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30 September 1996 Regular polygons and their application to digital curves
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Abstract
In this note, we discuss various kinds of 2D unit cells, or surface-unit cells, made by regular polygons (simplexes) in the plane R X R. Mathematically, the plane can be divided by simplexes or regular polygons (decomposition). If we only allow one kind of surface-unit in the plane, there are only three possible choices: regular triangle (3-regular- polygon), square (4-regular-polygon), or 6-regular-polygon. Using Euler's formula for planar graphs, we give a type of topological proofs to that a closed digital curve has at least 6 points in a 3-regular-polygon decomposition plane, has at least 8 points in a 4-regular-polygon decomposition plane, and has at least 12 points in a 6-regular-polygon decomposition plane, respectively. On the other hand, a plane can also be divided by combinations of two kinds of regular polygons. We have obtained two types of {3,6}-regular-polygon combinations, two types of {4,8}-regular-polygon combinations, and one type of {3,12}-regular-polygon combination. We also discuss the application of polygons or closed paths to digital surfaces in 3D digital spaces.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Li Chen, Jianping Zhang, and Donald H. Cooley "Regular polygons and their application to digital curves", Proc. SPIE 2826, Vision Geometry V, (30 September 1996); https://doi.org/10.1117/12.251786
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