Product operator on cell complexes
Fausto Bernardini, Vincenzo Ferrucci, Alberto Paoluzzi, Valerio Pascucci · 1993
The intersection of extrusions is a useful tool to generate complex pll models starting from two or more mi D (mi ~p) cell complexes.This operation is particularly useful in the context of architectural design, where the 3D model of a building may be automatically generated starting from plan views and sections, both represented as 2D cell complexes [8].In this paper a more general product operator is introduced which allows for the unification of operations like extrusion, standard intersection, intersection of extrusions and Cartesian product of cell-decomposed polyhedra, A naive implementationof such an operator is a hard t~k even in 3D, as it seems to require an extensive use of Booleans.In this paper a dimension-independent and efficient solution for this problem is given, using only some linear algebra and the Cartesian product of graphs.q