# A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures

A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures A New Method of Interpolation and S m o o t h Curve Fitting Based on Local Procedures HIROSHI A K I M A ESSA Research Laboratories,* Boulder, Colorado ABSTRACT. A new mathematical method is developed for interpolation from a given set of data points in a plane and for fitting a smooth curve to the points. This method is devised in such a way that the resultant curve will pass through the given points and will appear smooth and natural. It is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given points. In this method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points. Comparison indicates that the curve obtained by this new method is closer to a manually drawn curve than those drawn by other mathematical methods. KEYWORDSAND PHRASES: interpolation, polynomial, slope of curve, smooth curve fitting CR CATEGORIES: 5.13 1. Introduction To determine a relation b e t w http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

# A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures

Journal of the ACM (JACM), Volume 17 (4) – Oct 1, 1970
14 pages

/lp/association-for-computing-machinery/a-new-method-of-interpolation-and-smooth-curve-fitting-based-on-local-9EaN4BaLtM
Publisher
Association for Computing Machinery
ISSN
0004-5411
DOI
10.1145/321607.321609
Publisher site
See Article on Publisher Site

### Abstract

A New Method of Interpolation and S m o o t h Curve Fitting Based on Local Procedures HIROSHI A K I M A ESSA Research Laboratories,* Boulder, Colorado ABSTRACT. A new mathematical method is developed for interpolation from a given set of data points in a plane and for fitting a smooth curve to the points. This method is devised in such a way that the resultant curve will pass through the given points and will appear smooth and natural. It is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given points. In this method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points. Comparison indicates that the curve obtained by this new method is closer to a manually drawn curve than those drawn by other mathematical methods. KEYWORDSAND PHRASES: interpolation, polynomial, slope of curve, smooth curve fitting CR CATEGORIES: 5.13 1. Introduction To determine a relation b e t w

### Journal

Journal of the ACM (JACM)Association for Computing Machinery

Published: Oct 1, 1970

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