In this paper we develop and test a simple automatic algorithm for constructing curvature- and torsion-continuous interpolants in R3 which are shape-preserving in a sense that takes into account the convexity, torsion, coplanarity and collinearity information contained in the polygonal line connecting the interpolation points. This algorithm exploits the asymptotic properties of a family of C2 polynomial splines of non-uniform degree, which tend to the above-mentioned polygonal line, as the segment degrees tend to infinity. The performance of the algorithm is tested for a three-dimensional data set, containing coplanar and collinear groups of points as well.
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Kaklis et al. (1997) studied this question.