Characterization of digital circles in triangular grid

摘要

In this paper we present some former results about properties of digital circles defined by neighbourhood sequences in the triangular grid. Das and Chatterji [Inform. Sci. 50 (1990) 123] analyzed the geometric behaviour of two-dimensional periodic neighbourhood sequences. We use a more general definition of neighbourhood sequences, which does not require periodicity [Publ. Math. Debrecen 60 (2002) 405], We study the development of wave-fronts and grow digital circles from a triangle with general neighbourhood sequences in triangular grid. We present the possible types of polygons, and characterize them by the initial part of the neighbourhood sequences. The symmetry and the convexity analysis of the digital circles is also presented. Besides those who are interested in the underlying theory there may be readers from the pattern recognition or the image processing communities or even the geometric modelling field who could find some of the consequences of the paper of interest.