A PhD thesis @ NALAG
This is a PhD thesis prepared by a member of the NALAG group or prepared with a (co)promotor from NALAG.
TW 2003_01
Joris Windmolders Advisor: Paul Dierckx Abstract We study Powell-Sabin (PS-)splines in their normalized B-spline representation for Computer Aided Geometric Design (CAGD). These piecewise quadratic polynomials with global C1-continuity have certain advantages compared to the widely used tensor product B-splines and NURBS. We investigate the extension of PS-splines to Non Uniform Rational Powell-Sabin splines (NURPS). These have more flexibility for interactive design and allow to represent quadrics exactly. We also study the particular case of PS-splines on uniform triangulations, give a subdivision scheme for these so-called UPS-splines and use it to derive a new wavelet transform on a triangular grid, as well as an algorithm for the graphical display of UPS-spline surfaces. We use UPS-splines in a generally applicable algorithm that solves the polygonal hole problem, based on interpolation and subdivision techniques. We discuss a software prototype for working with UPS-splines, called PS-surf. lirias 134835 / text.pdf / mailto: nalag team< |