Update operations on 3D simplicial decompositions of non-manifold objects

TitleUpdate operations on 3D simplicial decompositions of non-manifold objects
Publication TypeConference Papers
Year of Publication2004
AuthorsDe Floriani L, Hui A
Conference NameProceedings of the ninth ACM symposium on Solid modeling and applications
Date Published2004///
PublisherEurographics Association
Conference LocationAire-la-Ville, Switzerland, Switzerland
ISBN Number3-905673-55-X

We address the problem of updating non-manifold mixed-dimensional objects, described by three-dimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and vertex split, which are the most common operations performed for simplifying a simplicial complex. We examine the effect of such operations on a 3D simplicial complex, and we describe algorithms for edge collapse and vertex split on a compact representation of a 3D simplicial complex, that we call the Non-Manifold Indexed data structure with Adjacencies (NMIA). We also discuss how to encode the information needed for performing a vertex split and an edge collapse on a 3D simplicial complex. The encoding of such information together with the algorithms for updating the NMIA data structure form the basis for defining progressive as well as multi-resolution representations for objects described by 3D simplicial complexes and for extracting variable-resolution object descriptions.