C1 Hermite interpolation using MPH quartic Original Research Article

In this paper, we study the C1 Hermite interpolation problem using Minkowski Pythagorean Hodograph (MPH) quartics in R2,1. As a preliminary step, we characterize MPH curves in R2,1 by the roots of the hodographs of their complexified spine curves. We present two schemes for this interpolation problem: one is a subdivision scheme using direct C1 interpolation and the other is a two step scheme using a new concept, C1/2 interpolation.