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Shape preserving interpolation by cubic G1 splines in $${mathbb{R}^3}$$

Authors:	Gašper Jaklič Emil Žagar

Affiliation:	(1) FMF, University of Ljubljana, Ljubljana, Slovenia;(2) PINT, University of Primorska, Koper, Slovenia;(3) FMF and IMFM, University of Ljubljana, Ljubljana, Slovenia

Abstract:	In this paper, G ¹ continuous cubic spline interpolation of data points in ${mathbb{R}^3}$ , based on a discrete approximation of the strain energy, is studied. Simple geometric conditions on data are presented that guarantee the existence of the interpolant. The interpolating spline is regular, loop-, cusp- and fold-free.

Keywords:	Hermite interpolation Geometric continuity Spline Minimization
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