Construction of Digital Ellipse by Recursive Integer Intervals
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.
KeywordsDigital ellipse Digital geometry Integer intervals Integer algorithm
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