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.

This paper points out the main design goals of a novel representation scheme of geometric-topological data, named Linear Algebraic Representation (LAR), characterized by a wide domain, encompassing 2D and 3D meshes, manifold and non-manifold geometric and solid models, and high-resolution 3D images. To demonstrate its simplicity and effectiveness for dealing with huge amounts of geometric data, we apply LAR to the extraction of a clean solid model of the hepatic portal vein subsystem from micro-CT scans of a pig liver

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 paper introduces computational topology algorithms to discover the 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.

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