Algorithms based on Pythagorean hodographs (PH) both in Euclidean plane and Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in Euclidean plane and Minkowski space are very closely related. In this ...

Interpolation theory suggests a generalization of the usual Vandermonde determinant to numbers with multiplicities. We prove a discriminant formula for this generalized Vandermonde determinant and give an application to the Hermite interpolation problem.

The problem of interpolating a set-valued function with convex images is addressed by means of directed sets. A directed set will be visualised as a usually non-convex set in Rn consisting of three parts together with its normal directions: the convex, the concave and the mixed-type part. In the Banach space of the directed sets, a mapping resembling the Kergin map is established. The interpola...

We show that Möbius transformations preserve the rotationminimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean-hodograph curves and also rational frames. Based on these observations we derive an algorithm for G Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minim...