Download E-books Mathematical Aspects of Geometric Modeling (CBMS-NSF Regional Conference Series in Applied Mathematics) PDF

By Charles A. Micchelli

This monograph examines intimately yes options which are beneficial for the modeling of curves and surfaces and emphasizes the mathematical thought that underlies those principles. the 2 central topics of the textual content are using piecewise polynomial illustration (this subject matter seems to be in a single shape or one other in each chapter), and iterative refinement, also referred to as subdivision. the following, 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 results in the development of prewavelets of compact help. the rest of the booklet offers with thoughts of "visual smoothness" of curves, in addition to the interesting notion of producing gentle multivariate piecewise polynomials as volumes of "slices" of polyhedra.

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