Name
Abstract | ||
|---|---|---|
In this paper a class of subdivision schemes generalizing the algorithm of Loop is presented. The stencils have the same support as those from the algorithm of Loop, but allow a variety of weights. By varying the weights a class of C 1 regular subdivision schemes is obtained. This class includes the algorithm of Loop and the midpoint schemes of order one and two for triangular nets. The proof of C 1 regularity of the limit surface for arbitrary triangular nets is provided for any choice of feasible weights. The purpose of this generalization of the subdivision algorithm of Loop is to demonstrate the capabilities of the applied analysis technique. Since this class includes schemes that do not generalize box spline subdivision, the analysis of the characteristic map is done with a technique that does not need an explicit piecewise polynomial representation. This technique is computationally simple and can be used to analyze classes of subdivision schemes. It extends previously presented techniques based on geometric criteria. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s00607-006-0211-1 | Computing |
Keywords | DocType | Volume |
subdivision,characteristic map,triangular net,arbitrary triangular net,subdivision scheme,applied analysis technique,subdivision algorithm,generalized Loop subdivision scheme,characteristic map.,explicit piecewise polynomial representation,regular subdivision scheme,loop,feasible weight,box spline subdivision | Journal | 79 |
Issue | ISSN | Citations |
2 | 1436-5057 | 4 |
PageRank | References | Authors |
0.47 | 9 | 2 |