Regular polygons and their application to digital curves

Li Chen; Jianping Zhang; Donald H. Cooley

doi:10.1117/12.251786

30 September 1996 Regular polygons and their application to digital curves

Li Chen, Jianping Zhang, Donald H. Cooley

Proceedings Volume 2826, Vision Geometry V; (1996) https://doi.org/10.1117/12.251786
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

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.

Citation Download Citation

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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KEYWORDS

3D applications

3D image processing

Binary data

Computer science

Computer vision technology

Fourier transforms

Image processing

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