Subdivision for Powell-Sabin spline surfaces

In this paper we present an algorithm for calculating the B-spline representation of a Powell-Sabin spline surface on a refinement of the given triangulation. The resulting subdivision scheme is a triadic scheme; every original edge is split into three new edges. The presented rules are derived using the fact that triadic subdivision can be seen as two steps of sqrt(3)-subdivision. The scheme is numerically stable and generally applicable, there are no restrictions on the initial triangulation.nrpages: 19status: publishe

Uniform Powell-Sabin spline wavelets

This paper discusses how the subdivision scheme for uniform Powell-Sabin spline surfaces makes it possible to place those surfaces in a multiresolution context. We first show that the basis functions are translates and dilates of one vector of scaling functions. This defines a sequence of nested spaces. We then use the subdivision scheme as the prediction step in the lifting scheme and add an update step to construct wavelets that describe a sequence of complement spaces. Finally, as an example application, we use the new wavelet transform to reduce noise on a uniform Powell-Sabin spline surface.nrpages: 15status: publishe

Dyadic and sqrt(3) subdivision for uniform Powell Sabin splines

We give the two different possibilities for subdivision of Powell-Sabin splines on uniform triangulations. In the first case, dyadic subdivision, a new vertex is introduced on each edge between two old vertices. In the second case, sqrt(3)-subdivision, a new vertex is introduced in the center of each triangle of the triangulation. We give subdivision rules for both cases.© 2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.status: publishe

Powell-Sabin splines en computergesteund geometrisch ontwerpen

SIGLEAvailable from KULeuven, Campusbib. Exacte Wetenschappen, Celestijnenlaan 300A, 3001 Heverlee, Belgium / UCL - Université Catholique de LouvainBEBelgiu