Abstract
One approach to finding surfaces interpolating to scattered data is to construct a triangulation associated with the data, and then to construct a piecewise polynomial surface over the triangulation. Until recently, it has been widely accepted that for this purpose it is best to use the Delaunay triangulation. Recently, however, it was shown [Dyn et al. '89, '90, Rippa '89] that for continuous piecewise linear surfaces, dramatic improvements in the fit can be achieved if the triangulation is made to depend on the data. In this paper we discuss a method for interpolating scattered data using C 1 piecewise cubic surfaces based on data-dependent triangulations.
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