Interpolation on a Net of Convex Quadrilaterals.

by Morton A. Kaplan, R. A. Papetti

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An investigation of certain interpolation techniques that may be used for computing, for instance, the effects of the detonation of nuclear or conventional explosives. The computational problem is one of forming a surface of interpolation over a mesh of convex quadrilateral cells. The requirements that the surface be continuous and practical to generate lead to the consideration of interpolation across a space quadrilateral by a set of ruled surfaces. A single surface is selected from this set by the use of certain invariance requirements and by simplicity. This surface, a one-sheet hyperboloid, is shown to achieve its maximum and minimum values on its boundary and to have no relative maxima or minima in its interior. The resulting interpolation scheme reproduces the most widely used form of rectangular interpolation in the special case when the quadrilateral is a rectangle. Triangular interpolation is also discussed. 40 pp. Ref. (Author)

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