Conformal Geometry Computational Algorithms and Engineering Applicat
This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspecti
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Conformal Geometry Computational Algorithms and Engineering Applications
Conformal Geometry
Miao Jin Xianfeng Gu Ying He Yalin Wang •
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Conformal Geometry Computational Algorithms and Engineering Applications
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Miao Jin The Centre for Advanced Computer Studies University of Louisiana Lafayette, LA USA Xianfeng Gu State University of New York Stony Brook, NY USA
Ying He School of Computer Science and Engineering Nanyang Technological University Singapore Singapore Yalin Wang School of Computing, Informatics and Decision Systems Engineering Arizona State University Tempe, AZ USA
ISBN 978-3-319-75330-0 ISBN 978-3-319-75332-4 https://doi.org/10.1007/978-3-319-75332-4
(eBook)
Library of Congress Control Number: 2018934929 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
For those who love geometry.
Preface
Conformal means angle preserving in mathematics. Conformal geometry studies conformal structure of general surfaces. Conformal structure is a natural geometric structure and a special atlas on surfaces such that angles among tangent vectors can be coherently defined on different local coordinate systems. Conformal structure governs many physics phenomena including heat diffusion and electric–magnetic fields. Computational conformal geometry focuses on algorithmic study of conformal geometry and offers powerful tools to handle a broad range of geometric problems in engineering fields. It links modern geometry theories to real engineering applications. The power of computational conformal geometry in engineering fields stems from the following fundamental reasons.
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