船体曲线曲面的B样条光顺

根据给定的船体型值点，以三次非均匀B样条为光顺函数，采用整体光顺方法，以应变能最小、曲率变化均匀为准则，以控制点为未知量，建立最优化问题的约束方程并求解，实现船体曲线的光顺。根据曲线的相对曲率线图，将优化后的光顺B样条船体曲线与插值B样条曲线、传统最小二乘法逼近曲线进行了比较。构[循规蹈矩本曲面，以UV方向上的单参数曲线族或站线、水线、纵剖线方向的截面曲线族为研究对象，以曲线族的应变能之和最小为准则，进行光顺处理，最后，以NURBS为统一数学表达式，根据光顺后得到的控制点网络，应用双三次非均匀有理B样条得到光顺的船体曲面。

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.