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Selection of triangle sets for the analysis of randomly spaced data

Magnus, E.R. (1980) Selection of triangle sets for the analysis of randomly spaced data. Honours thesis, Murdoch University.

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A triangulation scheme is proposed to provide a foundation in the direct analysis of randomly spaced data. It presents a framework for producing the maximum possible information about spatial differences in the data set, such as the extraction of a wind field from a set of barometric pressures recorded at stations that report irregularly or are mobile.

Five theorems regarding triangular nets are proven. They allow calculation of the number of non-overlaping triangles, as well as generalizations that prove that any net of triangles can be converted into any other net through the adjustment of diagonals of quadrilaterals a feature of the algorithm.

The triangulation algorithm is given and explained, followed by a FORTRAN program listing, including supporting graphical programs which plot the data, the triangular net and illustrate the concept of the selection process. A definition of optimality is included which is based on triangle shape; this definition is used to derive an algorithm which seeks the most optimal triangular net.

The results indicate that a powerful tool is available for data analysis, a tool limited only by data accuracy which is independent of the inconsistencies of manual, subjective analysis.

Item Type: Thesis (Honours)
Murdoch Affiliation(s): School of Mathematical and Physical Sciences
Notes: Note to the author: If you would like to make your thesis openly available on Murdoch University Library's Research Repository, please contact: Thank you.
Supervisor(s): Kloeden, Peter E. and Scott, William
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