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A Digital-Geometric Algorithm for Generating a Complete Spherical Surface in ℤ3

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Applied Algorithms (ICAA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8321))

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Abstract

We show that the construction of a digital sphere by circularly sweeping a digital semicircle (generatrix) around its diameter results in appearance of some holes (absentee voxels) in its spherical surface of revolution. This incompleteness calls for a proper characterization of the absentee voxels whose restoration in the surface of revolution can ensure the required completeness. In this paper, we present a characterization of the absentee voxels using certain techniques of digital geometry and show that their count varies quadratically with the radius of the semicircular generatrix. Next, we design an algorithm to fill up the absentee voxels so as to generate a spherical surface of revolution, which is complete and realistic from the viewpoint of visual perception. Test results have also been furnished to substantiate our theoretical findings. The proposed technique will find many potential applications in computer graphics and 3D imaging.

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Author information

Authors and Affiliations

  1. Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India

    Sahadev Bera & Bhargab B. Bhattacharya

  2. Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India

    Partha Bhowmick

Authors
  1. Sahadev Bera
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  2. Partha Bhowmick
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  3. Bhargab B. Bhattacharya
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Editor information

Editors and Affiliations

  1. Computer Science and Engineering, Heritage Institute of Technology, Chowbaga Road, Anandapur, 700107, Kolkata, India

    Prosenjit Gupta

  2. Department of Computer Engineering and Informatics, University of Patras, 26500, Patras, Greece

    Christos Zaroliagis

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Bera, S., Bhowmick, P., Bhattacharya, B.B. (2014). A Digital-Geometric Algorithm for Generating a Complete Spherical Surface in ℤ3 . In: Gupta, P., Zaroliagis, C. (eds) Applied Algorithms. ICAA 2014. Lecture Notes in Computer Science, vol 8321. Springer, Cham. https://doi.org/10.1007/978-3-319-04126-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-04126-1_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04125-4

  • Online ISBN: 978-3-319-04126-1

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