Characterization and Construction of Rational Circles on the Integer Plane
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.
KeywordsDiscrete circle Rational circle Discrete curve Digital geometry Number theory
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