A piecewise parabolic C1 approximation technique for curved boundaries

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Abstract

The parabola, in parametric form, is discussed as a suitable approximation to curved boundaries. The four degrees of freedom are specified locally by Hermite interpolation. This piecewise curve approximation can then be thought of as a locally defined C′ spline. A geometric norm, i.e. one which is invariant under the axes change is constructed and the approximation technique is analysed in this norm. A selection of graphical studies of piecewise approximations to a variety of curves, using this method, is given. © 1979.

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McLeod, R. J. Y., & Mitchell, A. R. (1979). A piecewise parabolic C1 approximation technique for curved boundaries. Computers and Mathematics with Applications, 5(4), 277–284. https://doi.org/10.1016/0898-1221(79)90088-9

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