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An Analysis of Tension Methods for Convexity-Preserving Interpolation
August 1987 (vol. 7 no. 8)
pp. 7-14
G. Fletcher, North Carolina State University
David McAllister, North Carolina State University
We introduce a Hermite-interpolating space general enough to include most commonly used tensioned interpolants, with conditions that allow others to be easily constructed. Each of these spaces may be associated with a convexity interval that gives a quantitative measure of its ability to produce convexity-preserving interpolants. This analysis is applied to produce a simple algorithm for constructing piecewise univariate C1 interpolants that preserve convexity of the data by adaptive tension application.

1. A. W.Overhauser, "Analytic Definition of Curves and Surfaces by Parabolic Blending," , Ford Motor Co. 1968
2. H.Akima, "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures,"pp. 589-602 Oct. 1970 J. ACM
3. G.Renner, "A Method of Shape Description for Mechanical Engineering Practice,"pp. 137-142 March/ June 1983 Computers in Industry
4. Boor, A Practical Guide to Splines , Springer-Verlag 1978pp. 304-305
5. D. G.Schweikert, "An Interpolation Curve Using a Spline in Tension," J. Math. and Physics Vol. 45, No. 3, pp. 312-317 1966
6. H.Spath, Spline Algorithms for Curves and Surfaces , Utilitas Mathematica, Inc. 1974pp. 152 W.D. Hoskins and H.W. Sagar, translators
7. A. K.Cline, "Scalar and Planar Valued Curve Fitting Using Splines Under Tension,"pp. 218-220 Apr. 1974 Comm. ACM
8. R. V.Soanes Jr. , "VP-Splines, an Extension of Twice Differentiable Interpolation," , Research Triangle 1976
9. L. L.Schumaker, "On Shape-Preserving Quadratic Spline Interpolation,"pp. 854-863 Aug. 1983 SIAM J. Numerical Analysis
10. C. E.Frost and G. L.Kinzel, "An Automatic Adjustment Procedure for Rational Splines," Computers & Graphics Vol. 6, No. 4, pp. 171-176 1982

G. Fletcher, David McAllister, "An Analysis of Tension Methods for Convexity-Preserving Interpolation," IEEE Computer Graphics and Applications, vol. 7, no. 8, pp. 7-14, Aug. 1987, doi:10.1109/MCG.1987.276914
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