文献类型：期刊文献

英文题名：On a new proximity condition for manifold-valued subdivision schemes

作者：Duchamp, Tom[1]; Xie, Gang[2]; Yu, Thomas[3]

机构：[1] Department of Mathematics, University of Washington, PO Box 354350, Seattle, WA, 98195-4350, United States; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China; [3] Department of Mathematics, Drexel University, 206 Korman Center, 3141 Chestnut Street, Philadelphia, PA, 19104, United States

年份：2014

卷号：83

起止页码：65

外文期刊名：Springer Proceedings in Mathematics and Statistics

收录：EI(收录号：20151600762244)

语种：英文

外文关键词：Equivalence classes - Dynamical systems - Three dimensional computer graphics - Approximation algorithms

摘要：An open theoretical problem in the study of subdivision algorithms for approximation of manifold-valued data has been to give necessary and sufficient conditions for a manifold-valued subdivision scheme, based on a linear subdivision scheme, to share the same regularity as the linear scheme. This is called the smoothness equivalence problem. In a companion paper, the authors introduced a differential proximity condition that solves the smoothness equivalence problem. In this paper, we review this condition, comment on a few of its unanticipated features, and as an application, show that the single basepoint log-exp scheme suffers from an intricate breakdown of smoothness equivalence. We also show that the differential proximity condition is coordinate independent, even when the linear scheme is not assumed to possess the relevant smoothness. ? Springer International Publishing Switzerland 2014.