Regularization of B-spline objects

By a d  -dimensional B-spline object (denoted as OdOd), we mean a B-spline curve (d=1d=1), a B-spline surface (d=2d=2) or a B-spline volume (d=3d=3). By regularization of a B-spline object OdOd we mean the process of relocating the control points of OdOd 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 OdOd, d=1,2,3d=1,2,3, based on solving weak form L2L2-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.

Research highlights
► Uniform redistribution of multivariate B-spline's control points.
► Evolutionary PDE's as minimization of geometric functionals.
► Quality uniform sampling and meshing of B-splines.