TAILIEUCHUNG - Geometry and Computing Series Editors Herbert Edelsbrunner

The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982), and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging, computational geometry, visualization ). Following a historical and didactic approach, the book introduces the mathematical background of the subject, beginning with curves and surfaces, going on with convex subsets,. | Geometry and Computing Series Editors Herbert Edelsbrunner LeifKobbelt Konrad Polthier Editorial Advisory Board Jean-Daniel Boissonnat Gunnar Carlsson Bernard Chazelle Xiao-Shan Gao Craig Gotsman Leo Guibas Myung-Soo Kim Takao Nishizeki Helmut Pottmann Roberto Scopigno Hans-Peter Seidel Steve Smale Peter Schroder Dietrich Stoyan Jean-Marie Morvan Generalized Curvatures With 107 Figures 1 Springer Jean-Marie Morvan Universite Claude Bernard Lyon 1 Institut Camille Jordan Batiment Jean Braconnier 43 bd du 11 Novembre 1918 69622 Villeurbanne Cedex France morvanjeanmarie@ On the cover the data of Michelangelo s head are courtesy of Digital Michelangelo Project the image of Michelangelo s head with the lines of curvatures are courtesy of the GEOMETRICA project-team from INRIA. ISBN 978-3-540-73791-9 e-ISBN 978-3-540-73792-6 Springer Series in Geometry and Computing Library of Congress Control Number 2008923176 Mathematics Subjects Classification 2000 52A 52B 52C 53A 53B 53C 49Q15 28A33 28A75 68R 2008 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 987654321 .

• Điện - Điện tử
• curvature measures
• Geometry and Computing
• computer science
• curves and surfaces
• convex subsets
• smooth submanifolds
• subsets of positive reach