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Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition

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Discrete Geometry and Mathematical Morphology (DGMM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12708))

Abstract

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.

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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).

Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Lidija Čomić

  2. University of Poitiers, Laboratory XLIM, ASALI, UMR CNRS 7252, BP 30179, 86962, Futuroscope Chasseneuil, France

    Rita Zrour, Gaëlle Largeteau-Skapin & Eric Andres

  3. Institute of Science and Technology (IST) Austria, 3400, Klosterneuburg, Austria

    Ranita Biswas

Authors
  1. Lidija Čomić
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  2. Rita Zrour
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  3. Gaëlle Largeteau-Skapin
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  4. Ranita Biswas
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  5. Eric Andres
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Corresponding author

Correspondence to Rita Zrour .

Editor information

Editors and Affiliations

  1. Uppsala University, Uppsala, Sweden

    Joakim Lindblad

  2. Uppsala University, Uppsala, Sweden

    Filip Malmberg

  3. Uppsala University, Uppsala, Sweden

    Nataša Sladoje

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Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., Andres, E. (2021). Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition. In: Lindblad, J., Malmberg, F., Sladoje, N. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2021. Lecture Notes in Computer Science(), vol 12708. Springer, Cham. https://doi.org/10.1007/978-3-030-76657-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-76657-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-76656-6

  • Online ISBN: 978-3-030-76657-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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