Streaming Hermite interpolation using cubic splinelets

Abstract

C2-continuous Hermite interpolation of streaming data with the use of cubic splinelets – building blocks for C2-continuous cubic splines – is presented. Two specific types of splinelets, denoted as A and B, are formally defined (in closed form for equidistant internal knots) and then comparatively evaluated in a series of numerical experiments. The presented results show that the interpolant based on the cubic spline of type B outperforms not only its quintic correspondent, but also the (C1-continuous only!) cubic Hermite spline. The proposed approach can be directly applied to streams that do or do not contain data related to the second derivative of the interpolated function, and to multidimensional curves/trajectories defined parametrically. One other possible application would be processing data sets that are too large to fit in memory.