CARTESIAN PRODUCT OF SIMPLICIAL AND CELLULAR STRUCTURES

Abstract

Classical topology-based operations such as extrusion (or more generally Minkowski sums) are defined by a cartesian product of combinatorial structures describing the topology of geometric space subdivisions. In this paper, we define the cartesian product operation for four different structures: semi-simplicial sets, generalized maps, oriented maps and chains of maps. We follow a homogeneous framework allowing to define the cartesian product for any simplicial and cellular structures derived from simplicial sets and combinatorial maps. This results from the relationships already established between these structures and those used in computational geometry and geometric modeling. For esch structure we have studied, we additionally provide a time-optimal computation algorithm.