BI-CURVE AND MULTI-PATCH SMOOTHING WITH APPLICATION TO THE SHIPYARD INDUSTRY Xoán A. Leiceaga (1) Oscar Ruiz (2) Carlos Vanegas (3) Eva Soto (1) Jose Prieto (2) Manuel Rodríguez (1) (1) GED, Universidade de Vigo, Vigo, España leiceaga@uvigo.es (2) CAD/CAM/CAE Laboratory, EAFIT University, Medellín, Colombia oruiz@eafit.edu.co (3) Dept. Computer Science, Purdue University, Lafayette, IN, USA cvanegas@cs.purdue.edu ABSTRACT Algorithms are proposed and implemented in a commercial system which allow for the C 1 -continuity matching between adjacent B-spline curves and B-spline patches. These algorithms only manipulate the positions of the control points, therefore respecting the constraint imposed by the sizes of the available commercial steel plates. The application of the algorithms respect the initial hull partition made by the designers and therefore the number and overall shape and position of the constitutive patches remains unchanged. Algorithms were designed and tested for smoothing the union of (a) two B-spline curves sharing a common vertex, (b) two B-spline surfaces sharing a common border, and (c) four B-spline surfaces sharing a common vertex. For this last case, an iterative heuristic degree- of-freedom elimination algorithm was implemented. Very satisfactory results were obtained with the application of the presented algorithms in shipyards in Spain. 1 Introduction and Literature Review B-spline curves and surfaces have been used extensively in the past to define ship-hull geometry for design purposes [1, 2]. The popularity of B-spline for free-form surface design lies in their useful characteristics, such as local support, the convex hull, and variation-diminishing properties [3]. Theoretical background of B-spline curves and surfaces can be found in Farin [4]. A discussion of their suitability for ship hull surface definition can be found in Rogers [5].