Towards meshless volume visualization [Elektronische Ressource] / Eduardo Jose Tejada-Gamero
214 Pages
English

Towards meshless volume visualization [Elektronische Ressource] / Eduardo Jose Tejada-Gamero

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Towards Meshless Volume VisualizationVon der Fakulta¨t Informatik, Elektrotechnik und Informations-technik der Universita¨t Stuttgart zur Erlangung der Wu¨rdeeines Doktors der Naturwissenschaften (Dr. rer. nat.)genehmigte AbhandlungVorgelegt vonEduardo Jose Tejada-Gameroaus ArequipaHauptberichter: Prof. Dr. T. ErtlMitberichter: Prof. Dr. D. WeiskopfProf. Dr. L. G. NonatoTag der mu¨ndlichen Pru¨fung: 26. Ma¨rz 2008Institut fu¨r Visualisierung und Interaktive Systemeder Universita¨t Stuttgart2008Berichte aus der InformatikEduardo Jose Tejada-GameroTowards Meshless Volume VisualizationGedruckt mit Unterstu¨tzung des Deutschen Akademischen AustauschdienstesD93 (Diss. Universita¨t Stuttgart)Shaker VerlagAachen 2008Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the DeutscheNationalbibliografie; detailed bibliographic data are available in the Internet athttp://dnb.d-nb.de.Zugl.: Stuttgart, Univ., Diss., 2008Copyright Shaker Verlag 2008All rights reserved. No part of this publication may be reproduced, stored in aretrieval system, or transmitted, in any form or by any means, electronic,mechanical, photocopying, recording or otherwise, without the prior permissionof the publishers.Printed in Germany.ISBN 978-3-8322-7389-7ISSN 0945-0807Shaker Verlag GmbH• P.O. BOX 101818• D-52018 AachenPhone: 0049/2407/9596-0• Telefax: 0049/2407/9596-9Internet: www.shaker.

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Published 01 January 2008
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Towards Meshless Volume Visualization
Von der Fakulta¨t Informatik, Elektrotechnik und Informations-
technik der Universita¨t Stuttgart zur Erlangung der Wu¨rde
eines Doktors der Naturwissenschaften (Dr. rer. nat.)
genehmigte Abhandlung
Vorgelegt von
Eduardo Jose Tejada-Gamero
aus Arequipa
Hauptberichter: Prof. Dr. T. Ertl
Mitberichter: Prof. Dr. D. Weiskopf
Prof. Dr. L. G. Nonato
Tag der mu¨ndlichen Pru¨fung: 26. Ma¨rz 2008
Institut fu¨r Visualisierung und Interaktive Systeme
der Universita¨t Stuttgart
2008Berichte aus der Informatik
Eduardo Jose Tejada-Gamero
Towards Meshless Volume Visualization
Gedruckt mit Unterstu¨tzung des Deutschen Akademischen Austauschdienstes
D93 (Diss. Universita¨t Stuttgart)
Shaker Verlag
Aachen 2008Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche
Nationalbibliografie; detailed bibliographic data are available in the Internet at
http://dnb.d-nb.de.
Zugl.: Stuttgart, Univ., Diss., 2008
Copyright Shaker Verlag 2008
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior permission
of the publishers.
Printed in Germany.
ISBN 978-3-8322-7389-7
ISSN 0945-0807
Shaker Verlag GmbH• P.O. BOX 101818• D-52018 Aachen
Phone: 0049/2407/9596-0• Telefax: 0049/2407/9596-9
Internet: www.shaker.de• e-mail: info@shaker.deA Paola y Andre´s,
quienes son la luz en mi vida.CONTENTS
List of Abbreviations and Acronyms 1
Abstract and Chapter Summaries 3
Zusammenfassung und Kapitelzusammenfassungen 9
1 Introduction 15
1.1 Goals of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Outline of This Thesis . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Interactive Visualization 21
2.1 Visualization Pipeline . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Surface Visualization . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Surface data . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Surface reconstruction . . . . . . . . . . . . . . . . . . . 23
2.2.3 Surface rendering . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Volume Visualization . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Volume data . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.2 Volume data reconstruction . . . . . . . . . . . . . . . . . 29
2.3.3 Volume rendering . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Visualization and Graphics Processing Units . . . . . . . . . . . . 41
2.4.1 The rendering pipeline . . . . . . . . . . . . . . . . . . . 41
2.4.2 General-purpose GPU programming . . . . . . . . . . . . 43
3 Meshless Approximation Methods 45
3.1 Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Moving Least-Squares . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Orthogonal Polynomials in Moving Least-Squares . . . . . . . . . 47
3.3.1 Indexing orthogonal polynomials . . . . . . . . . . . . . 48
3.3.2 Constructing orthogonal polynomials . . . . . . . . . . . 49
3.3.3 Avoiding repetitive computations . . . . . . . . . . . . . 50
3.4 Approximate Approximation . . . . . . . . . . . . . . . . . . . . 51
3.4.1 Approximate moving least-squares approximation . . . . 51
3.4.2 Connecting RBF and Iterated AMLS . . . . . . . . . . . 52
III Contents
4 Meshless Surfaces from Point Clouds 55
4.1 Meshless Surface Approximation . . . . . . . . . . . . . . . . . . 56
4.2 Curvature-driven Projection Operator . . . . . . . . . . . . . . . 62
4.2.1 Principal directions and curvatures . . . . . . . . . . . . . 64
4.2.2 Projection and rendering procedures . . . . . . . . . . . . 66
4.3 Approximate MLS Surfaces . . . . . . . . . . . . . . . . . . . . 71
4.3.1 Iterated AMLS implicits . . . . . . . . . . . . . . . . . . 74
4.3.2 Introducing sharp edges . . . . . . . . . . . . . . . . . . 79
4.4 Adaptive Partition of Unity Implicits . . . . . . . . . . . . . . . . 82
4.4.1 Multi-level partition of unity implicits . . . . . . . . . . . 84
14.4.2 TheJ triangulation . . . . . . . . . . . . . . . . . . . . 85A
4.4.3 Robust adaptive partition of unity implicits . . . . . . . . 87
4.4.4 Extensions to the method . . . . . . . . . . . . . . . . . . 91
4.5 GPU-based Rendering of Meshless Surfaces . . . . . . . . . . . . 96
4.5.1 Rendering surfaces based on projection operators . . . . . 97
4.5.2 Rendering implicit surfaces . . . . . . . . . . . . . . . . 101
5 Meshless Surfaces from Volumes 105
5.1 Meshless Surface Extraction from Volume Data . . . . . . . . . . 105
5.2 Moving Least-squares Iso-surfaces . . . . . . . . . . . . . . . . . 108
5.2.1 Computing MLS surfaces from volumetric data . . . . . . 109
5.2.2 Hardware-accelerated MLS Iso-surfaces and HG-surfaces 110
5.3 Point-based Stream Surfaces . . . . . . . . . . . . . . . . . . . . 114
5.3.1 Streamlines and path-lines generation . . . . . . . . . . . 115
5.3.2 Point-based surface rendering . . . . . . . . . . . . . . . 120
5.3.3 LIC on the point-based surface . . . . . . . . . . . . . . . 122
6 Meshless Volume Visualization 127
6.1 Meshless Methods for Volume Visualization . . . . . . . . . . . . 129
6.2 Moving Least-Squares Volume Visualization . . . . . . . . . . . . 131
6.2.1 Detail-preserving volume data approximation . . . . . . . 132
6.2.2 Matrix-free detail-preserving volume data approximation . 134
6.3 Approximate MLS Volume Visualization . . . . . . . . . . . . . . 138
6.3.1 Ellipsoidal weight functions revisited . . . . . . . . . . . 139
6.3.2 Anisotropic iterated approximate moving least-squares . . 140
6.3.3 Gradient estimation . . . . . . . . . . . . . . . . . . . . . 142
6.3.4 GPU-based rendering . . . . . . . . . . . . . . . . . . . . 143
6.4 Moving Least-Squares Volume Deformation . . . . . . . . . . . . 147
6.4.1 Affine, similarity and rigid deformations . . . . . . . . . . 148
6.4.2 Nonlinear polynomial deformation . . . . . . . . . . . . . 155
6.4.3 GPU-based MLS displacement map computation . . . . . 156Contents III
6.4.4 Other approaches for moving least-squares deformation . 161
6.4.5 Comparison with physically-based mesh deformation . . . 164
7 Meshless Methods in Visualization 171
Color Plates 177
Bibliography 189IV Contents