Title: Regularized arrangements of cellular complexes,
Abstract: In this paper we propose a novel algorithm to combine two or more cellular
complexes, providing a minimal fragmentation of the cells of the resulting
complex. We introduce here the idea of arrangement generated by a collection of
cellular complexes, producing a cellular decomposition of the embedding space.
The algorithm that executes this computation is called \emph{Merge} of
complexes. The arrangements of line segments in 2D and polygons in 3D are
special cases, as well as the combination of closed triangulated surfaces or
meshed models. This algorithm has several important applications, including
Boolean and other set operations over large geometric models, the extraction of
solid models of biomedical structures at the cellular scale, the detailed
geometric modeling of buildings, the combination of 3D meshes, and the repair
of graphical models. The algorithm is efficiently implemented using the Linear
Algebraic Representation (LAR) of argument complexes, i.e., on sparse
representation of binary characteristic matrices of $d$-cell bases, well-suited
for implementation in last generation accelerators and GPGPU applications.