Curves and Surfaces PDF
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Curves and Surfaces Edited by Pierre-Jean Laurent Université Joseph Fourier Grenoble, France Alain Le Méhauté Ecole Nationale Supérieure Télécommunications de Bretagne, France Larry L. Schumaker Vanderbilt University Nashville, Tennessee, USA ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto This book is printed on acid-free paper. ® Copyright ©1991 by Academic Press, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. ACADEMIC PRESS, INC. 1250 Sixth Avenue, San Diego, CA 92101 United Kingdom Edition published by ACADEMIC PRESS LIMITED 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data Curves and surfaces / edited by Pierre-Jean Laurent, Alain Le Méhauté, Larry L. Schumaker. p. cm. Papers from the International Conference on Curves and Surfaces, held June 21-27, 1990 in Chamonix-Mont-Blanc, and organized by the Association Française d'approximation. Includes bibliographical references. ISBN 0-12-438660-1 1. Approximation theory — Congresses. 2. Spline theory— Congresses. 3. Surfaces — Computer simulation — Congresses. 4. Curves—Computer simulation—Congresses. I. Laurent, Pierre- Jean. II. Le Méhauté, Alain. III. Schumaker, Larry L., IV. International Conference on Curves and Surfaces (1990 Chamonix-Mont-Blanc, France) V. Association française d ' approximation. QA221.C87 1991 511'.4-dc20 91-12201 CIP Printed in the United States of America 91 92 93 94 9 8 7 6 5 4 3 2 1 PREFACE During the week of June 21-27, 1990, an International Conference on Curves and Surfaces was held in Chamonix-Mont-Blanc (France). It was orga- nized by the Association Française d'Approximation (A. F. A.). The organizing committee consisted of R. Arcangéli (Pau), M. Attéia (Toulouse), P. Chenin (Grenoble), J. C. Fiorot (Valenciennes), J. Gâches (Toulouse), B. Lacolle (Grenoble), P.-J, Laurent (Grenoble), A. Le Méhauté (Lille), C. Rabut (Toulouse), P. Sablonnière (Rennes), L. L. Schumaker (Nashville, USA), and P. Valentin (Elf-Solaize). The Conference was attended by 203 mathematicians from 22 different countries, and the program included 10 invited one-hour lectures and 114 re- search talks. The survey lectures dealt with several particularly active sub- areas of approximation theory, including approximation of images, computer- aided geometric design, constrained approximation, multivariate splines, sur- face compression, tomography, and wavelets. A number of the research talks were presented in minisymposia on Geometric Continuity, Optimal Recov- ery and Information Based Complexity, Data Storage and Reduction, Quasi- interpolants, and Radial Functions, organized by B. A. Barsky, M. Kon, T. Ly- die, C. Chui, and N. Dyn, respectively. We would like to thank the following institutions and companies for their financial support: Université Joseph Fourier, Grenoble; Université de Pau et des Pays de l'Adour; Université Paul Sabatier, Toulouse; Laboratoire d'Analyse Numérique (Université de Lille I); Université de Valenciennes; Inst. Nat. Sci- ences Appliquées de Toulouse; Institut IMAG; Laboratoire de Modélisation et de Calcul (Grenoble); Centre National de la Recherche Scientifique (C.N.R.S.); Société de Mathématiques Appliquées et Industrielles (S.M.A.L); Direction des Recherches et Etudes Techniques (DRET); US Air Force European Office of Aerospace Research and Development (EOARD); US Army Research, Develop- ment and Standardization Group, UK (USARDSG); US Navy, Office of Naval Research, European Office; Régie Nationale des Usines Renault; Elf-Aquitaine; IBM-France; CCSA-CELAR, and Vanderbilt University. Local organization of the Conference was carried out by the Laboratoire de Modélisation et de Calcul of IMAG Institute (Grenoble). We would like to thank D. Iglesias, his colleagues at the printing service, and also the secretaries of the institute, especially Khadija Rassouli and Claude Rivet, for the high quality of their work. In addition to the members of the organizing committee, several of our colleagues and students helped with the organization of the Conference. In particular, we would like to thank A. Antoniadis, M. Duc- Jacquet, D. Girard, A. Eberhard, R. Kulkarni, M. L. Mazure and F. Utreras, as well as the following students: F. R. Degott, L. Deshpande, A. Kaufmann, N. Szafran, and M. Tazeroualti. Finally, we want to express our special thanks to Guizou Laurent, Michelle Le Méhauté, and Gerda Schumaker. Nashville, Tennessee January 15, 1991 x CONTRIBUTORS Numbers in parentheses indicate pages on which authors1 contributions begin. LAURENT ALT (1), TDI, 22, rue Hégésippe Moreau 75018 Paris and LIENS, Ecole Normale Supérieure, 45, rue d'Ulm 75005 Paris, France LUCA AMODEI (5), Equipe MAD, Centre National de Recherches Météorolo- giques, 42, Avenue Gustave Coriolis, 31057 Toulouse, France ANESTIS ANTONIADIS (11), LMCÎMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France [[email protected]] MARC ATTÉIA (17), Laboratoire d'Analyse Numérique, Université Paul Saha- tier, 31062 Toulouse, France BRIAN A. BARSKY (307), Computer Science Division, University of Califor- nia, Berkeley, CA 94720 [[email protected]] GÜNTER BASZENSKI (27), Computer Center, Univ. Bochum, 4630 Bochum 1, Germany [[email protected]] JEAN-LUC BAUCHAT (33), ENSAM, 8 Bd Louis XIV, 59046 Lille, France MOHAMMED N. BENBOURHIM (5), Laboratoire d'Analyse Numérique, Uni- versité Paul Sabatier, 31062 Toulouse, France Luc BlARD (37), LMC IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France M. I. G. BLOOR (139), Department of Applied Mathematics, University of Leeds, Leeds LST 9JT, England TERRANCE E. BOULT (43), Department of Computer Science, Columbia Uni- versity, New York, NY 10027 [[email protected]] JEAN LOUIS DE BOUGRENET DE LA TOCNAYE (59), GTI, Département MSC, Ecole Nationale Supérieure des Télécommunications de Bretagne, BP 832, 29285 Brest, France MARTIN BUHMANN (51), Mathematics Department, Cambridge University, Cambridge, CB3 9EW England [[email protected]] VALÉRIE BURDIN (59), GTI, Département MSC, Ecole Nationale Supérieure des Télécommunications de Bretagne, BP 832, 29285 Brest, France [[email protected]] JOHN F. CANNY (315), Computer Science Division, EECS Dept, University of California, Berkeley, CA 94720 [[email protected]] JEAN-CHARLES CANONNE (67), Université de Valenciennes, LaboMath. Ap- pli. au Calcul, Le Mont Houy, 59326 Valenciennes, France xi xii Contributors RALPH CARLSON (71), L-316, Lawrence Livermore Labs, Livermore, CA 94550 [[email protected]] ANDREW CHAN (75), Dept. of Electrical Engineering, Texas A&M University, College Station, TX 77843-3128 [[email protected]] XlN CHEN (433), Telecom Paris, Dept IMA, 46, rue Barrault, 75634 Paris, France PATRICK CHENIN (37), LMC - IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France CHARLES K. CHUI (75, 83), Department of Mathematics, Texas Α&εΜ Univ., College Station, TX 77843 [[email protected]] PHILIPPE CINQUIN (279), TIME - TIM 3 - IMAG, Faculté de Médecine, 38700 La Tronche, France [[email protected]] ELAINE COHEN (91), Department of Computer Science, University of Utah, Salt Lake City, Utah 84112 [[email protected]] YVES CORREC (103), CCSA - CELAR, 35170 Bruz, France WOLFGANG DAHMEN (107), Inst. f. Mathematik WE3, Freie Universität, Arnimallee 2-6, D-1000 Berlin 33, Germany [[email protected]] JEAN PIERRE DEDIEU (135), Laboratoire d'Analyse Numérique, Université Paul Sabatier, 31062 Toulouse, France CHRISTOPHER DEKANSKI (139), Department of Applied Mathematics, Uni- versity of Leeds, Leeds LST 9JT, England LALITA DESHPANDE (143), LMC IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France A. TlDJANE DiALLO (149), Département de Mathématiques, Université de Conakry, BP 188 Conakry, Republic of Guinea MARINA DI NATALE (157), Dipartimento di Matematica delVUniversità, via C. Saldini, 50, 20133 Milano, Italy WEN-HUI DU (161, 165, 433), Thomson Digital Image, 22, rue Hégésippe Moreau, 75018 Paris, France NlRA DYN (51, 169), Dept of Math., Tel-Aviv University, Tel-Aviv, Israel [[email protected]] CHANTAL FAVARDIN (135), Laboratoire d'Analyse Numérique, Université Paul Sabatier, 31062 Toulouse, France L. A. FERRARI (177, 449), Dept. of Electrical and Computer Engineering, University of California at Irvine, 1ERE 208C, Irvine, CA 92717 Contributors xiii JEAN-CHARLES FIOROT (33, 67, 181, 185), ENSIMEV - Lab MACS, Uni- versité de Valenciennes, Le Mont Houy, 59326 Valenciennes, France STEVEN FORTUNE (189), ATT Bell Laboratories, Room 2C-459, 600 Moun- tain Ave, Murray Hill, NJ 07974 [[email protected]] SERGIO DE FREITAS (193), Dept. de Matematica, Universidade de Matogrosso do Sul, Campus Universitârio, Campo Grande, MS, Brasil FRED FRITSCH (71), L-316, Lawrence Livermore Labs, Livermore, CA 94550 H. FUKUNAGA (505), Waseda University, Dept. of Mec. Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan FENG GAO (197), Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1W5 Canada [[email protected]] FAOUZI GHORBEL (59), Groupe Traitement d'Images, Dépt. Mathématiques et Systèmes de Communication, Ecole Nationale Supérieure des Télé- communications de Bretagne, BP 832, 29285 Brest, France DIDIER GIRARD (143), LMC IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France [[email protected]] LAURA GOTUSSO (157), Dipartimento di Matematica del Politecnico, Piazza Leonardo da Vinci 32, 20131 Milano, Italy GÉRARD GRÉGOIRE (11), LMC - IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France [[email protected]] MUSTAPHA BEL GUERMAH (367), ENST, Dept. of Computer Science, 46 Rue Barrault, Paris 75634, France CARLA GUERRINI (321), Universita Bologna, Dip. Matematica, Piazza porta San Donato 5, 40127 Bologna, Italy [[email protected]] WEIMIN HAN (247), Department of Mathematics, University of Maryland, College Park, MD 20742 [[email protected]] PIERRE JEANNIN (33, 67, 181), Université de Lille 1, Lab. ANO, UFRIEEA Bât M3, 59655 Villeneuve d'Ascq, France RONG-QING JlA (209), Department of Mathematics, University of Oregon, Eugene, OR 97403 [email protected]] EMERY JOU (247), Computer Science Center, University of Maryland, College Park, MD 20742 [[email protected]] ALAIN KAUFMANN (251), LMC - IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France [[email protected]] PER ERIK KOCH (255), University of Trondheim, Dept. of Mathematical Sciences, 7034 Trondheim-NTH, Norway [[email protected]] xiv Contributors MARK KON (259), Department of Mathematics, Boston University, Boston, MA 02215 [[email protected]] DAVID KRIEGMAN (267), Center for Systems Science, Department of Electri- cal Engineering, Yale University, New Haven, CT 06520-1968 REKHA KULKARNI (271), Dept Mathematics, I.I.T. Bombay, Powai, Bombay, 400 076 India MOHAMMED LAGHCHIM LAHLOU (275), Laboratoire LANS, INSA, 20, avenue des Buttes de Coësmes, 35043 Rennes, France PIERRE-JEAN LAURENT (271), LMC - IMAG, Université Joseph Fourier, BP 53X, 38041 Grenoble, France [[email protected]] S. LAVALLÉE (279), TIMB - TIM 3 - IMAG, Faculté de Médecine, 38700 La Tronche, France F. LEITNER (279), TIMB - TIM 3 - IMAG, Faculté de Médecine, 38700 La Tronche, France ALAIN LE MÉHAUTÉ (103), Département Mathématiques, Ecole Nationale Supérieure Télécommunications de Bretagne, BP 832, 29285 Brest, France [[email protected]] MARK LERNER (43), Department of Computer Science, Columbia University, New York, NY 10027 DAVID LEVIN (169), Dept. of Math., Tel-Aviv University, Tel-Aviv, Israel WILL LIGHT (285), Department of Mathematics, University of Leicester, Uni- versity Road, Leicester, England C. F. LOUWE KOOUMANS (293), TU Delft, faculteit 10, vakgroep K, Jaffalaan 9, NL-2628 BX Delft, Holland [louwe @ tudobm.tudelft.nl] TOM LYCHE (255), Institutt for informatikk, Universitetet i Oslo, P. O. Box 1080, Blindem, 0316 Oslo 3, Norway [[email protected]] WALLY R. MADYCH (297), Dept. Math., Univ. of Connecticut, Storrs, CT 06268 [[email protected]] DlNESH MANOCHA (307, 315), Computer Science Division, EECS Dept., Uni- versity of California, Berkeley, CA 94720 ISABELLE MARQUE (279), TIMB - TIM 3- IMAG, Faculté de Médecine 38700 La Tronche, France CHARLES A. MICCHELLI (209), Department of Mathematical Sciences, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 [[email protected]] LAURA MONTEFUSCO (321), Universita Bologna, Dip. Matematica, Piazza porta San Donato 5, 40127 Bologna, Italy Contributors xv PIERRE MONTES (325), Ecole Polytechnique, Département de Génie Civil, Université de Montréal, Montréal, Québec, Canada H3W 2G1 KNUT M0RKEN (331), Institutt for informatikk, Universitetet i Oslo, P. O. Box 1080, Blindem, 0316 Oslo 3, Norway [[email protected]] GREGOR MÜLLENHEIM (337), Katholische Universität Eichstätt, Ostenstr. 18, 8078 Eichstätt, Germany FRAN NARCOWICH (341), Dept of Mathematics, Texas A&M University, Col- lege Station, TX 77843 FRANK NATTERER (349), inst. Numer. und Instr. Mathematik, Wilhelms- Universität Münster, Einsteinstrasse 62, 4400 Münster, Germany [[email protected]] MARIAN NEAMTU (359, 363), University of Twente, Department of Applied Mathematics, P. O. Box 217, 7500 AE Enschede, Holland [[email protected]] M. NllZEKI (505), Waseda University, Dept. of Mec. Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan OSCAR PALACIOS (457), Univ. Autonoma Metropolitana, av. Michoacan y la Purisima, Iztapalapa D. F., Mexico 09340, Mexico D. PANG (177), Dept. of Electrical and Computer Engineering, University of California at Irvine, 1ERE 208C, Irvine, CA 92717 R. PAVANI (157), Dipartimento di Matematica del Politecnico, p.za Leonardo da Vinci 32, 20131 Milano, Italy PIA PFLUGER (363), Math. Instituut, Univ. Van Amsterdam, Roeterstraat 15, 1018 Wb Amsterdam, Holland [[email protected]] JEAN PONCE (267), Beckman Institute, University of Illinois, 405 North Mathews Avenue, Urbana, IL 61801 [[email protected]] CHRISTINE POTIER (367, 477), ENST, Dept of Computer Science, 46 Rue Barrault, Paris 75634, France [[email protected]] M. J. D. POWELL (371), Mathematics Department, Cambridge University, Cambridge, CB3 9EW England [mjdp@camnum%atm.amtp.cam.ac.uk] JÜRGEN PRESTIN (383), Universität Rostock, Sektion Mathematik, Univer- sitätsplatz 1, 2500 Rostock, Germany LUIGIA PUCCIO (321), Dipertimento di Matematica Universita1 di Messina, Sant'Agata Messina, Italy EWALD QUAK (387), Dept of Mathematics, Texas A&:M Univ., College Sta- tion, TX 77843 [[email protected]] XVI Contributors CHRISTOPHE RABUT (391), Institut National des Sciences Appliquées, Service de mathématiques, Avenue de Rangueil, 31077 Toulouse, France THOMAS RANDO (403), Department of Computer Science and Engineering, U-155, University of Connecticut, Storrs, CT 06269-3155 GEBOR RENNER (407), Computer and Automation Institute, Hungarian Aca- demy of Sciences, Kende u. 13-17, 1111 Budapest, Hungary JOHN ROULIER (403), Department of Computer Science and Engineering, U- 155, University of Connecticut, Storrs, CT 06269-3155 [j rou@br c vax. brc. uconn. edu] CHRISTIAN ROUX (59), GTJ, Département Mathématiques et Systèmes de Communication, Ecole Nationale Supérieure des Télécommunications de Bretagne, BP 832, 29285 Brest, France [[email protected]] DELFINA ROUX (157), DipartimentodiMatematicadelVUniversita, viaC. Sal- dini, 50, 20133 Milano, Italy [[email protected]] MALCOLM SABIN (411, 415), FEGS Ltd, 5 Coles Lane, Oakington, Cam- bridge, CB4 5BA England PAUL SABLONNIÈRE (421), I. JV. S. A. de Rennes, Laboratoire LANS, 20 av. des Buttes de Coësmes, 35043 Rennes, France FAROUK SAIR (433), Telecom Paris, Dept. IMA, 46, rueBarrault, 75634 Paris, France KARL SCHERER (427), Inst f. Angew. Math., Wegelerstrasse 6, 5300 Bonn, Germany FRANCIS SCHMITT (161, 165, 433), Telecom Paris, Dept. IMA, 46, rue Bar- rault, 75634 Paris, France [[email protected]] LARRY L. SCHUMAKER (27, 387), Department of Mathematics, Vanderbilt University, Nashville, TN 37240 [[email protected]] HANS PETER SEIDEL (437), University of Waterloo, Dept of Computer Sci- ence, Waterloo, Ontario N2L 3G1 Canada [[email protected]] CARLO H. SEQUIN (445), Computer Science Division, University of California, Berkeley, CA 94720 LEON SHIRMAN (445), 429 Norwell St., El Cerrito, CA 94530 [shirman@miro .berkeley.edu] MARTINE SILBERMANN (449), Dept. of Electrical and Computer Engineering, University of California at Irvine, 1ERE 208C, Irvine, CA 92717 [[email protected]] JOACHIM STÖCKLER (83), FB Mathematik, Univ. Duisburg, Lotharstr. 65, 4100 Duisburg, Germany [[email protected]] Contributors xvn MARTIN STRENG (453), University of Twente, Department of Applied Math- ematics, p.o. box 217, 7500 AE Enschede, Holland SALIM TALEB (185), Université de Lille 1, Lab. d'Analyse Numérique, UFR IEEA Bât M3, 59655 Villeneuve d'Ascq, France GEOVAN TAVARES (193), Departamento de Matemâtica, Pontiûcia Universi- dade Catolica, Marques de Säo Vicente 225, 22453 Rio de Janeiro, RJ, Brasil [[email protected]] LEONARDO TRAVERSONI (457), Univ. Autonoma Metropolitana, av. Michoa- can y la Purisima, Iztapalapa D. F., Mexico 09340, Mexico K. F. USTUNER (177), Dept. of Electrical and Computer Engineering, Uni- versity of California at Irvine, 1ERE 208C, Irvine, CA 92717 FLORENCIO UTRERAS (461), Departamento de Ingenieria Matemâtica, Facul- tad de Ciencias Fisicas y Matemâticas, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile [[email protected]] CASPER G. C. VAN DIJK (481), Delft University of Technology, Faculty of Industrial Design Engineering, Jaffalaan 9, NL-2628 BX Delft, Hol- land CHRISTINE VERCKEN (367, 477), Dept. INF, ENST, 46, rue Barrault, 75634 Paris, France [[email protected]] JORIS S. M. VERGEEST (481), Delft University of Technology, Faculty of In- dustrial Design Engineering, Jaffalaan 9, NL-2628 BX Delft, Holland [vergeest @ tudobm. tudelft. nl] ANNELICKE E. VRIES-BAAYENS (485), Faculty of Industrial Design Engineer- ing, Delft University of Technology, P. O. Box 5029, 2600 G A Delft, Holland GRACE G. WAHBA (491), Department of Statistics, Univ. of Wisconsin, 1210 West Dayton Street, Madison, WI 53705 [[email protected]] S. Y. WANG (449), Dept. of Electrical and Computer Engineering, University of California at Irvine, 1ERE 208C, Irvine, CA 92717 JOE WARD (83, 341), Dept. of Mathematics, Texas AkM University, College Station, TX 77843 [[email protected]] WOLFGANG WETTERLING (453), University of Twente, Department of Ap- plied Mathematics, p.o. box 217, 7500 AE Enschede, Holland [[email protected]] M. J. WILSON (139), Department of Applied Mathematics, University of Leeds, Leeds LST 9JT, England I. YAD-SHALOM (169), Dept. of Math., Tel-Aviv University, Tel-Aviv, Israel
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