ROBUST COMPUTATION OF THE ROTATION MINIMIZING FRAME FOR SWEEP SURFACEMODELING

The rotation minimizing frame is superior to the Frenet frame for mode ling sweep surfaces [F. Klok, Computer Aided Geometric Design 3, 217-2 29 (1986)] However, the existing techniques for computing the rotation minimizing frame either have low approximation degree or are unrobust numerically. We present a method to compute an approximate rotation m inimizing frame in a robust and efficient manner. The following proble m is studied. Given an axial curve A(u) in space and a 2D cross-sectio n curve C(v), generate a sweep surface S(u, v) = A(u) + F(u)C(v), wher e F(u) is a rotation minimizing frame defined on A(u). Our method work s by approximating A(u) with a G(1) circular-are spline curve and then sweeping C(v) with a rotation minimizing frame along the approximatin g circular-are spline curve; the sweep surface thus generated is an ap proximation of S(u, v). The advantages of this method are: (1)the appr oximate rotation minimizing frame is computed robustly, with its error being much smaller than would be obtained by Klok's linear method wit h the same number of segmentations; (2) the sweep surface generated is a NURBS surface if the cross-section curve is a NURBS curve; (3) the method is easily adapted to generating a smooth and closed sweep surfa ce when A(u) is a closed smooth curve. (C) 1997 Elsevier Science Ltd.