Discrete Circles: an arithmetical approach with non-constant thickness

International audienceIn the present paper, we introduce an arithmetical definition of discrete circles with a non-constant thickness and we exhibit different classes of them depending on the arithmetical discrete lines. On the one hand, it results in the characterization of regular discrete circles with integer parameters as well as J. Bresenham's circles. As far as we know, it is the first arithmetical definition of the latter one. On the other hand, we introduce new discrete circles, actually the thinnest ones for the usual discrete connectedness relations

Approximation of Discs by Octagons on Pixel-Plane via Jaccards Proximity Criterion: Theoretical Approach and Experimental Results Analysis

In the present paper we study approximation of discs by octagons on the pixel plane. To decide which octagon approximates better the given disc we use Jaccard's distance. The table of Jaccard's distances (calculated by a software created for these purposes) are presented at the end of the paper. The results for proximity are given in the form of a graph. Some properties of considered octagons are also studie