Simplicial-based multiresolution volume datasets management: an overview

A number of approaches exist to support multi-resolution management: naýve sub sampling, wavelet techniques, methods based on hierarchical space subdivisions (e.g. octrees), methods based on simplicial decomposition. The term multi-resolution is often used to indicate either discrete or continuous level of detail (LOD) representation. We will cover mostly the second aspect, and therefore we point our attention to those methods that allow to manage selective refinements (or the inverse operation, i.e. selective coarsening) in a dynamic manner, according to the interactive requests of the application. Simplicial meshes have been often used in the visualization of volume dataset. The simplicity of the basic cell allows to easily manage isosurface extraction (field is linearly interpolated, no ambiguity) and to implement in an e±cient manner direct volume rendering (DVR) solutions. Moreover, tetrahedral-based DVR solution can now be implemented using o®-the-shelf graphics hardware, gaining impressive speed-ups with respect to software solutions. Therefore, simplicial decompositions have been often considered in the design of multi-resolution methods, not only because easy to render but also because they easily adapt to di®erent shapes or to the data field structure/ topology. This paper presents an overview and a comparison of the different approaches based on multi-resolution simplicial decomposition, which have been proposed in the context of volume visualization. We subdivide the existing methods in two main classes, which depend on the refinement kernel used to manage the selective refinement/coarsening: regular or irregular. Regular techniques starts from a coarse irregular base domain and apply recursive regular refinement, resulting in large meshes organized as uniform grid patches. Irregular techniques are independent from the topology of the underlying mesh and as consequence during the refinement procedure new vertices can be inserted at more convenient locations instead of predefined positions; not being forced to follow a regular subdivision scheme irregular techniques result to be more flexible and suitable to resolve complex geometric features and geometry changes.