Recent publications have documented the development and successful application of weighting function techniques for analytically modeling discretely measurable two-dimensional irregular surfaces. The weighting function techniques produce an analytic functional model valid over the entire input data set. The globally valid function is comprised of an arbitrarily large family of locally valid functions which join together with m-th order continuity assured. The locally valid functions are typically low order polynomials, so that analysis of the functional model is efficient and inexpensive. The theory of the weighting function techniques has been extended to N-dimensional functions, allowing mathematical modeling of discretely measurable functions of an arbitrary number of independent parameters, with m-th order continuity assured. Analytic formula for the weighting function coefficients for N-dimensional, m-th order continuity have been developed. This technique has been employed to store and analyze mass remotely sensed topographic data for contour maps and three-dimensional graphical displays.

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