Pierre-Jean Laurent; Alain Le Mehaute's Curves and Surfaces PDF

By Pierre-Jean Laurent; Alain Le Mehaute

ISBN-10: 0124386601

ISBN-13: 9780124386600

There's a good deal of present curiosity in mathematical tools for representing and manipulating advanced curves and surfaces in a electronic computing device atmosphere. This edited paintings is a suite of either brief survey papers and lengthy learn papers, addressing a few issues very important to improvement within the box. between those are three-D reconstruction, skinny plate splines, geometric continuity, snapshot compression, and radial services. The survey papers concentrate on a number of fairly lively subareas of approximation idea, together with tomography, wavelets, limited approximation, multivariate splines, approximation of pictures, and floor compression

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Specifically, using the notation φ for both the mentioned univariate function and for the n-variate, rotationally invariant function associated with it, we study interpolants to an n-variate, real-valued function / from the space Vh = clos span {φ(> - jh) : j G ZZ n }, the closure being relative to the topology of uniform convergence over compact domains. , Buhmann (1990), Madych and Nelson (1990), Powell (1991), Wu and Schaback (1990)), because of its well-known suitability for practical applications, see, for instance, Hardy (1990).

Triangular Facet Surfaces 29 If the quadrilateral Qe is of the form a) or b), then we call e swapable. If it has either the form c) or d), we call e non-swapable. The reason for this terminology is clear: in Case a) we can swap the diagonal of the quadrilateral to obtain a new one where the edge e now runs from α,·+ι to fy-i. In Case b), the new edge would run from α,·_ι to &j+i. Definition 2. We say that a triangulation T is locally optimal provided that ct(T) cannot be reduced by swapping any edge i.

L. ), pp. 51-58. Copyright ©1991 by Academic Press, Boston. ISBN 0-12-438660-1 All rights of reproduction in any form reserved. 2) 51 52 M. D. Buhmann and N. Dyn where c denotes here and throughout a generic positive constant and where we require that / G C n + 1 (]R n ) and has bounded partial derivatives of total orders n and n-f-1. 2) can sometimes be removed (Buhmann, 1990). 2) cannot be improved, in the sense that the right-hand side cannot be replaced by o(hn+1) even if we restrict our function class to functions / which are infinitely differentiate and have all derivatives bounded.

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Curves and Surfaces by Pierre-Jean Laurent; Alain Le Mehaute

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