An Analysis of Tension Methods for Convexity-Preserving Interpolation

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.