A Method of Bivariate Interpolation and Smooth Surface Fitting for Values Given at Irregularly Distributed Points

Hiroshi Akima

ene 1975 · U.S. Department of Commerce, Office of Telecommunications

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A method of bivariate interpolation and smooth surface fitting is developed for z value s given at points irregularly distributed in the x-y plane . The interpolating function is a fifth-degree polynomial in x and y defined in each triangular cell which has projections of three data points in the x-y plane as its vertexes. Each polynomial is determined by the given values of z and estimated values of partial derivatives at the vertexes of the triangle. Procedures for dividing the x-y plane into a number of triangle s, for estimating partial derivative s at each data point ,and for determining the polynomial in each triangle are de scribed. A simple example of the application of the proposed method is shown. User information and Fortran listings are given on a computer subprogram package that implements the proposed method.