Abstract
Recent trends from the Euclidean to the digital geometry in solving various problems on the digital plane are presented in this paper. The notional difference of digital geometry with the Euclidean and the allied geometries has also been pointed out to show how the problems are conceivable in the digital paradigm. Significant contributions in solving these problems using number theory, theory of words, and theory of fractions in general, and digital geometry in particular, have been briefed. The paper is mainly focused on digital straightness and digital circularity, with their related problems, theories, and different perspectives in solving various geometric problems in the digital domain, such as analysis, characterization, segmentation, and approximation.
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