  The problem of decomposing non-manifold object has already been studied in
solid modeling. However, the few proposed solutions are limited to the problem
of decomposing solids described through their boundaries. In this thesis we
study the problem of decomposing an arbitrary non-manifold simplicial complex
into more regular components. A formal notion of decomposition is developed
using combinatorial topology. The proposed decomposition is unique, for a given
complex, and is computable for complexes of any dimension. A decomposition
algorithm is proposed that is linear w.r.t. the size of the input. In three or
higher dimensions a decomposition into manifold parts is not always possible.
Thus, in higher dimensions, we decompose a non-manifold into a decidable super
class of manifolds, that we call, Initial-Quasi-Manifolds. We also defined a
two-layered data structure, the Extended Winged data structure. This data
structure is a dimension independent data structure conceived to model
non-manifolds through their decomposition into initial-quasi-manifold parts.
Our two layered data structure describes the structure of the decomposition and
each component separately. In the second layer we encode the connectivity
structure of the decomposition. We analyze the space requirements of the
Extended Winged data structure and give algorithms to build and navigate it.
Finally, we discuss time requirements for the computation of topological
relations and show that, for surfaces and tetrahedralizations, embedded in real
3D space, all topological relations can be extracted in optimal time. This
approach offers a compact, dimension independent, representation for
non-manifolds that can be useful whenever the modeled object has few
non-manifold singularities.
