Abstract: In order to solve problems that exist in recovering datasets topology and retrieving features from point clouds，a new surface reconstruction method for piecewise smooth surfaces from point clouds is proposed.First，assemble a graph of local surface patches consisting of a set of basis functions，then establish topological connectivity among the nodes that respect sharp features，the last，search optimal coefficients for the basis functions in each node by solving a sparse optimization problem.The final representation allowes for robust finding of crease and border edges which separate the piecewise smooth parts.As output of the new method，a clean，manifold surface mesh which preserves feature lines is extracted.The experimental results show the effectiveness of the method with reconstructions of piecewise smooth surfaces.

Key words: piecewise smooth surfaces, patch-graph, sparse optimization, feature points, feature lines, segmentation, energy function

摘要： 针对离散点云拓扑关系恢复及特征提取困难的问题，提出了一种健壮有效的分段光滑曲面重构方法。获得由基函数集定义的局部曲面面片图，建立尖锐特征节点的拓扑连接，通过求解一个稀疏优化问题，获得每个节点基函数的最优系数，并输出清洁的流形网格曲面。实例证明，该算法实用性好，对分段光滑曲面重构效果理想。

关键词: 分段光滑曲面, 面片图, 稀疏优化, 特征点, 特征线, 数据分割, 能量函数, ,