任意多边形上基于ADMM的最小二乘坐标  

Least Square Coordinates for Arbitrary Polygons Based on ADMM

作　　者：范侠丽 王伟娜 邓重阳[1] 李亚娟[1] FAN Xiali;WANG Weina;DENG Chongyang;LI Yajuan(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2020年第4期45-50,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61872121,61761136010)。

摘　　要：重心坐标为多边形域上的数据插值提供了一种简便而有效的方法,可以把域内的任意点表示为一组控制顶点的线性组合。已有重心坐标大都需要预先对多边形区域进行三角剖分。提出一种最小二乘正则化模型广义重心坐标,用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)进行求解,且不需要对区域预先进行三角剖分,可用于任意简单多边形。理论分析和算法实例表明,此坐标是非负的、光滑的。Barycentric coordinates provide a convenient and efficient way to interpolate data values on polygon domains. They are widely used to represent a point inside the domain as a linear combination of a set of control points. Most of the existing coordinates need partition for polygon domains. This paper introduces a new generalized barycentric coordinate of least square regularization model for arbitrary simple polygons, which can be solved by Alternating Direction Method of Multipliers(ADMM) without partition of the domains. Theoretical analysis and numerical examples demonstrate that the coordinates are non-negative and smooth.

关 键 词：重心坐标 交替方向乘子法 非负性 光滑性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]