Regularization of B-spline objects

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 a 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 method is very effective. Key words: Spline objects, Regularization, L2 -gradient flow, Finite element method. MR (2000) Classification: 65D17

• Type: Journal
• Year: 2011
• Where: CAGD
• Authors: Guoliang Xu, Chandrajit L. Bajaj
• Keywords: B-spline, B-spline Object Od, CAGD 2011, Regularization Method, Theoretical Computer Science