The Taub Faculty of Computer Science Events and Talks

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds.

In this talk, we formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes leading to a compact pointerless representation for conforming meshes generated by regular simplex bisection. We then introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We discuss the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of this representation for modeling multiresolution terrain and volumetric datasets.