A unified Pythagorean hodograph approach to the medial axis transform and offset approximation

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 paper, we continue the discussion of the interplay between spatial MPH curves and their associated planar PH curves from the point of view of Hermite interpolation. Based on this approach we design a new, simple interpolation algorithm. The main advantage of the presented unifying method lies in the fact that it uses, only after some simple additional computations, an arbitrary algorithm for interpolation by planar PH curves also for interpolation by spatial MPH curves. We present the functionality of our method on G Hermite data, nevertheless one could obtain also higher order algorithms.