Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 257804, 15 pages
Research Article

Localization between Curved Shell Plate and Its Unfolded Shape in Different Coordinate Systems for Ship-Hull Plate Forming

1Department of Naval Architecture and Ocean Engineering, Inha University, Incheon 402-751, Republic of Korea
2Department of Ship and Ocean System, Inha Technical College, Incheon 402-751, Republic of Korea

Received 12 November 2010; Accepted 10 May 2011

Academic Editor: Alexander P. Seyranian

Copyright © 2011 Se Yun Hwang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper describes a mathematical formulation for the efficient localization of 3D surfaces including free-form surfaces and flat surfaces. An important application of this paper is to register flat surface calculated from unfolding process with a curved surface extracted from ship CAD prior to the multipoint press forming works. The mathematical formulation handles the registration and comparison of two free surfaces represented by sparse points based on the iterative closest point (ICP) algorithm and localization that can be applicable to ship-hull plate forming. The ICP algorithm gives an adequate set of initial translation and rotation for surface objects with little correspondence through the minimization of mean square distance metric. Comparison of surfaces is explained in order to determine a corresponding set which gives the optimized press stroke between unfold surface and referential object surface. It thereby allows the optimized press works in ship-hull forming. The combination of registration and comparison is applied to decide the shape equivalence of correspondent surfaces as well as to estimate the transform matrix between point sets where similarity is low. Experimental results show the capabilities of the registration on unfolding surface and curved surface.