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Open Access Publications from the University of California

Data Point Selection for Piecewise Trilinear Approximaiton


A technique for the iterative selection of 3D points with associated function values (trivariate data) is presented. The selection algorithm is based on assigning weights to the given data and selecting the most important ones. Weights are assigned using a lcoal least square polynomial approxiamation to the data based on a triangulation of the 3D points. The obsolute curvature of the graph of such a local approximant defines the weight for the assiciated data points. The boundary (convex hull) of the original point set is preserved by keeping boundary points defining the convex hull. Interior data points are selected according to their weights. The insertion of a selected data point requires a local modification of the triangulation.

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