Guide to Computational Geometry Processing_ Foundations, Algorithms, and Methods [Bærentzen, Gravesen, Anton & Aanæs 2012-05-31].pdf

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Guide to Computational Geometry
Processing
Jakob Andreas Bærentzen
r
Jens Gravesen
François Anton
r
Henrik Aanæs
r
Guide to
Computational
Geometry
Processing
Foundations, Algorithms, and Methods
Jakob Andreas Bærentzen
Department of Informatics and
Mathematical Modelling
Technical University of Denmark
Kongens Lyngby, Denmark
François Anton
Department of Informatics and
Mathematical Modelling
Technical University of Denmark
Kongens Lyngby, Denmark
Henrik Aanæs
Department of Informatics and
Mathematical Modelling
Technical University of Denmark
Kongens Lyngby, Denmark
Jens Gravesen
Department of Mathematics
Technical University of Denmark
Kongens Lyngby, Denmark
ISBN 978-1-4471-4074-0
ISBN 978-1-4471-4075-7 (eBook)
DOI 10.1007/978-1-4471-4075-7
Springer London Heidelberg New York Dordrecht
Library of Congress Control Number: 2012940245
© Springer-Verlag London 2012
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
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storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection
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The use of general descriptive names, registered names, trademarks, service marks, 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.
While the advice and information in this book are believed to be true and accurate at the date of pub-
lication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any
errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect
to the material contained herein.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book grew out of a conversation between two of the authors. We were dis-
cussing the fact that many of our students needed a set of competencies, which they
could not really learn in any course that we offered at the Technical University of
Denmark. The specific competencies were at the junction of computer vision and
computer graphics, and they all had something to do with “how to deal with” dis-
crete 3D shapes (often simply denoted “geometry”).
The tiresome fact was that many of our students at graduate level had to pick up
things like registration of surfaces, smoothing of surfaces, reconstruction from point
clouds, implicit surface polygonization, etc. on their own. Somehow these topics did
not quite fit in a graphics course or a computer vision course. In fact, just a few years
before our conversation, topics such as these had begun to crystallize out of com-
puter graphics and vision forming the field of geometry processing. Consequently,
we created a course in computational geometry processing and started writing a set
of course notes, which have been improved over the course of a few years, and now,
after some additional polishing and editing, form the present book.
Of course, the question remains: why was the course an important missing piece
in our curriculum, and, by extension, why should anyone bother about this book?
The answer is that optical scanning is becoming ubiquitous. In principle, any
technically minded person can create a laser scanner using just a laser pointer, a web
cam, and a computer together with a few other paraphernalia. Such a device would
not be at the 20 micron precision which an industrial laser scanner touts these days,
but it goes to show that the principles are fairly simple. The result is that a number
of organizations now have easy access to optical acquisition devices. In fact, many
individuals have too—since the Microsoft Kinect contains a depth sensing camera.
Geometry also comes from other sources. For instance, medical CT, MR and 3D
ultrasound scanners provide us with huge volumetric images from which we can
extract surfaces.
However, often we cannot directly use this acquired geometry for its intended
purpose. Any measurement is fraught with error, so we need to be able to filter the
geometry to reduce noise, and usually acquired geometry is also very verbose and
simplification is called for. Often we need to convert between various representa-
tions, or we need to put together several partial models into one big model. In other
words, raw acquired geometry needs to be processed before it is useful for some
envisioned purpose, and this book is precisely about algorithms for such processing
of geometry as is needed in order to make geometric data useful.
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