| Affiliation: | a State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China
b Department of Computer Science and Institute of Computational Engineering & Sciences, University of Texas at Austin, Austin, TX 78712, United States |
| Abstract: | By a d-dimensional B-spline object (denoted as Od), we mean a B-spline curve (d=1), a B-spline surface (d=2) or a B-spline volume (d=3). By regularization of a B-spline object Od we mean the process of relocating the control points of Od such that it approximates an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for Od, d=1,2,3, based on solving weak form L2-gradient flows constructed from the minimization of certain regularizing energy functionals. These flows are integrated via the finite element method using B-spline basis functions. Our experimental results demonstrate that our new regularization methods are very effective. |
