NURBS曲线C^1连续参数优化算法  

A C^1 Continuous Algorithm to Optimize the Parameterization of NURBS Curves

作　　者：李效伟[1] 杨义军[1] 杨承磊[1] 孟祥旭[1] 李缨[2] 

机构地区：[1]山东大学计算机科学与技术学院,济南250101 [2]山东女子学院信息技术学院,济南250300

出　　处：《计算机辅助设计与图形学学报》2014年第12期2136-2141,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61202146;61272243);国家科技支撑计划(2013BAH39F00);山东省优秀中青年科学家科研奖励基金(BS2012DX014);山东省自然科学基金(ZR2011FL005);教育部留学回国人员科研启动基金

摘　　要：曲线的参数特性直接决定基于自由曲线的路径规划、运动控制等算法的质量.为了生成满足C1连续的近似弧长参数化,提出一种基于分段三次重新参数化的参数优化算法.首先利用Simpson方法离散积分能量,然后使用极值求解法求得初始解,最后通过LM(Levenberg-Marquardt)优化算法计算出曲线的最优参数表示.与C1连续的分段有理重新参数化方法相比,该算法能够在分段数量很少的情况下达到局部最优.最后通过实例说明了文中算法的有效性.Abstract. The results of path planning and motion control applications are highly dependent on the curves representations. In this paper, an algorithm is presented to optimize the parameterization of NURBS curves based on C^1 continuous piecewise-cubic reparameterization, which generates closer approximations to the arc-length parameterization. The formulated energy is discretized by the Simpson method, and its initial value is obtained by the extreme value method, which is further optimized by the Levenberg-Marquardt reparameterization method, better results show the performance of our algorithm. method. Compared with C^1 continuous piecewise-rational are obtained with less segmentation. Examples are given to

关 键 词：NURBS曲线 C^1连续 分段三次重新参数化 数值优化 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]