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Abel J. P. Gomes, Irina Voiculescu, Joaquim Jorge, Brian Wyvill, Callum Galbraith (eds.)-Implicit Curves and Surfaces_ Mathematics, Data Structures and Algorithms-Springer-Verlag London (2009)
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Implicit Curves and Surfaces:
Mathematics, Data Structures and Algorithms

Abel J.P. Gomes
•
Irina Voiculescu
Joaquim Jorge
•
Brian Wyvill
•
Callum Galbraith
Implicit Curves and Surfaces:
Mathematics, Data Structures
and Algorithms
ABC

Abel J.P. Gomes
Universidade da Beira Interior
Covilha
Portugal
Irina Voiculescu
Oxford University Computing
Laboratory (OUCL)
Oxford
United Kingdom
Joaquim Jorge
Universidade Tecnica de Lisboa
Lisboa
Portugal
Brian Wyvill
University of Victoria
Victoria BC
Canada
Callum Galbraith
University of Calgary
Calgary
Canada
ISBN 978-1-84882-405-8 e-ISBN 978-1-84882-406-5
DOI 10.1007/978-1-84882-406-5
Springer Dordrecht Heidelberg London New York
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Control Number: 2009926285
c
° Springer-Verlag London Limited 2009
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permit-
ted 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 of licenses issued by the Copyright Li-
censing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers.
The use of 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 laws and regulations and therefore free
for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions
that may be made.
Cover design: KuenkelLopka GmbH
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)

Preface
This book presents the mathematics, computational methods and data struc-
tures, as well as the algorithms needed to render implicit curves and surfaces.
Implicit objects have gained an increasing importance in geometric modelling,
visualisation, animation, and computer graphics due to their nice geometric
properties which give them some advantages over traditional modelling meth-
ods. For example, the point membership classification is trivial using implicit
representations of geometric objects—a very useful property for detecting col-
lisions in virtual environments and computer game scenarios. The ease with
which implicit techniques can be used to describe smooth, intricate, and ar-
ticulatable shapes through blending and constructive solid geometry show us
how powerful they are and why they are finding use in a growing number of
graphics applications.
The book is mainly directed towards graduate students, researchers and
developers in computer graphics, geometric modelling, virtual reality and com-
puter games. Nevertheless, it can be useful as a core textbook for a graduate-
level course on implicit geometric modelling or even for general computer
graphics courses with a focus on modelling, visualisation and animation. Fi-
nally, and because of the scarce number of textbooks focusing on implicit
geometric modelling, this book may also work as an important reference for
those interested in modelling and rendering complex geometric objects.
Abel Gomes
Irina Voiculescu
Joaquim Jorge
Brian Wyvill
Callum Galbraith
March 2009
V
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