A decomposition-based representation for 3D simplicial complexes

TitleA decomposition-based representation for 3D simplicial complexes
Publication TypeConference Papers
Year of Publication2006
AuthorsHui A, Vaczlavik L, De Floriani L
Conference NameProceedings of the fourth Eurographics symposium on Geometry processing
Date Published2006///
PublisherEurographics Association
Conference LocationAire-la-Ville, Switzerland, Switzerland
ISBN Number3-905673-36-3

We define a new representation for non-manifold 3D shapes described by three-dimensional simplicial complexes, that we call the Double-Level Decomposition (DLD) data structure. The DLD data structure is based on a unique decomposition of the simplicial complex into nearly manifold parts, and encodes the decomposition in an efficient and powerful two-level representation. It is compact, and it supports efficient topological navigation through adjacencies. It also provides a suitable basis for geometric reasoning on non-manifold shapes. We describe an algorithm to decompose a 3D simplicial complex into nearly manifold parts. We discuss how to build the DLD data structure from a description of a 3D complex as a collection of tetrahedra, dangling triangles and wire edges, and we present algorithms for topological navigation. We present a thorough comparison with existing representations for 3D simplicial complexes.