Diamond-based models for scientific visualization

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, in which a simplex (e.g. line segment, triangle, tetrahedron) is bisected 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 an underlying 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 a hypercube. This leads 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 atomic symmetry units within the underlying triangulation grid. We discuss the use of supercubes to associate information with coherent subsets of regularly sampled scalar fields and demonstrate the effectiveness of this representation for modeling multiresolution terrain and volumetric datasets.

@InProceedings{WD11,
  author       = {Weiss, K. and De Floriani, L.},
  title        = {Diamond-based models for scientific visualization},
  booktitle    = {Collana Talks@CRS4},
  number       = {20110715},
  month        = {july},
  year         = {2011},
  note         = {contatto: enrico.gobbetti@crs4.it},
  url          = {https://publications.crs4.it/pubdocs/2011/WD11},
}