@article{10.1145/3401988,
   author     = {Paoluzzi, Alberto and Shapiro, Vadim and Dicarlo, Antonio
and Furiani, Francesco and Martella, Giulio and Scorzelli,
Giorgio},
   title      = {Topological Computing of Arrangements with (Co)Chains},
   year       = 2020,
   issue_date = {October 2020},
   publisher  = {Association for Computing Machinery},
   address    = {New York, NY, {USA}},
   volume     = 7,
   number     = 1,
   issn       = {2374-0353},
   url        = {https://doi.org/10.1145/3401988},
   doi        = {10.1145/3401988},
   abstract   = {In many areas of applied geometric/numeric computational
mathematics, including geo-mapping, computer vision,
computer graphics, finite element analysis, medical imaging,
geometric design, and solid modeling, one has to compute
incidences, adjacencies, and ordering of cells, generally
using disparate and often incompatible data structures and
algorithms. This article introduces computational topology
algorithms to discover the two-dimensional (2D)/3D space
partition induced by a collection of geometric objects of
dimension 1D/2D, respectively. Methods and language are
those of basic geometric and algebraic topology. Only sparse
vectors and matrices are used to compute both spaces and
maps, i.e., the chain complex, from dimension zero to three.
The prototype software is written in Julia, the novel
language for scientific computing. The applications may vary
from 3D graphics to 3D printing, from images to scene
understanding, and from games to building information
modeling.},
   journal    = {{ACM} Trans. Spatial Algorithms Syst.},
   month      = oct,
   articleno  = {1},
   numpages   = {29},
   keywords   = {Computational topology, cellular complex, linear algebraic
representation, solid modeling, arrangement, image
understanding, LAR, chain complex},
}