Triangulations and Applications
This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, includ
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Øyvind Hjelle Morten Dæhlen
Triangulations and Applications With 126 Figures
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Øyvind Hjelle
Morten Dæhlen
Simula Research Laboratory AS P.O. Box 134 1325 Lysaker, Norway email: [email protected]
Department of Informatics University of Oslo P.O. Box 1080, Blindern 0316 Oslo, Norway email: mortend@ifi.uio.no
Library of Congress Control Number: 2006928289 Mathematics Subject Classification: 51-02 ISBN-10 3-540-33260-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-33260-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and techbooks using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN: 11693598
46/techbooks
543210
Preface
This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations. Throughout the book we relate the theory to selected applications, in particular surface construction, meshing and visualization. The field of triangulation is part of the huge area of computational geometry, and over many years numerous books and articles have been written on the subject. Important results on triangulations have appeared in theoretical books and articles, mostly within the realm of computational geometry. However, many important results on triangulations have also been presented in publications within other research areas, where they have played and play an important role in solving specific scientific and applied problems. We will touch upon some of these areas in this book. Triangulations, almost everywhere. The early development of triangulation comes from surveying and the art of constructing maps – cartography. Surveyors and cartographers used triangles as the basic geometric feature for calculating distances between points on the Earth’
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