基于T样条的船体曲面重构方法研究

Research on T-spline-based Hull Surface Reconstruction Method

  • 摘要: 针对传统 B 样条、NURBS 等船体几何表达方法存在的拓扑适配性差、控制点冗余、多面片拼接易产生接缝等局限,以及国内T样条技术应用依赖国外商业软件的现状,提出一种自主高效的基于T样条的船体曲面重构算法,实现复杂船体形状的精准、简洁表达。/t/n该算法采用三步式蒙皮建模策略:首先通过B样条曲线插值技术对船体型值点进行弦长参数化处理,生成各站截面曲线;其次基于截面曲线构建T样条曲面控制曲线,利用T样条节点矢量的独立性形成T型连接;最后通过控制曲线逼近优化,在预设误差容限内缩减控制点数量,结合全局节点矢量统一策略,实现多区域船体的无接缝一体化重构。/t/n以WigleyIII数学船型和KCS船为验证对象,结果表明:WigleyIII 船型在最大容许误差10⁻2(m)时的T样条曲面控制点数量较B样条减少 65.5%;对于KCS船型而言,随着最大容许误差的减小,曲面重构精度呈逐步收敛趋势,当最大容许误差设定为10⁻1(m)时,该方法可实现76.84%的控制点数量降幅,在保证工程适用性的同时显著简化模型复杂度。/t/n所提算法通过单一曲面替代传统多面片拼接模式,既解决了B样条、NURBS方法的固有缺陷,又摆脱了对国外商业软件的依赖,实现了 “少控制点、高精度、无接缝” 的船体几何表达,为船舶概念设计、性能仿真及自动化建模提供了可靠的几何基础。

     

    Abstract: Objectives Aiming at the limitations of traditional hull geometric representation methods such as B-spline and NURBS, including poor topological adaptability, redundant control points, and prone to seams in multi-patch splicing, as well as the current situation that the application of T-spline technology in China relies on foreign commercial software, an independent and efficient T-spline-based hull surface reconstruction algorithm is proposed to achieve accurate and concise representation of complex hull shapes. MethodsThe algorithm adopts a three-step skinning modeling strategy: first, B-spline curve interpolation technology is used to perform chord length parameterization on ship hull offset points to generate section curves at each station; second, T-spline surface control curves are constructed based on the section curves, and T-junctions are formed by utilizing the independence of T-spline knot vectors; finally, through control curve approximation and optimization, the number of control points is reduced within the preset error tolerance, and combined with the global knot vector unification strategy, seamless integrated reconstruction of multi-region hulls is realized. Results Taking the Wigley III mathematical ship model and the KCS (KRISO Container Ship) as validation objects, the results show that for the Wigley III ship model, when the maximum allowable error is 10⁻² m, the number of control points of the T-spline surface is reduced by 65.5% compared with that of the B-spline; for the KCS ship model, as the maximum allowable error decreases, the surface reconstruction accuracy shows a gradual convergence trend. When the maximum allowable error is set to 10⁻¹ m, the method can achieve a 76.84% reduction in the number of control points, significantly simplifying the model complexity while ensuring engineering applicability.Conclusions The proposed algorithm replaces the traditional multi-patch splicing mode with a single surface, which not only solves the inherent defects of B-spline and NURBS methods but also eliminates reliance on foreign commercial software. It realizes the hull geometric representation with "fewer control points, high precision, and seamless integration", providing a reliable geometric foundation for ship conceptual design, performance simulation, and automated modeling.

     

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