Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Distance functions in digital geometry
Information Sciences: an International Journal
Octagonal distances for digital pictures
Information Sciences: an International Journal
Handbook of pattern recognition & computer vision
Handbook of pattern recognition & computer vision
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
Digital Image Processing
On the rectangular grid representation of general CNN networks: Research Articles
International Journal of Circuit Theory and Applications - CNN Technology
Distances with neighbourhood sequences in cubic and triangular grids
Pattern Recognition Letters
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Number-theoretic interpretation and construction of a digital circle
Discrete Applied Mathematics
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Neighborhood Sequences in the Diamond Grid --- Algorithms with Four Neighbors
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Approximating Euclidean circles by neighbourhood sequences in a hexagonal grid
Theoretical Computer Science
Isoperimetrically optimal polygons in the triangular grid
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
On covering a digital disc with concentric circles in Z2
Theoretical Computer Science
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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.