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Shape-Preserving C 3 Interpolation: The Curve Case

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Abstract

We present a new method for the construction of shape-preserving curves interpolating a given set of 3D data. The interpolating functions are obtained using “quintic-like” spaces of polynomial splines with variable degrees. These splines are of class C 3 and are therefore curvature and torsion continuous and possess a very simple geometric structure, which permits to easily handle the shape-constraints.

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Authors and Affiliations

  1. Dip. di Scienze Matematiche ed Informatiche, Universitá di Siena, Via del Capitano 15, 53100, Siena, Italy

    P. Costantini

  2. Dip. di Matematica, Universitá di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    C. Manni

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  1. P. Costantini
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  2. C. Manni
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Costantini, P., Manni, C. Shape-Preserving C 3 Interpolation: The Curve Case. Advances in Computational Mathematics 18, 41–63 (2003). https://doi.org/10.1023/A:1021270530342

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