Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling

This article is devoted to cubic Pythagorean hodograph (PH) curves which en joy a number of remarkable properties, such as polynomial are-length functi on and existence of associated rational frames. First we derive a construct ion of such curves via interpolation of G(1) Hermite boundary data with Pyt hagorean hodograph cubics. Based on a thorough discussion of the existence of solutions we formulate an algorithm for approximately converting arbitra ry space curves into cubic PH splines, with any desired accuracy. In the se cond part of the article we discuss applications to sweep surface modeling. With the help of the associated rational frames of PH cubics we construct rational representations of sweeping surfaces. We present sufficient criter ia ensuring G(1) continuity of the sweeping surfaces. This article conclude s with some remarks on offset surfaces and rotation minimizing frames. (C) 1999 Elsevier Science Ltd. All rights reserved.