A method of bivariate interpolation and smooth surface fitting based on local procedures

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A method of bivariate interpolation and smooth surface fitting based on local procedures

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Communications of the ACM archive
Volume 17 , Issue 1 (January 1974) table of contents

Pages: 18 - 20

Year of Publication: 1974

ISSN:0001-0782

Author

Hiroshi Akima

U.S. Dept. of Commerce, Boulder, CO

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 11, Downloads (12 Months): 101, Citation Count: 4

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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.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	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.
	2	Hiroshi Akima, A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures, Journal of the ACM (JACM), v.17 n.4, p.589-602, Oct. 1970 [doi>10.1145/321607.321609]
	3	Hiroshi Akima, Algorithm 433: interpolation and smooth curve fitting based on local procedures [E2], Communications of the ACM, v.15 n.10, p.914-918, Oct. 1972 [doi>10.1145/355604.355605]
	4	Hiroshi Akima, Bivariate interpolation and smooth surface fitting based on local procedures, Communications of the ACM, v.17 n.1, p.26-31, Jan. 1974 [doi>10.1145/360767.360797]
	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, 1967
	6	Begnaud Francis Hildebrand, Introduction to numerical analysis: 2nd edition, Dover Publications, Inc., New York, NY, 1987
	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.
	8	Milne, W.E. Numerical Calculus. Princeton U. Press, Princeton, N.J., 1949, Ch. 3.

CITED BY 4

	Hiroshi Akima, A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points, ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.148-159, June 1978
	A. Preusser, Algorithm 671: FARB-E-2D: fill area with bicubics on rectangles—a contour plot program, ACM Transactions on Mathematical Software (TOMS), v.15 n.1, p.79-89, March 1989
	Jean-Laurent Mallet, Discrete smooth interpolation, ACM Transactions on Graphics (TOG), v.8 n.2, p.121-144, April 1989
	Hiroshi Akima, Bivariate interpolation and smooth surface fitting based on local procedures, Communications of the ACM, v.17 n.1, p.26-31, Jan. 1974