Stationary Subdivision

Erscheinungsjahr 1991
ISBN: 978-0-8218-2507-5
Verlag: American Mathematical Society

Buch, Englisch, Format (B × H): 177 mm x 257 mm, Gewicht: 353 g

Subdivision methods in computer graphics constitute a large class of recursive schemes for computing curves and surfaces. They seem to have their origin in the geometric problem of smoothing the corners of a given polyhedral surface - in fact, these methods are sometimes called "wood carver" algorithms because the repeated smoothing operations are analogous to sculpting wood. This book presents a systematic development of the basic mathematical principles and concepts associated with stationary subdivision algorithms. The authors pay special attention to the structure of such algorithms in a multidimensional setting and analyse the convergence issue using appropriate tools from Fourier analysis and functional analysis. The analytic structure of the limiting curves and surfaces is revealed in two ways: the smoothness of these surfaces is determined by certain algebraic properties of the algorithm, while the highest order derivatives of the limiting surfaces are shown to be fractals. Scientists interested in computer graphics, splines, wavelets, and multiresolution analysis will find the analytic and algebraic tools developed here more than useful.

Autoren/Hrsg.

Cavaretta, Alfred S.

Dahmen, Wolfgang

Micchelli, Charles

Inhaltsverzeichnis

Subdivision schemes; Convergence concepts and the associated functional equation; Contractivity of the subdivision operator; Subdivision from dimension compression; Solution of the functional equation; Algebraic properties of subdivision schemes; Matrix refinement equation; Smoothness of S-refinable functions and consequences.