基于模板采样和MLS能量函数的曲率计算  

Computing Curvatures Based on Template Sampling and MLS Energy Function

作　　者：王枭[1] 陈双敏[1] 陈叶芳[1] 辛士庆[1] 赵杰煜[1] 

机构地区：[1]宁波大学信息科学与工程学院,宁波315211

出　　处：《计算机辅助设计与图形学学报》2015年第6期1104-1109,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61300168);浙江省重中之重开放课题(XKXL1314;XKX11406;XKX11492);宁波市自然科学基金(2013A610058;2013A610053;2012A610065);科技部国际科技合作专项(2013DFG12810);国家"十二五"科技支撑计划项目(2012BAF12B11)

摘　　要：针对传统的曲率计算方法通常在顶点的k-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.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.

关 键 词：曲率 测地圆盘 模板采样 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]