Implicit Curves and Surfaces_ Mathematics, Data Structures, and Algorithms [Gomes, Voiculescu, Jorge, Wyvill & Galbraith 2009-05-15].pdf

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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:
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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
Acknowledgments
The authors are grateful to those who have kindly assisted with the editing of
this book, in particular Helen Desmond and Beverley Ford (Springer-Verlag).
We are also indebted to Adriano Lopes (New University of Lisbon, Portu-
gal), Afonso Paiva (University of S˜o Paulo, Brazil), Bruno Ara´jo (Technical
a
u
University of Lisbon, Portugal), Ron Balsys (Central Queensland University,
Australia) and Kevin Suffern (University of Technology, Australia) who gen-
erously have contributed beautiful images generated by their algorithms; also
to Tamy Boubekeur (Telecom ParisTech, France) for letting us to use the
datasets of African woman and Moai statues (Figures 8.7 and 8.10).
Abel Gomes thanks the Computing Laboratory, University of Oxford, Eng-
land, and CNR-IMATI, Genova, Italy, where he spent his sabbatical year writ-
ing part of this book. In particular, he would like to thank Bianca Falcidieno
and Giuseppe Patan` for their support and fruitful discussions during his
e
stage at IMATI. He is also grateful to Foundation for Science and Technology,
Institute for Telecommunications and University of Beira Interior, Portugal.
Irina Voiculescu acknowledges the support of colleagues at the Universi-
ties of Oxford and Bath, UK, who originally enticed her to study this field
and provided a stimulating discussion environment; also to Worcester College
Oxford, which made an ideal thinking retreat.
Joaquim Jorge is grateful to the Foundation for Science and Technology,
Portugal, and its generous support through project VIZIR.
Brian Wyvill is grateful to all past and present students who have con-
tributed to the Implicit Modelling and BlobTree projects; also to the Natural
Sciences and Engineering Research Council of Canada.
Callum Galbraith acknowledges the many researchers from the Graphics
Jungle at the University of Calgary who helped shape his research. In particu-
lar, he would like to thank his PhD supervisor, Brian Wyvill, for his excellent
experience in graduate school, and Przemyslaw Prusinkiewicz for his expert
guidance in the domain of modelling plants and shells; also to the University
of Calgary and the Natural Sciences and Engineering Research Council of
Canada for their support.
VII

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