Piecewise Linear Prewavelets on Arbitrary Triangulations

Michael S. Floater
SINTEF Applied Mathematics, Norway

Ewald G. Quak
SINTEF Applied Mathematics, Norway

Abstract

Arbitrary triangulations are of great interest in a variety of application areas such as the treatment of partial differential equations or the description of large data sets, e.g., in terrain modelling or computer graphics. Finding piecewise linear prewavelets of small support for sequences of uniformly refined triangulations has thus been a goal under different circumstances (Kotyczka & Oswald, Stevenson for PDEs, Floater & Quak for terrain modelling). In this talk, the authors' results concerning smallest support, stability, linear independence and efficient filterbank algorithms are presented and compared with related ones by Stevenson.