Geometric Modeling and Applications Set
coordinated by Marc Daniel
Volume 3
First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
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© ISTE Ltd 2019
The rights of Jean-Luc Mari, Franck Hétroy-Wheeler and Gérard Subsol to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2019946683
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-041-6
Three-dimensional surface meshes, composed of collections of planar polygons, are the most common discrete representation of the surface of a virtual shape. These 3D surface meshes need to be inspected in order to understand or evaluate their overall structure or some details. This can be done by extracting relevant geometric or topological features. Such shape characteristics can simplify the way the object is looked at, can help recognition and can describe and categorize it according to specific criteria.
Shape characteristics can be defined in many ways. This book takes the point of view of discrete mathematics, which aims to propose discrete counterparts to concepts mathematically defined in continuous terms. More specifically, in this book, we review how standard geometric and topological notions of surfaces can be defined and computed for a 3D surface mesh, as well as their use for shape analysis. In particular, recent methods are described to extract feature lines having a meaning related to either geometry or topology. Differential estimators such as discrete principal curvatures are detailed as they play a critical role in the computation of salient structures. An emphasis is then placed on topology since the global structure and the connectivity of features play an important role in the understanding of a shape. Several applications are finally developed, showing that each of them needs specific adjustments to generic approaches. These applications are related to medicine, geology, botany and other sciences.
Focusing on shape features, the topic of this book is narrower but more detailed than other shape analysis books, which do not, or only briefly, refer to feature definition and computation. It is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems. We hope that our book will be a useful review of existing work for all of them.
Finally, we would like to thank Marc Daniel for giving us the opportunity to write this book and Aldo Gonzalez-Lorenzo for his reading of chapter 2 and for his constructive remarks.
Jean-Luc MARI
Franck HÉTROY-WHEELER
Gérard SUBSOL
August 2019