Simplex and Diamond Hierarchies: Models and Applications

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 extensiv...

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Veröffentlicht in:Computer graphics forum Jg. 30; H. 8; S. 2127 - 2155
Hauptverfasser: Weiss, K., De Floriani, L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford, UK Blackwell Publishing Ltd 01.12.2011
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie:istex:95A8D0D548E6B8C11F576A6A3F27430EAF70C9A2
ArticleID:CGF1853
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2011.01853.x