Number-Theoretic Construction of Digital Circles
 P. Bhowmick and B. B. Bhattacharya, "Number-Theoretic Interpretation and Construction of a Digital Circle," Discrete Applied Mathematics, 156(12), 2008, pp. 2381–2399. The squares of the abscissas of the grid points lying on the digital circle corresponding to radius  and having ordinate  lie in the interval  , where  and  are defined by:So the algorithm goes on calculating the consecutive square numbers, adding a point to the current run for each square number. It changes the run when the square number moves to the next interval. It may be noted that the  square number  can be obtained easily (without using any multiplication) from the previous square number  , since  , which is equivalent to adding a "gnomon".For details visit : http://dx.doi.org/10.1016/j.dam.2007.10.022  "Number-Theoretic Construction of Digital Circles" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/NumberTheoreticConstructionOfDigitalCircles/ Contributed by: Aniket Jha (BTech Student IIT KGP), Partha Bhowmick (IIT KGP), and B. B. Bhattacharya (ISI Kolkata) | ||||||||||||||
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