Abstract
We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated Żrst and second derivatives) we construct a four{dimensional family of PH interpolants of degree 9 and introduce a symetrically invariant parameterization of this family.
This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve.
Secondly, it has the best possible approximation order 6. Thirdly, it is symmetric in the sense that the interpolant of the \reversed' set of boundary data is simply the \reversed' original interpolant.
This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree 9 which is globally C2.