On the connectivity and smoothness of discrete spherical circles.(English)Zbl 1486.68205
Barneva, Reneta P. (ed.) et al., Combinatorial image analysis. 17th international workshop, IWCIA 2015, Kolkata, India, November 24–27, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9448, 86-100 (2015).
Summary: A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.
For the entire collection see [Zbl 1327.68009].
For the entire collection see [Zbl 1327.68009].
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
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