Use of bivariate spline functions in preprocessors for ship structure design

Abstract

The use of computers in overall ship structure design is severely restricted by the difficulties in preparing input data with the required speed. Data management problems are only partly responsible for these difficulties even though ships are large and quite complex. The inability to parametrize the hull surface in a convenient form is a major source of trouble. Since the hull form, dimensions, and internal arrangements vary from one design cycle to another it is essential to find a hull surface parametrization that can be computed rapidly and modified readily. Bivariate splines, constructed by taking a tensor product of piece-wise polynomial univariate splines, appear to be quite suitable for this purpose. A satisfactory global parametrization of fairly arbitrary ship surfaces becomes possible. The input parameters include a sparse set of coordinates (offsets) and slopes which are readily available during the early stages of ship design. Since the bivariate spline smooths as well as interpolates, all the input coordinates and slopes do not have to be known with precision. There are several practical problems in using these tensor product splines for use in defining a ship surface. The paper will discuss methods for solving them. The tensor product splines require input data over a rectangular mesh. This presents a problem since ship surfaces can not be defined over rectangular domain. This problem is solved by a coordinate transformation. Computation of the bivariate spline requires a solution of a large number of linear simultaneous equations. Since accuracy is important, the paper will discuss methods for solving these equations.