参数曲线到隐式曲面的正交投影算法  

An Algorithm for Curve Orthogonal Projections onto Implicit Surfaces

作　　者：徐海银[1] 方雄兵[1] 胡利安[1] 吴晓峰[1] 李端玲[2] 

机构地区：[1]华中科技大学计算机科学与技术学院,武汉430074 [2]北京邮电大学自动化学院,北京100876

出　　处：《计算机辅助设计与图形学学报》2010年第12期2103-2110,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(51075167)

摘　　要：针对参数曲线到隐式曲面的正交投影问题,提出一种二阶迭代算法.利用参数曲线上的点与隐式曲面上正交投影曲线的坐标点所满足的正交条件,推导出正交投影曲线坐标点对空间参数曲线的参数的一阶和二阶导数;在此基础上建立了基于二阶泰勒逼近的正交投影曲线坐标点追踪方法,并给出了2种不同的步长控制方式;同时,考虑到二阶泰勒公式省去的高阶项,给出了相应的一阶误差校正方法.仿真结果表明,该算法具有良好的精确性和较高的效率.In this paper a second order iteration algorithm for projecting a space parametric curve perpendicularly onto an implicit surface is presented.First,the first and second derivatives of the coordinate points of the orthogonal projection curve with respect to the parameter of the space parametric curve are obtained by using the orthogonal conditions possessed jointly by points of the space parametric curve and of the orthogonal projection curve.A marching approach based on second-order Taylor approximation is further proposed to compute the coordinate points of the orthogonal projection curve and two methods for controlling the iteration step are also given.Finally,a first-order technique is put forward to correct the iteration errors introduced by the truncated higher-order terms in the second-order Taylor＇s formula.Simulations indicate that the presented algorithm has good accuracy and efficiency.

关 键 词：正交投影 隐式曲面 追踪步长 龙格-库塔方法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]