Construction of Digital Ellipse by Recursive Integer Intervals

  • Papia MahatoEmail author
  • Partha Bhowmick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9647)


In this paper, we revisit the problem of ellipse construction in the integer plane. Our perspective is elementary number-theoretic analysis of a digital ellipse having an integer point as its center and two integer values specifying the lengths of its semi-major and semi-minor axes. We characterize a digital ellipse to derive certain recurrences on the integer intervals that contain the integer values of a specific square term corresponding to the integer points comprising the digital ellipse. This, in turn, helps in designing ellipse drawing algorithm on the integer plane. We propose two algorithms—one using floating-point-based distance computation, and another using purely integer operations. Some test results have also been presented to exhibit further research possibilities related to digital ellipse.


Digital ellipse Digital geometry Integer intervals Integer algorithm 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyKharagpurIndia

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