Determining simplicity and computing topological change in strongly normal partial tilings of R2 or R3
✍ Scribed by Punam K. Saha; Azriel Rosenfeld
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 185 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0031-3203
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✦ Synopsis
A convex polygon in R, or a convex polyhedron in R, will be called a tile. A connected set P of tiles is called a partial tiling if the intersection of any two of the tiles is either empty, or is a vertex or edge (in R: or face) of both. P is called strongly normal (SN) if, for any partial tiling P-P and any tile P3P, the neighborhood N(P, P) of P (the union of the tiles of P that intersect P) is simply connected. Let P be SN, and let NH(P, P) be the excluded neighborhood of P in P (i.e., the union of the tiles of P, other than P itself, that intersect P). We call P simple in P if N(P, P) and NH(P, P) are topologically equivalent. This paper presents methods of determining, for an SN partial tiling P, whether a tile P3P is simple, and if not, of counting the numbers of components and holes (in R: components, tunnels and cavities) in NH(P, P).