Determining Simplicity and Computing Topological Change in Strongly Normal Partial Tilings of R2 or R3
Abstract
A convex polygon in R2, or a convex polyhedron in R3, 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 R3: or face) of both. P is called strongly normal (SN) if, for any partial tiling P' P and any tile P epsilon P', 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 N*(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 N*(P,P) are topologically equivalent. This paper presents methods of determining, for an SN partial tiling P, whether a tile P epsilon P' is simple, and if not, of counting the numbers of components and holes (in R3: components, tunnels and cavities) in N*(P,P).
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1998
- Accession Number
- ADA353990
Entities
People
- Azriel Rosenfeld
- Punam K. Saha
Organizations
- University of Maryland