For data satisfying certain generalized convexity conditions, the existence and uniqueness of a piecewise quadratic curvature continuous parametric spline interpolant in R2is proved. Convexity is preserved by the interpolation, and the numerical construction of the interpolant can be carried out efficiently. The interpolation is 4-th order accurate, and a number of examples shows both the applicability and the limitations of this interpolation scheme. © 1989.
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