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

By Pierre-Jean Laurent; Alain Le Mehaute

There's a good deal of present curiosity in mathematical tools for representing and manipulating complex curves and surfaces in a electronic machine atmosphere. This edited paintings is a set of either brief survey papers and lengthy study papers, addressing a few issues very important to improvement within the box. between those are 3D reconstruction, skinny plate splines, geometric continuity, photograph compression, and radial capabilities. The survey papers specialize in a number of relatively lively subareas of approximation concept, together with tomography, wavelets, restricted approximation, multivariate splines, approximation of pictures, and floor compression

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Du Wen Hui, Etude sur la représentation des surfaces complexes: application à la reconstruction de surfaces échantillonnées, Thèse de doctorat, Sup Télécom, Paris (1988). 5. , A construction for Visual C1 continuity of polynomial surface patches, Computer Graphies and Image Processing, 20 (1982), 272-2 82. XIXeme 6. Fiorot, J . C , and P. Jeannin, Courbes Bézier rationnelles, Congrès National d'Analyse Numérique, Port-Barcarès, France, 1986. 7. C. and P. R. Acad. Sei. Paris, 305, série I (1987), 435-440.

Gasca, and C. ), Kluwer, 1990, 275-309. Supported in part by the Alexander von Humboldt Foundation of Bonn, Germany, and by the National Science Foundation under Grant DMS-8902331. G 1 and G 2 Continuity Between (SBR) Surfaces J. L. Bauchat, J. C. Fiorot and P. Jeannin A b s t r a c t . For about four years, the (BR) curves and the (SBR) surfaces have been introduced in order to describe any rational curve and respectively any rational surface by means of control nets of mass vectors. Here, we give sufficient G and G continuity conditions between two adjacent (SBR) in terms of mass vectors.

Solve the intersection equation f(x(t),y(t),z(t)) = 0, of the ray R and the algebraic surface S defined by f(x, y, z) — 0. Curves and Surfaces P. J. Laurent, A. Le Méhauté, and L. L. ), pp. 37-42. Copyright ©1991 by Academic Press, Boston. ISBN 0-12-438660-1 All rights of reproduction in any form reserved. 37 38 Luc Biard and Patrick Chenin 3. For each intersection point M ( x , y, z) obtained, evaluate its parameters u and v as function of x, y and z , in order to determine whether or not the point M belongs to the patch 5o (inversion step).

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