of 1D maps. Journal of Applied and Computational Topology.
2023. doi:10.1007/s41468-023-00126-9
apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M.
(2023). Geometric characterization of the persistence of 1D maps. Journal of
Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.”
Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00126-9.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric
characterization of the persistence of 1D maps,” Journal of Applied and Computational
Topology. Springer Nature, 2023.
ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric
characterization of the persistence of 1D maps. Journal of Applied and Computational
Topology.
mla: Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D
Maps.” Journal of Applied and Computational Topology, Springer Nature,
2023, doi:10.1007/s41468-023-00126-9.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal
of Applied and Computational Topology (2023).
date_created: 2023-07-02T22:00:44Z
date_published: 2023-06-17T00:00:00Z
date_updated: 2023-10-18T08:13:10Z
day: '17'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s41468-023-00126-9
ec_funded: 1
file:
- access_level: open_access
checksum: 697249d5d1c61dea4410b9f021b70fce
content_type: application/pdf
creator: alisjak
date_created: 2023-07-03T09:41:05Z
date_updated: 2023-07-03T09:41:05Z
file_id: '13185'
file_name: 2023_Journal of Applied and Computational Topology_Biswas.pdf
file_size: 487355
relation: main_file
success: 1
file_date_updated: 2023-07-03T09:41:05Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: Journal of Applied and Computational Topology
publication_identifier:
eissn:
- 2367-1734
issn:
- 2367-1726
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Geometric characterization of the persistence of 1D maps
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '10773'
abstract:
- lang: eng
text: The Voronoi tessellation in Rd is defined by locally minimizing the power
distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined
by locally maximizing the negative power distance to other such points. We prove
that the average of the two piecewise quadratic functions is piecewise linear,
and that all three functions have the same critical points and values. Discretizing
the two piecewise quadratic functions, we get the alpha shapes as sublevel sets
of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel
sets of the discrete function on the Voronoi tessellation. For the same non-critical
value, the corresponding shapes are disjoint, separated by a narrow channel that
contains no critical points but the entire level set of the piecewise linear function.
acknowledgement: Open access funding provided by the Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera Di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera Di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
last_name: Saghafian
citation:
ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous
and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete
and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2
apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M.
(2022). Continuous and discrete radius functions on Voronoi tessellations and
Delaunay mosaics. Discrete and Computational Geometry. Springer Nature.
https://doi.org/10.1007/s00454-022-00371-2
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations
and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature,
2022. https://doi.org/10.1007/s00454-022-00371-2.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous
and discrete radius functions on Voronoi tessellations and Delaunay mosaics,”
Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842,
2022.
ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous
and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete
and Computational Geometry. 67, 811–842.
mla: Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi
Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry,
vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete
and Computational Geometry 67 (2022) 811–842.
date_created: 2022-02-20T23:01:34Z
date_published: 2022-04-01T00:00:00Z
date_updated: 2023-08-02T14:31:25Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-022-00371-2
external_id:
isi:
- '000752175300002'
file:
- access_level: open_access
checksum: 9383d3b70561bacee905e335dc922680
content_type: application/pdf
creator: dernst
date_created: 2022-08-02T06:07:55Z
date_updated: 2022-08-02T06:07:55Z
file_id: '11718'
file_name: 2022_DiscreteCompGeometry_Biswas.pdf
file_size: 2518111
relation: main_file
success: 1
file_date_updated: 2022-08-02T06:07:55Z
has_accepted_license: '1'
intvolume: ' 67'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 811-842
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Continuous and discrete radius functions on Voronoi tessellations and Delaunay
mosaics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 67
year: '2022'
...
---
_id: '11658'
abstract:
- lang: eng
text: The depth of a cell in an arrangement of n (non-vertical) great-spheres in
Sd is the number of great-spheres that pass above the cell. We prove Euler-type
relations, which imply extensions of the classic Dehn–Sommerville relations for
convex polytopes to sublevel sets of the depth function, and we use the relations
to extend the expressions for the number of faces of neighborly polytopes to the
number of cells of levels in neighborly arrangements.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.
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: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
id: f86f7148-b140-11ec-9577-95435b8df824
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements:
Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings
on Mathematics.'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications.
Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz
Zentrum für Informatik.'
chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations
with Applications.” Leibniz International Proceedings on Mathematics. Schloss
Dagstuhl - Leibniz Zentrum für Informatik, n.d.'
ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth
in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz
International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum
für Informatik.'
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in
arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International
Proceedings on Mathematics.'
mla: 'Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations
with Applications.” Leibniz International Proceedings on Mathematics, Schloss
Dagstuhl - Leibniz Zentrum für Informatik.'
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz
International Proceedings on Mathematics (n.d.).
date_created: 2022-07-27T09:27:34Z
date_published: 2022-07-27T00:00:00Z
date_updated: 2022-07-28T07:57:48Z
day: '27'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: b2f511e8b1cae5f1892b0cdec341acac
content_type: application/pdf
creator: scultrer
date_created: 2022-07-27T09:25:53Z
date_updated: 2022-07-27T09:25:53Z
file_id: '11659'
file_name: D-S-E.pdf
file_size: 639266
relation: main_file
file_date_updated: 2022-07-27T09:25:53Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Leibniz International Proceedings on Mathematics
publication_status: submitted
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
status: public
title: 'Depth in arrangements: Dehn–Sommerville–Euler relations with applications'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '11660'
abstract:
- lang: eng
text: 'We characterize critical points of 1-dimensional maps paired in persistent
homology geometrically and this way get elementary proofs of theorems about the
symmetry of persistence diagrams and the variation of such maps. In particular,
we identify branching points and endpoints of networks as the sole source of asymmetry
and relate the cycle basis in persistent homology with a version of the stable
marriage problem. Our analysis provides the foundations of fast algorithms for
maintaining collections of interrelated sorted lists together with their persistence
diagrams. '
acknowledgement: 'This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme,
grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. '
alternative_title:
- LIPIcs
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: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to
the persistence of 1D maps. I: Geometric characterization of critical point pairs.
LIPIcs.'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization
of critical point pairs. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik.'
chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization
of Critical Point Pairs.” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, n.d.'
ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A
window to the persistence of 1D maps. I: Geometric characterization of critical
point pairs,” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.'
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window
to the persistence of 1D maps. I: Geometric characterization of critical point
pairs. LIPIcs.'
mla: 'Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric
Characterization of Critical Point Pairs.” LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik.'
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs
(n.d.).
date_created: 2022-07-27T09:31:15Z
date_published: 2022-07-25T00:00:00Z
date_updated: 2022-07-28T08:05:34Z
day: '25'
ddc:
- '510'
department:
- _id: GradSch
- _id: HeEd
ec_funded: 1
file:
- access_level: open_access
checksum: 95903f9d1649e8e437a967b6f2f64730
content_type: application/pdf
creator: scultrer
date_created: 2022-07-27T09:30:30Z
date_updated: 2022-07-27T09:30:30Z
file_id: '11661'
file_name: window 1.pdf
file_size: 564836
relation: main_file
file_date_updated: 2022-07-27T09:30:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: LIPIcs
publication_status: submitted
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: 'A window to the persistence of 1D maps. I: Geometric characterization of critical
point pairs'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '9604'
abstract:
- lang: eng
text: Generalizing Lee’s inductive argument for counting the cells of higher order
Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse
theoretic quantities for piecewise constant functions on planar arrangements.
Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number
of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for
1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s
first k-1 sublevel sets. We get similar expressions for the vertices, edges, and
polygons of the order-k Voronoi tessellation.
alternative_title:
- LIPIcs
article_number: '16'
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: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
last_name: Saghafian
citation:
ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells
of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz
International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16'
apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian,
M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with
morse theory. In Leibniz International Proceedings in Informatics (Vol.
189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16'
chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner,
and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3
with Morse Theory.” In Leibniz International Proceedings in Informatics,
Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory,” in
Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.
ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz
International Proceedings in Informatics. SoCG: International Symposium on Computational
Geometry, LIPIcs, vol. 189, 16.'
mla: Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in
ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics,
vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.
short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:,
Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2021.
conference:
end_date: 2021-06-11
location: Online
name: 'SoCG: International Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-27T22:01:48Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T14:02:28Z
day: '02'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.16
ec_funded: 1
file:
- access_level: open_access
checksum: 22b11a719018b22ecba2471b51f2eb40
content_type: application/pdf
creator: asandaue
date_created: 2021-06-28T13:11:39Z
date_updated: 2021-06-28T13:11:39Z
file_id: '9611'
file_name: 2021_LIPIcs_Biswas.pdf
file_size: 727817
relation: main_file
success: 1
file_date_updated: 2021-06-28T13:11:39Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- '9783959771849'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting cells of order-k voronoi tessellations in ℝ3 with morse
theory
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9824'
abstract:
- lang: eng
text: We define a new compact coordinate system in which each integer triplet addresses
a voxel in the BCC grid, and we investigate some of its properties. We propose
a characterization of 3D discrete analytical planes with their topological features
(in the Cartesian and in the new coordinate system) such as the interrelation
between the thickness of the plane and the separability constraint we aim to obtain.
acknowledgement: 'This work has been partially supported by the Ministry of Education,
Science and Technological Development of the Republic of Serbia through the project
no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from
the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and
the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’,
Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic
grid - coordinate system and discrete analytical plane definition. In: Discrete
Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163.
doi:10.1007/978-3-030-76657-3_10'
apa: 'Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021).
Body centered cubic grid - coordinate system and discrete analytical plane definition.
In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163).
Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10'
chicago: Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and
Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical
Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63.
Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.
ieee: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered
cubic grid - coordinate system and discrete analytical plane definition,” in Discrete
Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp.
152–163.
ista: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered
cubic grid - coordinate system and discrete analytical plane definition. Discrete
Geometry and Mathematical Morphology. DGMM: International Conference on Discrete
Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.'
mla: Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete
Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology,
vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.
short: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete
Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
conference:
end_date: 2021-05-27
location: Uppsala, Sweden
name: 'DGMM: International Conference on Discrete Geometry and Mathematical Morphology'
start_date: 2021-05-24
date_created: 2021-08-08T22:01:29Z
date_published: 2021-05-16T00:00:00Z
date_updated: 2022-05-31T06:58:21Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/978-3-030-76657-3_10
ec_funded: 1
intvolume: ' 12708'
language:
- iso: eng
month: '05'
oa_version: None
page: 152-163
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete Geometry and Mathematical Morphology
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030766566'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Body centered cubic grid - coordinate system and discrete analytical plane
definition
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12708
year: '2021'
...
---
_id: '9249'
abstract:
- lang: eng
text: Rhombic dodecahedron is a space filling polyhedron which represents the close
packing of spheres in 3D space and the Voronoi structures of the face centered
cubic (FCC) lattice. In this paper, we describe a new coordinate system where
every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid.
In order to illustrate the interest of the new coordinate system, we propose the
characterization of 3D digital plane with its topological features, such as the
interrelation between the thickness of the digital plane and the separability
constraint we aim to obtain. We also present the characterization of 3D digital
lines and study it as the intersection of multiple digital planes. Characterization
of 3D digital sphere with relevant topological features is proposed as well along
with the 48-symmetry appearing in the new coordinate system.
acknowledgement: "This work has been partially supported by the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109,
‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no.
I 02979-N35. "
article_processing_charge: No
article_type: original
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic
dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158.
doi:10.1515/mathm-2020-0106
apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital
objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and
Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106
chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital
Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and
Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106.
ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects
in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications,
vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.
ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in
rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications.
4(1), 143–158.
mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical
Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp.
143–58, doi:10.1515/mathm-2020-0106.
short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology
- Theory and Applications 4 (2020) 143–158.
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2021-03-22T09:01:50Z
day: '17'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/mathm-2020-0106
ec_funded: 1
file:
- access_level: open_access
checksum: 4a1043fa0548a725d464017fe2483ce0
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T08:56:37Z
date_updated: 2021-03-22T08:56:37Z
file_id: '9272'
file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf
file_size: 3668725
relation: main_file
success: 1
file_date_updated: 2021-03-22T08:56:37Z
has_accepted_license: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 143-158
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Mathematical Morphology - Theory and Applications
publication_identifier:
issn:
- 2353-3390
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: Digital objects in rhombic dodecahedron grid
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...
---
_id: '6163'
abstract:
- lang: eng
text: We propose a new non-orthogonal basis to express the 3D Euclidean space in
terms of a regular grid. Every grid point, each represented by integer 3-coordinates,
corresponds to rhombic dodecahedron centroid. Rhombic dodecahedron is a space
filling polyhedron which represents the close packing of spheres in 3D space and
the Voronoi structures of the face centered cubic (FCC) lattice. In order to illustrate
the interest of the new coordinate system, we propose the characterization of
3D digital plane with its topological features, such as the interrelation between
the thickness of the digital plane and the separability constraint we aim to obtain.
A characterization of a 3D digital sphere with relevant topological features is
proposed as well with the help of a 48 symmetry that comes with the new coordinate
system.
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: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
ama: 'Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Rhombic dodecahedron grid—coordinate
system and 3D digital object definitions. In: 21st IAPR International Conference
on Discrete Geometry for Computer Imagery. Vol 11414. Berlin, Heidelberg:
Springer Berlin Heidelberg; 2019:27-37. doi:10.1007/978-3-030-14085-4_3'
apa: 'Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2019). Rhombic
dodecahedron grid—coordinate system and 3D digital object definitions. In 21st
IAPR International Conference on Discrete Geometry for Computer Imagery (Vol.
11414, pp. 27–37). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-030-14085-4_3'
chicago: 'Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres.
“Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.”
In 21st IAPR International Conference on Discrete Geometry for Computer Imagery,
11414:27–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. https://doi.org/10.1007/978-3-030-14085-4_3.'
ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Rhombic dodecahedron
grid—coordinate system and 3D digital object definitions,” in 21st IAPR International
Conference on Discrete Geometry for Computer Imagery, Marne-la-Vallée, France,
2019, vol. 11414, pp. 27–37.
ista: 'Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2019. Rhombic dodecahedron
grid—coordinate system and 3D digital object definitions. 21st IAPR International
Conference on Discrete Geometry for Computer Imagery. DGCI: International Conference
on Discrete Geometry for Computer Imagery, LNCS, vol. 11414, 27–37.'
mla: Biswas, Ranita, et al. “Rhombic Dodecahedron Grid—Coordinate System and 3D
Digital Object Definitions.” 21st IAPR International Conference on Discrete
Geometry for Computer Imagery, vol. 11414, Springer Berlin Heidelberg, 2019,
pp. 27–37, doi:10.1007/978-3-030-14085-4_3.
short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, in:, 21st IAPR International
Conference on Discrete Geometry for Computer Imagery, Springer Berlin Heidelberg,
Berlin, Heidelberg, 2019, pp. 27–37.
conference:
end_date: 2019-03-28
location: Marne-la-Vallée, France
name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
start_date: 2019-03-26
date_created: 2019-03-21T12:12:19Z
date_published: 2019-02-23T00:00:00Z
date_updated: 2022-01-27T14:25:17Z
day: '23'
doi: 10.1007/978-3-030-14085-4_3
extern: '1'
intvolume: ' 11414'
language:
- iso: eng
month: '02'
oa_version: None
page: 27-37
place: Berlin, Heidelberg
publication: 21st IAPR International Conference on Discrete Geometry for Computer
Imagery
publication_identifier:
isbn:
- 978-3-6624-6446-5
- 978-3-6624-6447-2
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
status: public
title: Rhombic dodecahedron grid—coordinate system and 3D digital object definitions
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 11414
year: '2019'
...
---
_id: '6164'
abstract:
- lang: eng
text: In this paper, we propose an algorithm to build discrete spherical shell having
integer center and real-valued inner and outer radii on the face-centered cubic
(FCC) grid. We address the problem by mapping it to a 2D scenario and building
the shell layer by layer on hexagonal grids with additive manufacturing in mind.
The layered hexagonal grids get shifted according to need as we move from one
layer to another and forms the FCC grid in 3D. However, we restrict our computation
strictly to 2D in order to utilize symmetry and simplicity.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Girish
full_name: Koshti, Girish
last_name: Koshti
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Koshti G, Biswas R, Largeteau-Skapin G, Zrour R, Andres E, Bhowmick P. Sphere
construction on the FCC grid interpreted as layered hexagonal grids in 3D. In:
19th International Workshop. Vol 11255. Cham: Springer; 2018:82-96. doi:10.1007/978-3-030-05288-1_7'
apa: 'Koshti, G., Biswas, R., Largeteau-Skapin, G., Zrour, R., Andres, E., &
Bhowmick, P. (2018). Sphere construction on the FCC grid interpreted as layered
hexagonal grids in 3D. In 19th International Workshop (Vol. 11255, pp.
82–96). Cham: Springer. https://doi.org/10.1007/978-3-030-05288-1_7'
chicago: 'Koshti, Girish, Ranita Biswas, Gaëlle Largeteau-Skapin, Rita Zrour, Eric
Andres, and Partha Bhowmick. “Sphere Construction on the FCC Grid Interpreted
as Layered Hexagonal Grids in 3D.” In 19th International Workshop, 11255:82–96.
Cham: Springer, 2018. https://doi.org/10.1007/978-3-030-05288-1_7.'
ieee: G. Koshti, R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, and P. Bhowmick,
“Sphere construction on the FCC grid interpreted as layered hexagonal grids in
3D,” in 19th International Workshop, Porto, Portugal, 2018, vol. 11255,
pp. 82–96.
ista: 'Koshti G, Biswas R, Largeteau-Skapin G, Zrour R, Andres E, Bhowmick P. 2018.
Sphere construction on the FCC grid interpreted as layered hexagonal grids in
3D. 19th International Workshop. IWCIA: International Workshop on Combinatorial
Image Analysis, LNCS, vol. 11255, 82–96.'
mla: Koshti, Girish, et al. “Sphere Construction on the FCC Grid Interpreted as
Layered Hexagonal Grids in 3D.” 19th International Workshop, vol. 11255,
Springer, 2018, pp. 82–96, doi:10.1007/978-3-030-05288-1_7.
short: G. Koshti, R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, P. Bhowmick,
in:, 19th International Workshop, Springer, Cham, 2018, pp. 82–96.
conference:
end_date: 2018-11-24
location: Porto, Portugal
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2018-11-22
date_created: 2019-03-21T12:16:58Z
date_published: 2018-11-22T00:00:00Z
date_updated: 2022-01-27T15:26:39Z
day: '22'
doi: 10.1007/978-3-030-05288-1_7
extern: '1'
intvolume: ' 11255'
language:
- iso: eng
month: '11'
oa_version: None
page: 82-96
place: Cham
publication: 19th International Workshop
publication_identifier:
eisbn:
- 978-3-030-05288-1
eissn:
- 1611-3349
isbn:
- 978-3-030-05287-4
issn:
- 0302-9743
publication_status: published
publisher: Springer
quality_controlled: '1'
status: public
title: Sphere construction on the FCC grid interpreted as layered hexagonal grids
in 3D
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 11255
year: '2018'
...
---
_id: '5799'
abstract:
- lang: eng
text: We construct a polyhedral surface called a graceful surface, which provides
best possible approximation to a given sphere regarding certain criteria. In digital
geometry terms, the graceful surface is uniquely characterized by its minimality
while guaranteeing the connectivity of certain discrete (polyhedral) curves defined
on it. The notion of “gracefulness” was first proposed in Brimkov and Barneva
(1999) and shown to be useful for triangular mesh discretization through graceful
planes and graceful lines. In this paper we extend the considerations to a nonlinear
object such as a sphere. In particular, we investigate the properties of a discrete
geodesic path between two voxels and show that discrete 3D circles, circular arcs,
and Mobius triangles are all constructible on a graceful sphere, with guaranteed
minimum thickness and the desired connectivity in the discrete topological space.
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 polyhedra of graceful spheres and
circular geodesics. Discrete Applied Mathematics. 2017;216:362-375. doi:10.1016/j.dam.2015.11.017
apa: Biswas, R., Bhowmick, P., & Brimkov, V. E. (2017). On the polyhedra of
graceful spheres and circular geodesics. Discrete Applied Mathematics.
Elsevier. https://doi.org/10.1016/j.dam.2015.11.017
chicago: Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Polyhedra
of Graceful Spheres and Circular Geodesics.” Discrete Applied Mathematics.
Elsevier, 2017. https://doi.org/10.1016/j.dam.2015.11.017.
ieee: R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the polyhedra of graceful spheres
and circular geodesics,” Discrete Applied Mathematics, vol. 216. Elsevier,
pp. 362–375, 2017.
ista: Biswas R, Bhowmick P, Brimkov VE. 2017. On the polyhedra of graceful spheres
and circular geodesics. Discrete Applied Mathematics. 216, 362–375.
mla: Biswas, Ranita, et al. “On the Polyhedra of Graceful Spheres and Circular Geodesics.”
Discrete Applied Mathematics, vol. 216, Elsevier, 2017, pp. 362–75, doi:10.1016/j.dam.2015.11.017.
short: R. Biswas, P. Bhowmick, V.E. Brimkov, Discrete Applied Mathematics 216 (2017)
362–375.
date_created: 2019-01-08T20:41:12Z
date_published: 2017-01-10T00:00:00Z
date_updated: 2021-01-12T08:03:33Z
day: '10'
doi: 10.1016/j.dam.2015.11.017
extern: '1'
intvolume: ' 216'
language:
- iso: eng
month: '01'
oa_version: None
page: 362-375
publication: Discrete Applied Mathematics
publication_identifier:
issn:
- 0166-218X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: On the polyhedra of graceful spheres and circular geodesics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 216
year: '2017'
...
---
_id: '5800'
abstract:
- lang: eng
text: This paper presents a novel study on the functional gradation of coordinate
planes in connection with the thinnest and tunnel-free (i.e., naive) discretization
of sphere in the integer space. For each of the 48-symmetric quadraginta octants
of naive sphere with integer radius and integer center, we show that the corresponding
voxel set forms a bijection with its projected pixel set on a unique coordinate
plane, which thereby serves as its functional plane. We use this fundamental property
to prove several other theoretical results for naive sphere. First, the quadraginta
octants form symmetry groups and subgroups with certain equivalent topological
properties. Second, a naive sphere is always unique and consists of fewest voxels.
Third, it is efficiently constructible from its functional-plane projection. And
finally, a special class of 4-symmetric discrete 3D circles can be constructed
on a naive sphere based on back projection from the functional plane.
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 the functionality and usefulness of Quadraginta octants
of naive sphere. Journal of Mathematical Imaging and Vision. 2017;59(1):69-83.
doi:10.1007/s10851-017-0718-4
apa: Biswas, R., & Bhowmick, P. (2017). On the functionality and usefulness
of Quadraginta octants of naive sphere. Journal of Mathematical Imaging and
Vision. Springer Nature. https://doi.org/10.1007/s10851-017-0718-4
chicago: Biswas, Ranita, and Partha Bhowmick. “On the Functionality and Usefulness
of Quadraginta Octants of Naive Sphere.” Journal of Mathematical Imaging and
Vision. Springer Nature, 2017. https://doi.org/10.1007/s10851-017-0718-4.
ieee: R. Biswas and P. Bhowmick, “On the functionality and usefulness of Quadraginta
octants of naive sphere,” Journal of Mathematical Imaging and Vision, vol.
59, no. 1. Springer Nature, pp. 69–83, 2017.
ista: Biswas R, Bhowmick P. 2017. On the functionality and usefulness of Quadraginta
octants of naive sphere. Journal of Mathematical Imaging and Vision. 59(1), 69–83.
mla: Biswas, Ranita, and Partha Bhowmick. “On the Functionality and Usefulness of
Quadraginta Octants of Naive Sphere.” Journal of Mathematical Imaging and Vision,
vol. 59, no. 1, Springer Nature, 2017, pp. 69–83, doi:10.1007/s10851-017-0718-4.
short: R. Biswas, P. Bhowmick, Journal of Mathematical Imaging and Vision 59 (2017)
69–83.
date_created: 2019-01-08T20:42:08Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2021-01-12T08:03:34Z
day: '01'
doi: 10.1007/s10851-017-0718-4
extern: '1'
intvolume: ' 59'
issue: '1'
language:
- iso: eng
month: '09'
oa_version: None
page: 69-83
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
issn:
- '09249907'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the functionality and usefulness of Quadraginta octants of naive sphere
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2017'
...
---
_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: 20th
IAPR International Conference. Vol 10502. Cham: Springer Nature; 2017:347-359.
doi:10.1007/978-3-319-66272-5_28'
apa: 'Dwivedi, S., Gupta, A., Roy, S., Biswas, R., & Bhowmick, P. (2017). Fast
and Efficient Incremental Algorithms for Circular and Spherical Propagation in
Integer Space. In 20th IAPR International Conference (Vol. 10502, pp. 347–359).
Cham: Springer Nature. https://doi.org/10.1007/978-3-319-66272-5_28'
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 20th IAPR International Conference, 10502:347–59.
Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-66272-5_28.'
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 20th IAPR International Conference, 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.” 20th IAPR International Conference,
vol. 10502, Springer Nature, 2017, pp. 347–59, doi:10.1007/978-3-319-66272-5_28.
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: 20th IAPR International Conference. Vol 10502. Cham: Springer
Nature; 2017:388-398. doi:10.1007/978-3-319-66272-5_31'
apa: 'Andres, E., Biswas, R., & Bhowmick, P. (2017). Digital primitives defined
by weighted focal set. In 20th IAPR International Conference (Vol. 10502,
pp. 388–398). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-66272-5_31'
chicago: 'Andres, Eric, Ranita Biswas, and Partha Bhowmick. “Digital Primitives
Defined by Weighted Focal Set.” In 20th IAPR International Conference,
10502:388–98. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-66272-5_31.'
ieee: E. Andres, R. Biswas, and P. Bhowmick, “Digital primitives defined by weighted
focal set,” in 20th IAPR International Conference, 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.” 20th
IAPR International Conference, vol. 10502, Springer Nature, 2017, pp. 388–98,
doi:10.1007/978-3-319-66272-5_31.
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'
...
---
_id: '5803'
abstract:
- lang: eng
text: Different distance metrics produce Voronoi diagrams with different properties.
It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi
diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions.
In this paper, we first show that this metric produces a persistent VD on the
2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly
approximates the corresponding VD on the 2D real plane. Next, we show that on
a 3D digital plane D, the Euclidean metric spanning over its voxel set does not
guarantee a digital VD which is persistent with the real-space VD. As a solution,
we introduce a novel concept of functional-plane-convexity, which is ensured by
the Euclidean metric spanning over the pedal set of D. Necessary proofs and some
visual result have been provided to adjudge the merit and usefulness of the proposed
concept.
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. Construction of persistent Voronoi diagram on 3D digital
plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature;
2017:93-104. doi:10.1007/978-3-319-59108-7_8'
apa: 'Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi
diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256,
pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi
Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104.
Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.'
ieee: 'R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on
3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer
Nature, 2017, pp. 93–104.'
ista: 'Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on
3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.'
mla: Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram
on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer
Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.
short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature,
Cham, 2017, pp. 93–104.
conference:
end_date: 2017-06-21
location: Plovdiv, Bulgaria
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2017-06-19
date_created: 2019-01-08T20:42:56Z
date_published: 2017-05-17T00:00:00Z
date_updated: 2022-01-28T07:48:24Z
day: '17'
department:
- _id: HeEd
doi: 10.1007/978-3-319-59108-7_8
extern: '1'
intvolume: ' 10256'
language:
- iso: eng
month: '05'
oa_version: None
page: 93-104
place: Cham
publication: Combinatorial image analysis
publication_identifier:
isbn:
- 978-3-319-59107-0
- 978-3-319-59108-7
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Construction of persistent Voronoi diagram on 3D digital plane
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10256
year: '2017'
...
---
_id: '5805'
abstract:
- lang: eng
text: Discretization of sphere in the integer space follows a particular discretization
scheme, which, in principle, conforms to some topological model. This eventually
gives rise to interesting topological properties of a discrete spherical surface,
which need to be investigated for its analytical characterization. This paper
presents some novel results on the local topological properties of the naive model
of discrete sphere. They follow from the bijection of each quadraginta octant
of naive sphere with its projection map called f -map on the corresponding functional
plane and from the characterization of certain jumps in the f-map. As an application,
we have shown how these properties can be used in designing an efficient reconstruction
algorithm for a naive spherical surface from an input voxel set when it is sparse
or noisy.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Nabhasmita
full_name: Sen, Nabhasmita
last_name: Sen
- 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: 'Sen N, Biswas R, Bhowmick P. On some local topological properties of naive
discrete sphere. In: Computational Topology in Image Context. Vol 9667.
Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23'
apa: 'Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological
properties of naive discrete sphere. In Computational Topology in Image Context
(Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23'
chicago: 'Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological
Properties of Naive Discrete Sphere.” In Computational Topology in Image Context,
9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.'
ieee: 'N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties
of naive discrete sphere,” in Computational Topology in Image Context,
vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.'
ista: 'Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of
naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol.
9667, 253–264.'
mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete
Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature,
2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.
short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context,
Springer Nature, Cham, 2016, pp. 253–264.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2019-01-08T20:44:24Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2022-01-28T08:01:22Z
day: '02'
department:
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_23
extern: '1'
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 253-264
place: Cham
publication: Computational Topology in Image Context
publication_identifier:
eisbn:
- 978-3-319-39441-1
eissn:
- 1611-3349
isbn:
- 978-3-319-39440-4
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On some local topological properties of naive discrete sphere
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9667
year: '2016'
...
---
_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: Discrete Geometry for Computer Imagery.
Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20'
apa: 'Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants
of naive sphere with application to circle drawing. In Discrete Geometry for
Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta
Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry
for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.'
ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive
sphere with application to circle drawing,” in Discrete Geometry for Computer
Imagery, 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.” Discrete Geometry for
Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.
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'
...
---
_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: Combinatorial Image Analysis. Vol 9448. Cham: Springer
Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7'
apa: 'Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity
and smoothness of discrete spherical circles. In Combinatorial image analysis
(Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7'
chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity
and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis,
9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.'
ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness
of discrete spherical circles,” in Combinatorial image analysis, 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.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016,
pp. 86–100, doi:10.1007/978-3-319-26145-4_7.
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'
...
---
_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. Theoretical Computer Science. 2015;624(4):56-72.
doi:10.1016/j.tcs.2015.11.018
apa: Biswas, R., & Bhowmick, P. (2015). From prima quadraginta octant to lattice
sphere through primitive integer operations. Theoretical Computer Science.
Elsevier. https://doi.org/10.1016/j.tcs.2015.11.018
chicago: Biswas, Ranita, and Partha Bhowmick. “From Prima Quadraginta Octant to
Lattice Sphere through Primitive Integer Operations.” Theoretical Computer
Science. Elsevier, 2015. https://doi.org/10.1016/j.tcs.2015.11.018.
ieee: R. Biswas and P. Bhowmick, “From prima quadraginta octant to lattice sphere
through primitive integer operations,” Theoretical Computer Science, 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.” Theoretical Computer Science,
vol. 624, no. 4, Elsevier, 2015, pp. 56–72, doi:10.1016/j.tcs.2015.11.018.
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'
...
---
_id: '5807'
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 different topological classes of spherical geodesic
paths and circles inZ3. Theoretical Computer Science. 2015;605(11):146-163.
doi:10.1016/j.tcs.2015.09.003
apa: Biswas, R., & Bhowmick, P. (2015). On different topological classes of
spherical geodesic paths and circles inZ3. Theoretical Computer Science.
Elsevier. https://doi.org/10.1016/j.tcs.2015.09.003
chicago: Biswas, Ranita, and Partha Bhowmick. “On Different Topological Classes
of Spherical Geodesic Paths and Circles InZ3.” Theoretical Computer Science.
Elsevier, 2015. https://doi.org/10.1016/j.tcs.2015.09.003.
ieee: R. Biswas and P. Bhowmick, “On different topological classes of spherical
geodesic paths and circles inZ3,” Theoretical Computer Science, vol. 605,
no. 11. Elsevier, pp. 146–163, 2015.
ista: Biswas R, Bhowmick P. 2015. On different topological classes of spherical
geodesic paths and circles inZ3. Theoretical Computer Science. 605(11), 146–163.
mla: Biswas, Ranita, and Partha Bhowmick. “On Different Topological Classes of Spherical
Geodesic Paths and Circles InZ3.” Theoretical Computer Science, vol. 605,
no. 11, Elsevier, 2015, pp. 146–63, doi:10.1016/j.tcs.2015.09.003.
short: R. Biswas, P. Bhowmick, Theoretical Computer Science 605 (2015) 146–163.
date_created: 2019-01-08T20:44:52Z
date_published: 2015-11-09T00:00:00Z
date_updated: 2021-01-12T08:03:37Z
day: '09'
doi: 10.1016/j.tcs.2015.09.003
extern: '1'
intvolume: ' 605'
issue: '11'
language:
- iso: eng
month: '11'
oa_version: None
page: 146-163
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: On different topological classes of spherical geodesic paths and circles inZ3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 605
year: '2015'
...