中文摘要：

针对传统的曲率计算方法通常在顶点的尼．阶邻域（k=-1，2，3）内进行，会不可避免地受到三角化质量和细密程度影响的问题，提出一种基于模板采样和移动最小二乘法（MLS）能量函数的曲率计算方法．该方法采用测地圆盘作为邻域，并根据离散指数映射和事先指定的二维模板快速采样；然后借助MLS能量函数直接给出计算高斯曲率和平均曲率的公式，得到相应的曲率值．实验结果表明，文中方法得到的曲率能够稳定地提取几何体的局部弯曲信息，与三角化的好坏和细密程度无关，对噪声不敏感．

英文摘要：

Most conventional curvature computational algorithms run in a k-ring neighborhood （k=1, 2, 3）, which is inevitably subject to meshing quality and resolution. To overcome the disadvantage, this paper proposes a novel algorithm for curvature computation based on template sampling and MLS energy functions. First, local discrete exponential maps centered at each vertex are computed as a preprocessing step. Second, the actual point set contributing to curvature computation is extracted by mapping a given 2D sampling template onto the curved surface. Finally, we directly compute curvatures based on MLS energy functions, without a surface fitting operation. Theoretically speaking, this algorithm avoids the inconsistence from triangulation. Experimental results show that the new approach is able to extract curvatures stably, robust to meshing quality and resolution, and insensitive to noises.