Abstract
A new method is suggested for choosing the “twist” parameters (or mixed partial derivatives), which arise when Coons patches are used for surface definition or interpolation over rectangular arrays of data points. The method is based on the observation that the component of the twist normal to the surface may be related to a geometrical invariant intrinsic to the surface, namely, the Gaussian curvature. This quantity can also be expressed independently of the twist and estimated on the basis of independent univariate data already available once the patch boundaries are specified (thus avoiding the incompatibilities inherent in bivariate discretizations). The tangential components of the twist vector may also be estimated by independent univariate means from prior data. The resulting surface has the given or estimated curvature at the data points. (Smoothness properties of certain composite surfaces are also analyzed in terms of invariants related to curvature.)
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