@conference {13319, title = {Non-manifold decomposition in arbitrary dimensions}, booktitle = {Discrete Geometry for Computer Imagery}, year = {2002}, month = {2002///}, pages = {59 - 115}, abstract = {In this paper we consider the problem of decomposing a nonmanifold n-dimensional object described by an abstract simplicial complex into an assembly of {\textquoteleft}more-regular{\textquoteright} components. Manifolds, which would be natural candidates for components, cannot be used to this aim in high dimensions because they are not decidable sets. Therefore, we define d-quasi-manifolds, a decidable superset of the class of combinatorial d-manifolds that coincides with d-manifolds in dimension less or equal than two. We first introduce the notion of d-quasi-manifold complexes, then we sketch an algorithm to decompose an arbitrary complex into an assembly of quasi-manifold components abutting at non-manifold joints. This result provides a rigorous starting point for our future work, which includes designing efficient data structures for non-manifold modeling, as well as defining a notion of measure of shape complexity of such models.}, doi = {10.1007/3-540-45986-3_6}, author = {De Floriani, Leila and Mesmoudi,M. and Morando,F. and Puppo,E.} }