基于NURBS技术的船体几何重构研究与实现

Research and implementation of hull geometry based on NURBS technology

为实现船体的几何重构,基于非均匀有理B样条(NURBS)技术针对DTMB5415船体几何重构展开研究。根据NURBS技术原理以及边界处理过程,求解过程结合非节点边界条件,采用一种无需型线切矢量的曲线控制顶点反算算法。利用C++语言编写的程序实现船体型线和船体曲面重构,分析了控制顶点和权因子特性对几何重构结果的影响,通过误差分析得出,复杂曲面重构最大误差为0.178 5 mm,验证了该算法的可靠性。并采用二分法、黄金分割法和斐波那契法对船体曲面与水面求交展开研究分析,结果表明二分法收敛速度更快。通过研究认为:该程序求解的NURBS技术对船体几何重构精度较好,且具有曲面变形、曲面拼接和曲面分割等功能。

In order to realize the geometrical reconstruction of the hull,this paper studies the geometrical reconstruction of the DTMB5415 hull based on the non-uniform rational B-spline(NURBS)technique.The principle of NURBS technique and the process of boundary processing are given.In combination with the non-node boundary conditions,the inverse algorithm of curve control vertex without shape line cut vector is adopted.Interpolation modeling of hull shape line and hull surface is realized by C++programming language,and the influence of control vertices and weight factor characteristics on the geometric configuration results is analyzed.Through error analysis,the maximum error of complex surface reconstruction is 0.1785 mm,which verifies the algorithm Reliability.And using dichotomy,golden section method and Fibonacci method to research and analyze the intersection of hull surface and water surface,the results show that the dichotomy method converges faster.Through research,it is believed that the NURBS technology solved by the program has good accuracy in hull geometric reconstruction,and has functions of surface deformation,surface splicing and surface segmentation.