Level Set Methods and Dynamic Implicit Surfaces.pdf

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Level Set Methods and Dynamic Implicit Surfaces Stanley Osher Ronald Fedkiw SPRINGER

Applied Mathematical Sciences Volume 153 Editors S.S. Antman J.E. Marsden L. Sirovich Advisors J.K. Hale J. Keller C.S. Peskin P. Holmes B.J. Matkowksy J. Keener A. Mielke K.R. Sreenivasan Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo

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Stanley Osher Ronald Fedkiw Level Set Methods and Dynamic Implicit Surfaces With 99 Figures, Including 24 in Full Color

Stanley Osher Department of Mathematics University of California at Los Angeles Los Angeles, CA 90095-1555 USA sjo@math.ucla.edu Ronald Fedkiw Department of Computer Science Stanford University Stanford, CA 94305-9020 USA fedkiw@cs.stanford.edu Editors: S.S. Antman Department of Mathematics and Institute for Physical Science California Institute of J.E. Marsden Control and Dynamical Systems, 107-81 and Technology Technology University of Maryland College Park, MD 20742-4015 USA USA ssa@math.umd.edu Pasadena, CA 91125 marsden@cds.caltech.edu L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA chico@camelot.mssm.edu Cover photos: Top left and right, hand and rat brain — Duc Nguyen and Hong-Kai Zhao. Center campﬁre — Duc Nguyen and Nick Rasmussen and Industrial Light and Magic. Lower left and center, water glasses — Steve Marschner and Doug Enright. Mathematics Subject Classiﬁcation (2000): 65Mxx, 65C20, 65D17, 65-02, 65V10, 73V Library of Congress Cataloging-in-Publication Data Osher, Stanley. Level set methods and dynamic implicit surfaces / Stanley Osher, Ronald Fedkiw p. cm. – (Applied mathematical sciences ; 153) Includes bibliographical references and index. ISBN 0-387-95482-1 (alk. paper) 1. Level set methods. III. Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 153 QA1.A647 vol. 153 [QC173.4] 510s–dc21 [515’.8] I. Fedkiw, Ronald P., 1968– 2. Implicit functions. II. Title. 2002020939 Printed on acid-free paper. ISBN 0-387-95482-1 c 2003 Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Av- enue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identiﬁed as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 SPIN 10874508 www.springer-ny.com Springer-Verlag New York Berlin Heidelberg A member of BertelsmannSpringer Science+Business Media GmbH

Dedicated with love to Katy, Brittany, and Bobbie

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Preface Scope, Aims, and Audiences This book, Level Set Methods and Dynamic Implicit Surfaces is designed to serve two purposes: Parts I and II introduce the reader to implicit surfaces and level set methods. We have used these chapters to teach introductory courses on the material to students with little more than a fundamental math background. No prior knowledge of partial diﬀerential equations or numerical analysis is required. These ﬁrst eight chapters include enough detailed information to allow students to create working level set codes from scratch. Parts III and IV of this book are based on a series of papers published by us and our colleagues. For the sake of brevity, a few details have been occasionally omitted. These chapters do include thorough explanations and enough of the signiﬁcant details along with the appropriate references to allow the reader to get a ﬁrm grasp on the material. This book is an introduction to the subject. We have given examples of the utility of the method to a diverse (but by no means complete) collection of application areas. We have also tried to give complete numerical recipes and a self-contained course in the appropriate numerical analysis. We be- lieve that this book will enable users to apply the techniques presented here to real problems. The level set method has been used in a rapidly growing number of areas, far too many to be represented here. These include epitaxial growth, opti- mal design, CAD, MEMS, optimal control, and others where the simulation

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