In the fields of solid modeling, very often 3D objects are modeled through a description of their 2D boundaries. Boundary description has the drawback that it does not allow the user to assign attributes that describe the properties of solid. In our work, we tackle the problem of representing non-manifold objects through 3D simplicial complexes. We explore all the non-manifold singularities in such complexes. We design a highly compact and update-able representation for encoding such a complex.
- L. De Floriani and A. Hui. A scalable data structure for three-dimensional non-manifold objects. In Proceedings ACM/Eurographics Symposium on Geometry Processing, pages 73--83, Aachen (Germany), 23--25 June 2003.
- L. De Floriani and A. Hui. Update operations on 3D simplicial decompositions of non-manifold objects. In 9th ACM Symposium on Solid Modeling and Applications, pages 169--180, Genova (Italy), 9--11 June 2004. ACM Press.
Data structures specialized for two- and three-dimensional complexes are abundant due to the demands from solid modeling. There are applications, such as visualization of time-varying data, which need data structures describing complexes of higher dimensions. We tackle the problem of representing non-manifold objects of any integer dimension. We design dimension-independent data structures that have the advantages of having simple design concepts, compact, and update-able.
- L. De Floriani, D. Greenfieldboyce, and A. Hui. A data structure for non-manifold simplicial d-complexes. In Proceedings ACM/Eurographics Symposium on Geometry Processing, Nice (France), 8--10 July 2004. ACM Press.
- L. De Floriani and A. Hui. A Dimension-Independent Representation for Multi-Resolution Non-Manifold Meshes. In Journal of Computing and Information Science in Engineering. 7(1), March 2007.
One approach to representing non-manifold shapes is by decomposition. In this approach, a non-manifold complex is described as a collection of simpler pieces. We explore various unique decompositions of 2D and 3D complexes. In such decompositions, each decomposed part exhibits manifold or close-to-manifold properties. The connectivity among these parts is captured in a hypergraph. We study the resultant topology of the hypergraphs.
- A. Hui, L Vaczlavik and L. De Floriani. A Decomposition-based Representation for 3D Simplicial Complexes. In 4th Eurographics Symposium on Geometry Processing, pages 101--110, Cagliari (Italy), June 26-28 2006. ACM Press.