Hiroshi Akima
Skip Abstract Section
Abstract
A method is designed for interpolating values given at points of a rectangular grid in a plane by a smooth bivariate function z = z(x, y). The interpolating function is a bicubic polynomial in each cell of the rectangular grid. Emphasis is on avoiding excessive undulation between given grid points. The proposed method is an extension of the method of univariate interpolation developed earlier by the author and is likewise based on local procedures.
- 1 Ackland, T. G. On osculatory interpolation, where the given values of the function are at unequal intervals. J. Inst. Actuar. 49 (1915), 369-375.Google Scholar
Cross Ref
- 2 Akima, Hiroshi. A new method of interpolation and smooth curve fittingbased on local procedures. J. ACM 17, 4 (Oct. 1970), 589-602. Google ScholarDigital Library
- 3 Akima, Hiroshi. Algorithm 433, Interpolation and smooth curve fitting based on local procedures. Comm. ACM 15, 10 (Oct. 1972), 914-918. Google ScholarDigital Library
- 4 Akima, Hiroshi. Algorithm 474. Bivariate interpolation and smooth surface fitting based on local procedures. Comm. ACM 17, 1 (Jan. 1974),26-31. Google ScholarDigital Library
- 5 GreviUe, T.N.E. Spline functions, interpolation, and numerical quadrature. In Mathematical Methods./or Digital Computers, Vol. 2, A. Ralston and H.S. Will (Eds.), Wiley, New York, 1967Google Scholar
- 6 Hildebrand, F.B. bttroduction to Numerical Analysis. McGraw-Hill, New York, 1956, Ch. 2, 3, and 9. Google ScholarDigital Library
- 7 Karup, Johannes. On a new mechanical method of graduation. In Transactions o f the Second lnternational Actuarial Congress. C. and E. Layton, London, 1899, pp. 78-109.Google Scholar
- 8 Milne, W.E. Numerical Calculus. Princeton U. Press, Princeton, N.J., 1949, Ch. 3.Google ScholarCross Ref
Index Terms
- A method of bivariate interpolation and smooth surface fitting based on local procedures
Recommendations
Algorithm 761: Scattered-data surface fitting that has the accuracy of a cubic polynomial
An algorithm for smooth surface fitting for scattered data has been presented. It has the accuracy of a cubic polynomial in most cases and is a local, triangle-based algorithm.
Comments