C1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs

In this paper the C Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates C data at one point and they are then joined together with a C continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally C continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.