Voronoi Diagrams
Let S be a finite point set in ℝ n . Since S is compact, for every point x∈ℝ n there exists a closest point in S (which is not necessarily unique) with respect to the Euclidean norm ∥⋅∥. The set of all points in ℝ n that have a fixed point s∈S as their ne
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Universitext Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Vincenzo Capasso Università degli Studi di Milano, Milan, Italy Carles Casacuberta Universitat de Barcelona, Barcelona, Spain Angus MacIntyre Queen Mary, University of London, London, UK Kenneth Ribet University of California, Berkeley, Berkeley, CA, USA Claude Sabbah CNRS, École Polytechnique, Palaiseau, France Endre Süli University of Oxford, Oxford, UK Wojbor A. Woyczynski Case Western Reserve University, Cleveland, OH, USA
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Michael Joswig r Thorsten Theobald
Polyhedral and Algebraic Methods in Computational Geometry
Michael Joswig Fachbereich Mathematik Technische Universität Darmstadt Darmstadt, Germany
Thorsten Theobald Institut für Mathematik, FB 12 Johann Wolfgang Goethe-Universität Frankfurt am Main, Germany
Originally published in the German language by Vieweg+Teubner, 65189 Wiesbaden, Germany, as “Joswig, M.; Theobald, T.; Algorithmische Geometrie” © Vieweg+Teubner | GWV Fachverlage GmbH, Wiesbaden, 2008 ISSN 0172-5939 ISSN 2191-6675 (electronic) Universitext ISBN 978-1-4471-4816-6 ISBN 978-1-4471-4817-3 (eBook) DOI 10.1007/978-1-4471-4817-3 Springer London Heidelberg New York Dordrecht Library of Congress Control Number: 2012955474 Mathematics Subject Classification: 51-01, 13P10, 52-01, 68U05 © Springer-Verlag London 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations
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