Filling polygonal holes with minimal energy surfaces on Powell-Sabin type triangulations

[摘要] In this paper we present two different methods for filling in a hole in an explicit 3D surface, defined by a smooth function f in a part of a polygonal domain D subset of R-2. We obtain the final reconstructed surface over the whole domain D. We do the filling in two different ways: discontinuous and continuous. In the discontinuous case, we fill the hole with a function in a Powell-Sabin spline space that minimizes a linear combination of the usual seminorms in an adequate Sobolev space, and approximates (in the least squares sense) the values of f and those of its normal derivatives at an adequate set of points. In the continuous case, we will first replace f outside the hole by a smoothing bivariate spline s(f), and then we fill the hole also with a Powell-Sabin spline minimizing a linear combination of given seminorms. In both cases, we obtain existence and uniqueness of solutions and we present some graphical examples, and, in the continuous case, we also give a local convergence result. (C) 2009 Elsevier B.V. All rights reserved.

[发布日期] 2010-06-15

[效力级别]  Proceedings Paper

[关键词] Filling holes;Minimal energy;Powell-Sabin;alpha-triangulation;Finite element