Development of hybrid skinning surface method for ship hull design

Abstract

Non Uniform Rational B-spline (NURBS), despite its acceptance as high-end CAD/CAM/CAGD standard for surface modeling, is still suffering from one major drawback in representing the surface of a ship hull. The present NURBS is still unable to regenerate the ship surface accurately as in the original drawing of the existing design specially with minimum number of control points. This inherent problem is often associated with the parameterization of data points in NURBS curve/surface. This research aims to develop a general NURBS skinning surface method for surfaces that comprise a set of cross sectional curves with particular application to ships hull surfaces. The developed method was based on proposed hybrid parameterization to approximately fit NURBS skinning surface to sets of cross sectional curves with minimum number of control points without sacrificing the original shape. This was achieved in three steps; the hybrid parameter values and averaging parameter knot vector were generated for each of individual cross sectional curve, then control points on NURBS curve with fitting approximation errors were then calculated, and the weights were set accordingly. The compatibility process was performed by applying knot removal within prespecified error tolerance (e) on cross sectional curves with highest indexes, and knot refinement on cross sectional with lowest indexes. Finally the compatible cross sectional curves were arranged accordingly to get the resultant skinning surface, thus the surface can be generated. The method was tested on several types of ships hull form and other objects in representing the surface with minimum number of control points without sacrificing the original shape. Within prespecified error tolerance (e), the results show that the proposed method has reduced number of control points for the compatible cross sections up to 90% in comparison to conventional skinning methods, up to 81.82% in comparison to Piegl method, and up to 68.63% in comparison to Hyungjun method. The method has also produced higher accuracy (75.0% – 100%) hull surfaces as compared to the surfaces generated by selected software that are widely used for ship hull design.