Fairing Algorithm for Ship Hull Curves and Surface with B-spline

An automatic global fairing algorithm is developed for ship hull form with cubic non uniform B spline function. Firstly interpolating sequences of given points using cubic non uniform B spline curves, The fairness criterion, strain energy minimization, of the algorithm is defined. The objective function is subject to both uniform change of curvatures of a curve and distance between original and modified control points. Establishing and resolving the linear optimization equation system, control points of cubic non uniform B spline curve are repositioned. Authors generate fairness curves of ship hull. Secondly, displaying curvature graph of the fairing cubic non uniform B spline curve, intepolating cubic non uniform B spline curve, least square method curve respectively to assess the curve fairness, some good conclusions are drawn. Finally, the above fairing curve algorithm is used to process fairing ship hull surface. Ship hull shape is presented by bicubic non uniform B spline surface interpolation to points net. Two families of curves, i.e., u, v directional isoparametric curves of surface, are hired to fair ship hull shaped surface. The strain energy minimization of two family curves is objective function. This optimization is subject to the same constraints as above fairing curves algorithm. Molded lines in ship subject, i.e., half breadth lines, body lines and sheer lines, can take place of isoparametric curves families. Calculating a linear optimization equation, repositioning the given control points net, and defining the boundary conditions of surface, fairing ship hull shape is presented successfully by bicubic Non Uniform Ratioal B Spline surface. Using the light model to assess the ship hull form surface, a desired result is gotten.