Simplicial diffeomorphisms

Mello, Vinícius M.; Velho, Luiz

doi:10.1016/j.cagd.2010.08.002

Cited by 1 publication

(2 citation statements)

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“…In such cases, there is a scalar value F( v ) associated with each vertex in the domain. The value of a sample within a cell can be approximated by linear interpolation on the vertices of the cell, although other models are possible [MV10].…”

Section: Querying An Rsb Hierarchymentioning

confidence: 99%

“…This is the basis for the highly adaptive subdivision surface scheme of Velho and Zorin [VZ01], which guarantees the extraction of conforming meshes with greater smoothness than existing subdivision schemes (such as the Catmull‐Clark subdivision [CC78]) while only doubling (rather than quadrupling) the number of cells involved in each refinement. This notion is formalized in [MV10], where other possible interpolation schemes are also discussed.…”

Section: Applications In Two Dimensionsmentioning

confidence: 99%

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Simplex and Diamond Hierarchies: Models and Applications

Weiss

Floriani

2011

Computer Graphics Forum

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Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains. Several papers on this subject deal with hierarchical simplicial decompositions generated through simplex bisection. Such decompositions, originally developed for finite elements, are extensively used as the basis for multiresolution 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 and in other applications. In this state of the art report, we distinguish between approaches that focus on a specific dimension and those that apply to all dimensions. The primary distinction among all such approaches is whether they treat the simplex or clusters of simplexes, called diamonds, as the modeling 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.

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Section: Querying An Rsb Hierarchymentioning

confidence: 99%