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

Eduardo Tejada

Sujets

• Informatik

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2008
• Nombre de lectures: 31
• Langue: English
• Poids de l'ouvrage: 13 Mo

Extrait

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
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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