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A data modeling abstraction for describing triangular mesh algorithms

  • R. Bruce Simpson
Article

Abstract

The use of a relational data model is proposed as the basis for a technique for expressing algorithms for unstructured meshes, or geometric incidences more generally. The result is an abstraction for meshes that is conceptually intermediate between the geometric abstractions of mathematical descriptions and the list representations of source code implementations. Algorithms are then described in terms of:
  • -conventional structured pseudocode,

  • -the mesh conceived as a globally accessible database,

  • -variables typed using the data model, and

  • -commands based on a database query and modification syntax.

It is argued that the resulting paradigm supports descriptions that are precise, complete, and relatively representation independent. It thus supports the role of algorithms in providing templates for coding, while also supporting the role of algorithms as vehicles for the communication and documentation of ideas.

A simple data model for planar triangular meshes is defined. Using it, the technique is demonstrated by a suite of familiar algorithms for constructing the Delaunay triangulation, using the divide-and-conquer and incremental approaches. Data dependencies in the model of triangular meshes are noted, and their implications for relating the model to several standard mesh representations is discussed.

AMS subject classification

G.4 I.3.5 

Key words

Triangulation algorithms Delaunay triangulation relational model divide-and-conquer finite element mesh 

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Copyright information

© BIT Foundation 1997

Authors and Affiliations

  • R. Bruce Simpson
    • 1
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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