Digital and Discrete Geometry by Li M. Chen

Author:Li M. Chen
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

9.2.3 Cell Complexes*

We have discussed simplicial complexes and digital complexes (cube complexes in Chap. 5). The more general complexes can be defined by replacing triangles or simplexes with any other shape. These are called cell complexes .

A more general form of cell complexes is called the CW complex. However, it is hard to use a computer to represent CW Complexes. In fact, there is no need to require that a cell have a polygonal boundary. It can be any curve as long as when two cells meet, they must have a simply connected component as the intersection (in other words, part of the boundary of the two cells is also a cell.).

We know that a kD unit ball is represented as,

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