Piecewise Approximation of Functions of Two Variables and Its Application in Topographical Data Reduction.
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TL;DR
A method to obtain variable-boundary piecewise polynomial approximations of functions of two variables f(x,y) is presented, using a two state scan to find segments where groups of certain coefficients do not differ significantly from their average value.
Abstract
Abstract : A method to obtain variable-boundary piecewise polynomial approximations of functions of two variables f(x,y) is presented. A two state scan is used. In the first stage one uses the one-dimensional algorithm for a set of parallel directions in the domain of f(x,y). Then a similar algorithm is applied on the coefficients of the polynomials, i.e., it finds segments where groups of certain coefficients do not differ significantly from their average value. Computer tests of the algorithm on map data gave significant data reduction ratios (about 40:1) for mean square error of approximation around 2% of the relative altitudes. (Author)