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Strongly normal sets of contractible tiles in N dimensions

✍ Scribed by T. Yung Kong; Punam Kumar Saha; Azriel Rosenfeld

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
370 KB
Volume
40
Category
Article
ISSN
0031-3203

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✦ Synopsis

The second and third authors and others have studied collections of (usually) convex "tiles"-a generalization of pixels or voxels-in R 2 and R 3 that have a property called strong normality (SN): for any tile P, only finitely many tiles intersect P, and any nonempty intersection of those tiles also intersects P. This paper extends basic results about strong normality to collections of contractible polyhedra in R n whose nonempty intersections are contractible. We also give sufficient (and trivially necessary) conditions on a locally finite collection of contractible polyhedra in R 2 or R 3 for their nonempty intersections to be contractible.

πŸ“œ SIMILAR VOLUMES

Determining simplicity and computing top
Determining simplicity and computing topological change in strongly normal partial tilings of R2 or R3
✍ Punam K. Saha; Azriel Rosenfeld πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 185 KB

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-