Simplex and Diamond Hierarchies: Models and Applications

• Published in: Computer graphics forum Vol. 30; no. 8; pp. 2127 - 2155
• Main Authors: Weiss, K., De Floriani, L.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.12.2011
• Subjects: Computer graphics; Data structures; Decomposition; Diamond tools; Finite element analysis; hierarchy of diamonds; hierarchy of simplices; I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling- Hierarchy and geometric transformations; I.3.6 [Computer Graphics]: Methodology and Techniques-Graphics data structures and data types; Image processing systems; interactive terrain visualization; Mathematical models; mesh-based multiresolution models; Modelling; multiresolution isosurfaces; nested refinement schemes; Regular simplex bisection; scalar field visualization; spatial access structures; Studies; Terrain
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/j.1467-8659.2011.01853.x

Hierarchical spatial decompositions are a basic modelling tool in a variety of application domains. Several papers on this subject deal with hierarchical simplicial decompositions generated through regular simplex bisection. Such decompositions, originally developed for finite elements, are extensively used as the basis for multi‐resolution models of scalar fields, such as terrains, and static or time‐varying volume data. They have also been used as an alternative to quadtrees and octrees as spatial access structures. The primary distinction among all such approaches is whether they treat the simplex or clusters of simplices, called diamonds, as the modelling primitive. This leads to two classes of data structures and to different query approaches. We present the hierarchical models in a dimension‐independent manner, and organize the description of the various applications, primarily interactive terrain rendering and isosurface extraction, according to the dimension of the domain.