On scattered data representations using bivariate splines
The objective of this survey paper is to present a study of scattered data representations using bivariate polynomial splines. All proofs are omitted.NEWLINENEWLINENEWLINEFirst, results on approximation order of spline spaces over arbitrary triangulations are discussed. In real applications, where the spline degree is required to be low, it is necessary to find an optimal triangulation so that the spline space can achieve the optimal approximation order. The author presents an algorithm to transform an arbitrary triangulation into an optimal triangulation for scattered data representation using quartic \(C^1\) splines.NEWLINENEWLINENEWLINEThen he considers the possibilities of finding optimal triangulations for cubic \(C^1\) splines resp. quadratic \(C^1\) splines. Some interpolation schemes and a stable local basis construction are also presented. Finally, the author describes some results on representing scattered data using splines on sphere and natural splines.NEWLINENEWLINEFor the entire collection see [Zbl 0954.65001].
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