Computer Aided Geometric Design 6 (1989) 87-96 North-Holland 87 zyxwvutsrqp Surface lofting and smoothing with skeletal-lines S. BED1 De~artmenl of Meckanical Engineeri~& Universiry of Waterioo, Ontario, Canada G.W. VICKERS Depmnent of Meckanical Engineering University of Victoriq B.C., Canah Received My 1987 Revised May 1988 Abstmet. A method of surface definition and smoothing using a set of three-dimensional skeletal-lines is given. The skeletal-lines represent the essential features of a surface and can be individually smoothed using the first divided difference. The modified skeletal-lines are automatically generated by back substitution from the smoothed first divided difference lines. In this way a surface can be defined and smoothly adjusted through a set of sparse. irregular, inconsistent data. Keywo& Surface definition and smoothing, skeletal-line representation, back substitution of fist divided difference. The critical surfaces in ship hulls, turbine blades, propellers, aeropume fuselages, etc. are defined in three orthographic views [Bedi & Vickers ‘871 showing various horizontal, vertical and oblique cross-sections, as shown in Fig. 1. The drawings are done to a smalI scale and may contain inherent design errors. The computer models of these surt^aces are often generated by identifying form parameters, such as sectional area, end angles, elc. [Clements ‘84, Hattori & Matida ‘77, Munchmeyer ‘821, or using a control polyhedron [Bamhill ‘85, Bezier ‘72, de Boor abear zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG Iine BODY PLAN Fig. 1. Naval architect’s design drawing showing station-fines, water-tines, shear-line and profile-line. 0167.83%/89/$3.50 0 1989. Rfsevier Science Publishers B.V. (North-Holland)