In this paper we introduce a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex.  This algorithm has several important applications, including Boolean operations over big geometric data, like the detailed geometric modeling of buildings, and the smooth combination of 3D meshes  . The algorithm operates over the LAR representation of argument complexes, based on sparse matrices, so being well-suited for implementation on last generation accelerators and GPGPU applications.
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 Merge of complexes. The arrangements of segment lines in 2D and polygons in 3D are special cases, like 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 operates over 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.
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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 Merge of complexes. The arrangements of segment lines in 2D and polygons in 3D are special cases, like the combination of closed triangulated surfaces or meshed models.
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