title: Regularization of B-Spline Objects.
abstract: By a d-dimensional B-spline object (denoted as ), 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  we mean the process of relocating the control points of  such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for , d = 1, 2, 3 based on solving weak form L(2)-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 method is very effective.
authors.affiliation: 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.
authors.forename: Guoliang
authors.initials: G
authors.lastname: Xu
authors.forename: Chandrajit
authors.initials: C
authors.lastname: Bajaj