By Charles A. Micchelli
This monograph examines intimately definite strategies which are invaluable for the modeling of curves and surfaces and emphasizes the mathematical thought that underlies those principles. the 2 primary topics of the textual content are using piecewise polynomial illustration (this subject looks in a single shape or one other in each chapter), and iterative refinement, also known 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 finally ends up in the development of prewavelets of compact help. the rest of the booklet offers with ideas of "visual smoothness" of curves, besides the interesting suggestion of producing gentle multivariate piecewise polynomials as volumes of "slices" of polyhedra.
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