G/sup 1/ scattered data interpolation with minimized sum of squares of principal curvatures

One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(x/sub i/, y/sub i/), i=1,...,n} /spl isin/ R/sup 2/ over a polygonal domain and a corresponding set of real numbers {z/sub i/}/sub i=1//sup n/, we wish to construct a surface S which has continuous varying tangent plane everywhere (G/sup 1/) such that S(x/sub i/, y/sub i/) = z/sub i/. Specifically, the polynomial being considered belong to G/sup 1/ quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G/sup 1/ continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method.

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