摘要
利用节点插入算法将三次NURBS曲线转化成一组三次有理Bézier曲线,结合有理Bézier曲线形式简单的优点,推导了由三次NURBS曲线与坐标轴所围成区域的面积的精确计算公式,只要给定曲线的节点矢量、控制顶点和权因子即可通过逐步代入求得区域的面积.并在此基础上给出了面积矩、形心、惯性矩等相关积分量的计算公式.最后初步研究了这种计算方法应用于船舶静力学性能计算的问题.与传统的数值逼近算法相比它克服了误差的存在.
The paper converted a cubic NURBS curve to piecewise cubic rational Bézier curves by knot insertion algorithm firstly,then deduced in detail the exact computational formula of the area bounded by cubic NURBS curve.Thus the area can be obtained only by the node vector,control points and the corresponding weights.And on this basis,the computational formula of correlation integral were given such as moment of area,centroid,moment of inertia.Finally,a study on the application of this method was performed in the calculation program of hydrostatical properties of ship.This algorithm overcomes the error and makes important sense in application compared to the traditional numerical approximation algorithm.
出处
《武汉理工大学学报（交通科学与工程版）》
2014年第3期652-657,共6页
Journal of Wuhan University of Technology（Transportation Science & Engineering）
基金
武汉理工大学自主创新研究基金项目资助(批准号:135214004)
