CW complexes: Topological mainframe for numerical representations of objects

Abstract

Dimensionally non-homogeneous pointsets with internal structure are the focus in a consequent number of studies in both computational geometry and discrete (or digital) geometry, and lead to various practical applications in geometric modeling and computer imagery. Our motivation is to revisit the well known notion of algebraic topology, the cell CW complex, and to use it as an abstract framework for numerical representation of inhomogeneous objects. Two representational issues, respectively in non-manifold solid modeling and in discrete object boundary reconstruction, are discussed in illustration of this general setting. © Springer-Verlag 2003.