基于非均匀B样条的船体型线设计软件的研究与应用

文章主要通过对船舶型线设计和非均匀B样条特性的研究,结合船舶型线设计软件,提出了非均匀B样条在船舶型线设计中的应用方法和原理,并提供了必要的数学证明。首先,讨论了利用曲线的分段连接点与控制点或控制多边形的边对应关系,确定非均匀B样条节点矢量的方法,从而解决了用非均匀B样条生成型线的先决问题;其次,提出了K次非均匀B样条曲线的节点插值方法,并讨论了在非封闭曲线和封闭曲线条件下如何反算样条曲线控制点的数学方法;然后,提出了r阶非均匀B样条的导矢算法;最后提出了国内船舶型线辅助设计软件有待进一步研究和发展的一些看法。

The Research and Application of Nubline Software Based on Nonuniform B-spline Curve

This paper mainly introduces the basic principle of some kernel technologies of Nonuniform B-spline Curves when they are applied in the design of ship hull.Based on the NUBLINE software,it illustrates the algorithm of generating and modifying surface shape of ship hull that consists of Nonuniform B-spline Curves and also demonstrates the way to compute the Nonuniform knot vectors,insert knots,recalculate the values of control points and the tangent vectors of Nonuniform B-spline.Moreover,this paper also provides a part of mathematical demonstrations for these formulas.At last,the further research on the CAD software of ship is pointed out by analysis.