DATA STRUCTURES FOR 3D MULTI-TESSELLATIONS: AN OVERVIEW Emanuele Danovaro, Leila De Floriani, Paola Magillo, Enrico Puppo Dipartimento di Informatica e Scienze dell’Informazione – Universit` a di Genova Via Dodecaneso, 35, 16146 Genova, ITALY {danovaro,deflo,magillo,puppo}@disi.unige.it Abstract Multiresolution models support the interactive visualization of large vol- umetric data through selective refinement, an operation which permits to focus resolution only on the most relevant portions of the domain, or in the proximity of interesting field values. A 3D Multi-Tessellation (MT) is a multiresolution model, consisting of a coarse tetrahedral mesh at low resolution, and of a set of updates refining such a mesh, arranged as a partial order. In this paper, we describe and compare different data structures which permit to encode a 3D MT and to support selective refinement. Introduction Several applications need analyzing and rendering volumetric scalar fields, sampled at a set of points in the three-dimensional Euclidean space. Examples can be found in scientific visualization, medical imag- ing, computed aided surgery, finite element analysis, etc. A tetrahedral mesh having its vertices at the data points is an appropriate represen- tation especially when the field is sampled at a set of points having an irregular spatial distribution [Nielson, 1997]. In order to analyze volume data sets of large size and to accelerate rendering, a multiresolution approach can be used. Multiresolution mod- els have been widely used for describing surfaces and two-dimensional height fields. Essentially, a multiresolution model consists of a coarse base mesh plus a set of pre-computed refinement updates that increase the resolution of the mesh (i.e., the density of its cells) locally. A mul- tiresolution model encodes the steps performed by a mesh simplification 1