基于Level Set方法的点采样曲面测地线计算及区域分解  

Geodesic Path Computation and Region Decomposition of Point-Based Surface Based on Level Set Method

作　　者：肖春霞[1] 冯结青[1] 缪永伟[1] 郑文庭[1] 彭群生[1] 

机构地区：[1]浙江大学CAD&CG国家重点实验室

出　　处：《计算机学报》2005年第2期250-258,共9页Chinese Journal of Computers

基　　金：国家"九七三"重点基础研究发展规划项目基金(2002CB312101);国家自然科学基金(60373036;60103017;60333010)资助.

摘　　要：点采样物体的几何处理是当前造型领域中的研究热点之一,如何有效地对点采样曲面进行区域分解是几何处理的基础性工作.该文首先提出了一种基于Level Set方法的点采样曲面上两点间最短路径的计算方法,用以解决区域分解中的边界曲线生成问题.为了保证求解Level Set微分方程的稳定性,文章采用移动最小平方(MLS)方法对点采样曲面进行均匀重采样和去噪音处理.在此基础上,又进一步提出了一个基于 Level Set方法的点采样曲面区域拾取算法.最后给出了上述算法在点采样物体的几何处理中的应用实例.实验结果表明该文提出的算法稳定、快速且容易实现.Geometric processing of point-based model is the new research topic in geometric modeling. The region decomposition is the fundamental problem in it. To determine the boundary curves for the region decomposition, a novel method to compute the geodesic path on the point-based model is proposed which is based on the level set method. The moving least square method (MLS) is adopted to uniformly re-sample and denoise the original object to assure the numerical stability while solving the level set partial differential equation. Combined with the geodesic path computation above, a region pick algorithm based on the level set method is proposed. Finally, the proposed algorithms are applied for the point-based geometric processing. The experimental results demonstrate that the proposed algorithms are robust, effective, and can be easily implemented.

关 键 词：LEVEL SET方法 测地线 区域分解 拾取 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]