document: Adaptive thinning for bivariate scattered data This paper studies adaptive thinning strategies for approximating a large set of scattered data by piecewise linear functions over triangulated subsets . Our strategies depend on both the locations of the data points in the plane , and the values of the sampled function at these points - adaptive thinning . All our thinning strategies remove data points one by one , so as to minimize an estimate of the error that results by the removal of a point from the current set of points -LRB- this estimate is termed `` anticipated error '' -RRB- . The thinning process generates subsets of `` most significant '' points , such that the piecewise linear interpolants over the Delaunay triangulations of these subsets approximate progressively the function values sampled at the original scattered points , and such that the approximation errors are small relative to the number of points in the subsets . We design various methods for computing the anticipated error at reasonable cost , and compare and test the performance of the methods . It is proved that for data sampled from a convex function , with the strategy of convex triangulation , the actual error is minimized by minimizing the best performing measure of anticipated error . It is also shown that for data sampled from certain quadratic polynomials , adaptive thinning is equivalent to thinning which depends only on the locations of the data points - nonadaptive thinning . Based on our numerical tests and comparisons , two practical adaptive thinning algorithms are proposed for thinning large data sets , one which is more accurate and another which is faster
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