Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration
Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-res
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Torsten Möller Bernd Hamann Robert D. Russell Editors
Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration With 183 Figures, 134 in Color and 15 Tables
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Torsten Möller
Robert D. Russell
School of Computing Science Simon Fraser University 8888 University Drive Burnaby BC, V5A 1S6 Canada [email protected]
Department of Mathematics Simon Fraser University 8888 University Drive Burnaby BC, V5A 1S6 Canada [email protected]
Bernd Hamann Department of Computer Science University of California, Davis 1 Shields Avenue Davis, CA 95616-8562 USA [email protected]
ISBN: 978-3-540-25076-0 e-ISBN: 978-3-540-49926-8 DOI: 10.1007/978-3-540-49926-8 Mathematics and Visualization ISSN 1612-3786 Library of Congress Control Number: 2008944010 Mathematics Subject Classification (2000): 35-XX, 65Dxx, 41-XX, 51-XX, 54-XX, 65-XX, 76-XX c 2009 Springer-Verlag Berlin Heidelberg ° 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 to prosecution under the German Copyright Law. 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. Cover design: deblik, Berlin Printed on acid-free paper springer.com
Preface
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and increasingly common environment-embedded sensors are the primary generators of massive data sets. Being able to derive scientific insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximations of an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, efficient algorithms supporting real-time analysis and manipulation (rotation, zoomi
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