Shape-preserving interpolation in R3

Received on 7 September 1993. Revised on 20 February 1996. In this paper we develop and test a simple automatic algorithmfor constructing curvature- and torsion-continuous interpolantsin R³ which are shape-preserving in a sense that takes intoaccount the convexity, torsion, coplanarity and collinearityinformation contained in the polygonal line connecting the interpolationpoints. This algorithm exploits the asymptotic properties ofa family of C² polynomial splines of non-uniform degree, whichtend to the above-mentioned polygonal line, as the segment degreestend to infinity. The performance of the algorithm is testedfor a three-dimensional data set, containing coplanar and collineargroups of points as well. E-mail address: kaklis{at}deslab.ntua.gr Tel.: +30-1-7721419Telefax: +30-1-7721408 E-mail address: menelaos{at}sccm.stanford.edu