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Surfaces defined on surfaces. (English) Zbl 0726.65013
The authors present two methods for constructing functions, defined over convex surfaces, interpolating data values at scattered points on the surfaces. These are local methods.
The first one is basically an extension of the 3D Shepard’s method that restrict the domain to a convex surface. The second one consists in an extension of the triangular-based method over a sphere to arbitrary convex surfaces.
The two methods are compared both numerically and by means of color interactive computer graphics on an example consisting in determination of the pressure at arbitrary locations on a wing, by using given discrete pressures measured on it. This example represents an illustration of a more general problem: given data at discrete locations on a surface, determine a function that interpolates these data over the entire surface.

65D17 Computer-aided design (modeling of curves and surfaces)
65D05 Numerical interpolation
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68U07 Computer science aspects of computer-aided design
41A05 Interpolation in approximation theory
Full Text: DOI
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