In this talk, we will consider the Hermite interpolation with PH spline curve. In particular, at each spline segment the C^1 data at two end points are interpolated by PH cubic biarc and the two arcs are joined together at some unknown common point sharing the same unknown tangent vector. The obtained biarc is expressed in a closed form with three free parameters. The problem of specifying two free angular parameters has been introduced in the literature for characterizing Hermite interpolation based on PH quintics and the strategy to determine these two parameters easily and suitably is identified by the acronym CC. We will export this strategy to our field. More precisely, we will present a method which requires only the evaluation of two analytic explicit expressions and which still guarantees that, when the PH cubic interpolant to Hermite data exists, it is reproduced by our algorithm. The asymptotic behavior of solution will be studied and the shape-preserving properties, particularly the torsion, will be presented. The resulting algorithm is implemented in Mathematica and somenumerical experiments that confirm the theoretical results will be shown.

These results were obtained during the visit of the speaker at the University of Florence last April, and are joint work with Alessandra Sestini (Università degli Studi di Firenze), Carla Manni (Università di Roma “Tor Vergata”) and Maria Lucia Sampoli (Università degli Studi di Siena).