ACTIVITIES

Multiresolution meshes: Triangle meshes are used to represent surfaces in several applications such as Geographic Information Systems (GISs), Virtual Reality (VR), Computer-Aided Design (CAD), Finite Element Methods (FEM). Tetrahedral meshes are used for scientific data visualization and analysis. All applications mentioned above can benefit from the use of multiresolution meshes. The research activity on multiresolution triangle meshes dates back to 1992. We have proposed models, construction algorithms, query algorithms in 2-D, in 3-D, and in a dimension-independent setting. We have also presented algorithms for performing specific operations of application fields.

Mesh compression: Mesh-based geometric models are often huge in size. This yields large files and delay in loading and transmission of such models. Thus, efficient techniques for compressing the description of a geometric model are required. We have proposed direct and progressive compression techniques, and studied compact data structures for multiresolution meshes in both 2-D and 3-D.

Shape reconstruction: In applications, models of spatial objects need to be built from different data sources and thus need different techniques. We have worked on parallel algorithms for Delaunay triangulations (2-D) and Delaunay tetrahedralizations (3-D). We have also worked on a multiresolution model to represent the shape of the reconstructed object.

Modeling of non-manifold objects: Non-regular, non-manifold meshes are used to describe spatial objects consisting of parts of mixed dimensions, and with a complex topology. In a multiresolution approach, such meshes can represent the shape of an object at a coarse level of abstraction, in which some parts of the object are represented with a lower dimensionality (e.g., the legs of a chair). We have studied multiresolution models, data structures, and algorithms for this case, a multiresolution iconic model to describe an object through hypergraphs of parts of different dimensions, and the decomposition of a non-manifold n-dimensional object into an assembly of simpler components.