Issue No.08 - August (1987 vol.7)
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.
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, August 1987, doi:10.1109/MCG.1987.276914