B-spline surfaces for ship hull design

Abstract

The use of true sculptured surface descriptions for design applications has been proposed by numerous authors. The actual implementation and use of interactive sculptured surface description techniques for design and production has been limited. The use of such techniques for ship hull design has been even more limited. The present paper describes a preliminary implementation of such a system for the design of ship hulls and for the production of towing tank models using numerical control techniques. The present implementation is based on a Cartesian product B-spline surface description. Implementation is on an Evans and Sutherland Picture System supported by a PDP-11/45 minicomputer. The B-spline surface is manipulated by its associated polygonal net. Both surface and net are three-dimensional. Techniques both good and bad for 3-D picking of a polygon point when the net, its associated surface, and the 3-D picking cue independently exist and can be independently manipulated in three space are presented and discussed. The shape of a B-spline surface of fixed order is controlled by the location of the polygon net points, the number of multiple points at a particular net point, and the knot vector. Frequently multiple points imply multiple knot vectors. Practical techniques for controlling and shaping the surface with and without this assumption are discussed and the results illustrated. Experience attained by interactively fitting a single fourth order B-spline surface patch to the forebody half of an actual ship hull described by three dimensional digitized points is discussed and the results illustrated.