By Charles A. Micchelli
This monograph examines intimately definite innovations which are invaluable for the modeling of curves and surfaces and emphasizes the mathematical idea that underlies those principles. the 2 relevant subject matters of the textual content are using piecewise polynomial illustration (this subject appears to be like in a single shape or one other in each chapter), and iterative refinement, often known as subdivision. right here, easy iterative geometric algorithms produce, within the restrict, curves with advanced analytic constitution. within the first 3 chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield set of rules for computing cardinal splines is tied into desk bound subdivision. This eventually ends up in the development of prewavelets of compact help. the rest of the booklet offers with innovations of "visual smoothness" of curves, in addition to the fascinating notion of producing tender multivariate piecewise polynomials as volumes of "slices" of polyhedra.