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Issue No.01 - January/February (1990 vol.10)
pp: 10-17
ABSTRACT
<p>The authors deal with anomalous oscillations often exhibited by cubic spline interpolating curves. These oscillations, which are not suggested by the data, can be treated with a shaping parameter called tension, which is introduced by generalizing the cubic spline formation in some fashion. The authors consider the associated problem of estimating the magnitude of the tensions necessary to achieve a desired shape. The analysis is based on a theory they reported earlier, called convexity interval analysis, and it leads to an algorithm that produces suitable tension values for given data automatically, without experimentation or interactive user direction. Three examples are given to illustrate the concepts.</p>
CITATION
Yates Fletcher, David F. McAllister, "Curves: Automatic Tension Adjustment for Interpolatory Splines", IEEE Computer Graphics and Applications, vol.10, no. 1, pp. 10-17, January/February 1990, doi:10.1109/38.45805
REFERENCES
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3. G.M. Nielson, "Some Piecewise Polynomial Alternatives to Splines Under Tension," inComputer Aided Geometric Design, R.E. Barnhill and R. Riesenfeld, eds., Academic Press, New York, 1974, pp. 209-235.
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5. G.Y. Fletcher and D.F. McAllister, "An Analysis of Tension Methods for Convexity-Preserving Interpolation,"CG&A, Vol. 7, No. 8, Aug. 1987, pp. 7-14.
6. H. Spath,Spline Algorithms for Curves and Surfaces, W.D. Hoskins and H.W. Sagar, trans., Utilitas Mathematics, Inc., 1974, p. 152.
7. R.W. Soanes, "VP-Splines, an Extension of Twice Differentiable Interpolation," ARO Report 76-3, Army Research Office, Research Triangle Park, N.C., 1976.
8. A.W. Overhauser, "Analytic Definition of Curves and Surfaces by Parabolic Blending," Tech. Report SL 68-40, Ford Motor Co., Detroit, 1968.
9. C. deBoor,A Practical Guide to Splines, Springer-Verlag, Berlin, 1978, p. 53.
10. H. Akima, "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures,"J. ACM, Vol. 17, No. 4, Oct. 1970, pp. 589-602.
11. W. Boehm, G. Farin, and J. Kahmann, "A survey of curve and surface methods in CAGD,"Comput. Aided Geometric Des., vol. 1, no. 1, pp. 1-60, July 1984.
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