E-Book Overview
An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.
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The IMA Volumes in Mathematics and its Applications Volume 151 Series Editors Fadil Santosa Markus Keel For other titles published in this series, go to www.springer.com/series/811 Ioannis Z. Emiris Frank Sottile Thorsten Theobald Editors Nonlinear Computational Geometry Editors Ioannis Z. Emiris Lab of Geometric & Algebraic Algorithms Department of Informatics & Telecommunications National and Kapodistrian University of Athens Panepistimiopolis, 15784 Greece http://cgi.di.uoa.gr/~emiris/index-eng.html Frank Sottile Department of Mathematics Texas A&M University College Station, TX 77843 USA http://www.math.tamu.edu/~sottile Thorsten Theobald FB 12 - Institut für Mathematik Johann Wolfgang Goethe-Universität Robert-Mayer-Str. 10 D-60325 Frankfurt am Main Germany http://www.math.uni-frankfurt.de/~theobald/ Series Editors Fadil Santosa Markus Keel Institute for Mathematics & its Applications University of Minnesota Minneapolis, MN 55455 USA ISSN 0940-6573 ISBN 978-1-4419-0998-5 DOI 10.1007/978-1-4419-0999-2 e-ISBN 978-1-4419-0999-2 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 200931559 Mathematics Subject Classification (2000): 14Q, 68U05, 68W30, 65D, 52A35 © Springer Science + Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science + Business Media, LLC, 233 Spring Street, New York, NY 10013, 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. Camera-ready copy provided by the IMA. Springer is part of Springer Science+Business Media (www.springer.com) FOREWORD This IMA Volume in Mathematics and its Applications NONLINEAR COMPUTATIONAL GEOMETRY contains papers presented at a highly successful one-week workshop held on May 29–June 2, 2007 on the same title. The event was an integral part of the 2006–2007 IMA Them