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Characterization and Construction of Rational Circles on the Integer Plane

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Combinatorial Image Analysis (IWCIA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9448))

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Abstract

Discretization of geometric primitives in the integer space is a well-researched topic in the subject of digital geometry. In this paper, we present some novel results related to discretization of circles on the integer plane when the center and the radius are specified by arbitrary rational numbers. These results reveal elementary number-theoretic properties of rational circles on the integer plane and lead to useful characterization in terms of certain integer intervals defined by the circle parameters. We show how it finally culminates to an efficient algorithm for construction of rational circles using integer operations. Related experimental results exhibit interesting similitudes between the characteristic patterns of rational circles and those of integer circles.

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Notes

  1. 1.

    In 2D discretization, a gap means a missing 2-cell [6]; it is also termed as absentee in [3].

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Authors and Affiliations

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

    Papia Mahato & Partha Bhowmick

Authors
  1. Papia Mahato
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  2. Partha Bhowmick
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Correspondence to Papia Mahato .

Editor information

Editors and Affiliations

  1. SUNY Fredonia, Fredonia, New York, USA

    Reneta P. Barneva

  2. Advanced Computing and Microelectronics, Indian Statistical Institute, Kolkata, Germany

    Bhargab B. Bhattacharya

  3. SUNY Buffalo State, Buffalo, New York, USA

    Valentin E. Brimkov

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Mahato, P., Bhowmick, P. (2015). Characterization and Construction of Rational Circles on the Integer Plane. In: Barneva, R., Bhattacharya, B., Brimkov, V. (eds) Combinatorial Image Analysis. IWCIA 2015. Lecture Notes in Computer Science(), vol 9448. Springer, Cham. https://doi.org/10.1007/978-3-319-26145-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-26145-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26144-7

  • Online ISBN: 978-3-319-26145-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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