用B样条拟合与绘制船体型线

Plotting Hull Lines by Means of B-Spline Fitting

由于B样条函数具有描述曲线与曲面的独特功能,近年来颇受船舶设计工作者的重视。本文论述了几个基本问题:B样条函数在不同阶次情况下的数学表达式及基函数的特征、性质和功能之间的差异;过已知型值点三次B样条曲线多边形控制顶点的求解;型线拟合与型线绘制中端点处理的方法。同时还给出了用该方法编制的图像交互显示与绘图软件包;作为实例,给出了用IBM/PC,AT微型机所带的6笔绘图仪绘制的多种船型的型线。对初步设计阶段来说具有足够的精度。

B-spline function can be used to plot curves and surfaces and so it has been warmly received and widely adopted by ship designers. This paper introduces the mathematical expressions of B-spline function and also deals with the differences of the characteristics and the nature of the basic function Besides, the paper gives the solutions to the control topnotch off the carved polygons and the methods to handle the end point of line-fdrmation fitting and line-plotting. At the same time, the paper presents drawing displays and software package for the plotting. The plotting instrument which is together with IBM/PC and AT microcomputers is also presented in the paper. Some examples of ship lines which are of adequate precision are given for the reference of the designers.