Data structures for 3D multi-tessellations: an overview

Multiresolution models support the interactive visualization of large volumetric 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 imaging, computed aided surgery, finite element analysis, etc. A tetrahedral mesh having its vertices at the data points is an appropriate representation 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 models 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 multiresolution model encodes the steps performed by a mesh simplification