SMOOTH INTERPOLATION WITH CUMULATIVE CHORD CUBICS

Smooth cumulative chord piecewise-cubics, for unparameterised data from regular curves in R-n, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C-1) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C-1 regular (geometrically smooth) piecewise-cubic interpolant. Sharpness of theoretical estimates of orders of approximation for length and trajectory is verified by numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data. This may be applicable in computer graphics and vision, image segmentation, medical image processing, and in computer aided geometrical design.