Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets

Planar polynomial curves have rational offset curves, if they are either Pythagorean-hodograph (PH) or indirect Pythagorean-hodograph (iPH) curves. In this paper, we derive an algebraic and two geometric characterizations for planar quartic iPH curves. The characterizations are given in terms of quantities related to the Bezier control polygon of the curve, and naturally extend to quartic and cubic PH and quadratic iPH curves. (C) 2020 Elsevier B.V. All rights reserved.