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  • polynomial interpolant approximation with geometric continuity is much better than hermite interpolation
    Journal of University of Science and Technology of China, 2003
    Co-Authors: Deng Jiansong
    Abstract:

    Generaly speaking, Bzier Curve interpolation with geometric continuity has more free parameter than corresponding Hermite interpolation, therefore with the same interpolation polynomial degree, the approximation error of the former is smaller. But sometimes there is a surprising big difference between them. In this paper, as approximating a quarter unit circle, we show that the error e *_3(t) of Cubic Hermite interpolation is of 400 times the error e_3(t) for Cubic Bzier Curve interpolation with geometric continuity, i.e., e *_3(t) _∞ ≥400 ·e_3(t)_∞. Furthermore, for the error e *_4(t,c) of Hermite interpolation of degree 4 with a free parameter c, we still have \%min\% c∈R \%max\% t∈ e *_4(t,c) ≥6.3 · \%max\% t∈ e_3(t) .