摘要
为便于运动机器人快速平滑地移动,对由线段构成的、能够规避障碍物的引导多边形进行光顺,得到G2连续的有理二次样条曲线.首先对引导多边形进行改进,插入部分中点作为新的控制顶点;然后求解每一段曲线的形状因子,并对所有的形状因子进行比较,取其中最大的形状因子来构造整条曲线,使之能够规避所有障碍物的凸包,同时能够保持G2连续.与已有方法相比,文中构造的曲线次数虽然较低,但仍能够保证曲线整体G2连续,且保形性良好;曲线与引导多边形的拐点数目相同,无需解高次方程,直接计算就可得到结果;控制多边形直观可见,便于对曲线形状进行控制.最后列举了2个数值实例,以验证文中算法是简单、有效的.
Given a set of obstacles in a plane, an algorithm for finding a G^2 continuous, obstacleavoiding curve in the plane is presented in this paper. First, we partition the guiding polyline into control polygon sections by inserting several midpoints of polyline. Then, we find respectively shape parameter of each curve section to avoid the vertices of the convex hull of an obstacle. Finally, we choose the maximal shape parameter to avoid all the obstacles. Comparing with previous methods, the curves constructed by our approach have the following advantages： 1） it is G^2 continuous but with low degree; 2） it is shape-preserving, and the number of inflection point is the same as the one of the guiding polyline path; 3） it is obtained directly, and we need not to solve the fourth order equations; 4） the control polygon is visual, and we can adjust the curve easily. Finally, two examples are presented to demonstrate the effectiveness and validity of the proposed algorithm.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2011年第4期582-585,593,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(61070065)
国家自然科学基金重点项目(60933007)
