Analyzing a generalized Loop subdivision scheme

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 C1 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 C1 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 t...

• Type: Journal
• Year: 2007
• Where: COMPUTING
• Authors: Ingo Ginkel, Georg Umlauf
• Keywords: Algorithm, COMPUTING 2007, Loop, Subdivision Schemes