Optimized NURBS Ship Hull Fitting using Simulated Annealing Ang Swee Wen Department Of Graphics and Multimedia Faculty of Computer Science and Information System Universiti Teknologi Malaysia angeline_aasw@hotmail.com Siti Mariyam Hj. Shamsuddin Department Of Graphics and Multimedia Faculty of Computer Science and Information System Universiti Teknologi Malaysia mariyam@fsksm.utm.my Yahya Samian Department Of Marine Technology Faculty of Mechanical Engineering Universiti Teknologi Malaysia yahya@fkm.utm.my Abstract The shape of a NURBS curve or surface is defined by the location of its control points, the control points’ weights, and the knot vectors. Most of the curve and surface design tried to modify the control points. However, it is still impossible to obtained accurate control points for a reconstructed NURBS curve or surface. The fitness of these surfaces is generally considered a subjective notion depending on the judgment of the designers (eg. visually pleasing, devoid of unnecessary bumps or wiggles, satisfying certain continuity requirements). One of the restriction in ship hull design is that the existing details of a ship design on paper or a ship that already been constructed physically couldn’t be reconstructed accurately and concisely in a ship hull design software. This research strives to solve this problem by creating fair ship hull surface using NURBS. An optimized NURBS ship hull fitting approach using simulated annealing is developed. Evaluation and analysis (accuracy, fairness and speed of processing) on the proposed approach is done. Keywords: NURBS, simulated annealing, ship hull, fitting, ship design, fairing and surface reconstruction. 1. Introduction This research reconstructs a concise and accurate approximated physical surface of the ship hull. It can take on many different characteristics, depending on the goal of the reconstruction, the origin of the offset, and tools or methods available to tackle the job. All of these are taken into account in developing the best approach. In the field of surface modeling of hull form, geometric complexity of hull form gives many difficulties. This leads to the issue of what is the best surface reconstruction method for ship hull? NURBS is the best available method as it is state in [6] that it is the dominant mathematical technique available and [1] standard of computer modeling for many industries. The generation of NURBS curves and surfaces are used for the fitting of the ship hull because of its high level of continuity, fairness and flexibility. Besides, the amounts of control points needed are less compared to other available parametric surfaces like parabolic blending, bezier, etc. 2 NURBS 2.1 NURBS formulation A NURBS curve of degree p is a piecewise polynomial curve defined as follows:    n i w i p i w P u N u C 0 , ) ( ) ( where , ,..., 0 , n i P w i  form the so-called control polygon defined by a set of weighted control points ) , , , ( i i i i i i i w i w z w y w x w P  , and n i u N p i ,..., 0 ), ( ,  , are the B-spline basis functions defined over a knot vector 1 ,..., 0 , }, ,..., { 1 0      m i u u u u U i i m Throughout this research the knot vector has the following form (open knot vector): Proceedings of the International Conference on Computer Graphics, Imaging and Visualisation (CGIV'06) 0-7695-2606-3/06 $20.00 © 2006