C~1 Hermite interpolation using MPH quartic

摘要

In this paper, we study the C~1 Hermite interpolation problem using Minkowski Pythagorean Hodograph (MPH) quartics in R~(2,1). As a preliminary step, we characterize MPH curves in R~(2,1) 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 C~1 interpolation and the other is a two step scheme using a new concept, C~(1/2) interpolation.