Generation of Discrete Bicubic G^1 B-Spline Ship Hullform Surfaces from a Given Curve Network Using Virtual Iso-Parametric Curves

We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;boundary curves and ＂reference curves＂,The boundary curves correspond to a set of rectangular（or triangular）topological type that can be representes with tensot-product （or degenerate）B-spline surface patches.Next,in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing ＂virtual＂isoparametric curves.Finally,a discrete G^1 continuous B-spline surface is gencrated by a surface fitting algorithm.Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.

Generation of Discrete Bicubic G1 B-Spline Ship Hullform Surfaces from a Given Curve Network Using Virtual Iso-Parametric Curves

We propose a method that automatically generates discrete bicubic G¹ continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and “reference curves”. The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches, surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing “virtual” iso-parametric curves. Finally, a discrete G¹ continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method. A preliminary version of this paper appeared in Proc. the 1st Korea-China Joint Conference on Geometric and Visual Computing. This work was supported by the Basic Research Program of the Korea Science and Engineering under Grant Nos. R01-2002-000-00061-0 and R01-2005-000-11257-0. Joong-Hyun Rhim is the technical director of EzGraph. Co., Ltd. He received the B.S. degree in 1995, and the M.S. degree in 1997 in Naval Architecture and Ocean Engineering from Seoul National University. His research interests include shipbuilding CAD/CAM systems and geometric modeling Doo-Yeoun Cho is a post doctoral researcher in the Dept. Naval Architecture and Ocean Engineering at Seoul National University, where he also received his B.S., M.S. and Ph.D. degrees in 1997, 1999 and 2005, respectively. His research interests include CAD/CAM, geometric modeling and computer graphics. Kyu-Yeul Lee is a professor in the Dept. of Naval Architecture and Ocean Engineering, and in the Research Institute of Marine Systems Engineering, at Seoul National University, Korea. He received his B.S. degree in 1971 at Seoul National University, and his M.S. degree in 1975 and Ph.D. degree in 1982 at Technical University of Hannover, Germany, all in Naval Architecture. His research interests include geometric modeling, design automation, optimization, and CAD in shipbuilding. Tae-Wan Kim is an associate professor in the Dept. of Naval Architecture and Ocean Engineering, and in the Research Institute of Marine Systems Engineering, at Seoul National University, Korea. He received the B.S. degree in Industrial Engineering from Hanyang University, Korea in 1985, the M.S. and Ph.D. degrees in computer science from Arizona State University, USA in 1993 and 1996. From 1996 to 1999 he worked as a software engineer at EDS Inc. (formerly SDRC), USA where he was involved in developing the I-DEAS CAD/CAM system. His research interests include geometric modeling, NURBS curves and surfaces, and CAD/CAM.