  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.
