Joris Windmolders

Automatic construction of control triangles for subdivided Powell-Sabin splines

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 √3 scheme; a new vertex is added inside every original triangle. Applying the √3 scheme twice yields a triadic scheme, every original edge is split into three new edges, but special care is needed at the boundaries. The scheme is numerically stable and generally applicable, there are no restrictions on the initial triangulation.

Subdivision of uniform Powell—Sabin splines

Abstract We propose a subdivision scheme for Powell–Sabin splines on uniform triangulations in their normalized B-spline representation. As an application we give an efficient algorithm for displaying the surface.

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.

Dyadic and /spl radic/3-subdivision for uniform Powell-Sabin splines

We give two different possibilities for subdivision of Powell-Sabin spline surfaces 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, /spl radic/3-subdivision, a new vertex is introduced in the center of each triangle of the triangulation. We give subdivision rules to find the new control points of the refined surface for both cases.