By Charles A. Micchelli

This monograph examines intimately definite thoughts which are worthwhile for the modeling of curves and surfaces and emphasizes the mathematical concept that underlies those rules. the 2 central topics 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. the following, uncomplicated 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 finally ends up in the development of prewavelets of compact aid. the rest of the ebook offers with suggestions of "visual smoothness" of curves, in addition to the exciting thought of producing delicate multivariate piecewise polynomials as volumes of "slices" of polyhedra.

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