基于Level Set方法的点采样曲面测地线计算及区域分解

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。

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

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.