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C1 Interpolation with Cumulative Chord Cubics

Kozera R., Noakes L.

Fundamenta Informaticae

2004

Vol. 61, nr 3,4

285--301

Cumulative chord C1 piecewise-cubics, for unparameterized data from regular curves in Rn, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C1) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C1 piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.