On control polygons of quartic Pythagorean–hodograph curves

In this paper, we study a necessary and sufficient condition for a planar quartic Bézier curve to possess a Pythagorean–hodograph (PH). Based on the definition of PH curve and complex representation of planar curve, we deduce geometric conditions in terms of the legs of the control polygon which guarantee the PH property. We also discuss the problem of G1 Hermite interpolation by planar PH quartics.