Journal Article10.1007/BF01036704
Triangle based interpolation
D. F. Watson,G. M. Philip +1 more
80
TL;DR: A curvilinear, C1,interpolation of the data set that is bounded by the linear interpolation and the weighted gradient planes and is tangent to the slant-top interpolation at the data points.
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Abstract: Triangle based interpolation is introduced by an outline of two classical planar interpolation methods, viz. linear triangular facets and proximal polygons. These are shown to have opposite local bias. By applying cross products of triangles to obtain local gradients, a method designated “slant-top proximal polygon interpolation” is introduced that is intermediate between linear facets and polygonal interpolation in its local bias. This surface is not continuous, but, by extending and weighting the gradient planes, a C1
surface can be obtained. The gradients also allow a roughness index to be calculated for each data point in the set. This index is used to control the shape of a blending function that provides a weighted combination of the gradient planes and linear interpolation. This results in a curvilinear, C1,interpolation of the data set that is bounded by the linear interpolation and the weighted gradient planes and is tangent to the slant-top interpolation at the data points. These procedures may be applied to data with two, three, or four independent variables.
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References
•Book
Statistics and data analysis in geology
John C. Davis
- 01 Jan 1973
TL;DR: In this article, a thoroughly revised edition presents important methods in the quantitative analysis of geologic data, such as probability, nonparametric statistics, and Fourier analysis, as well as data analysis methods such as the semivariogram and the process of kriging.
6.7K
Scattered data interpolation: tests of some methods
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.