Processing of meshes and geometry for visualization applications [Elektronische Ressource] / vorgelegt von Katrin Bidmon

Katrin Bidmon

Sujets

• Informatik

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2010
• Nombre de lectures: 29
• Langue: English
• Poids de l'ouvrage: 42 Mo

Extrait

Processing of Meshes and Geometry for
Visualization Applications
Von der Fakultat fur Informatik, Elektrotechnik und
Informationstechnik der Universitat Stuttgart
zur Erlangung der Wurde eines Doktors
der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung
Vorgelegt von
Katrin Bidmon
aus Geislingen an der Steige
Hauptberichter: Prof. Dr. Thomas Ertl
Mitberichter: Prof. Dr. Hans Hagen
Tag der mundlichen Prufung: 6. Oktober 2010
Visualisierungsinstitut der Universitat Stuttgart
2010Contents
List of Abbreviations 5
Abstract 7
Zusammenfassung 9
1 Introduction 11
1.1 The Basic Visualization Process . . . . . . . . . . . . . . . . . . 15
1.2 Mathematics for Geometry Processing . . . . . . . . . . . . . . 18
1.2.1 The Geometry of Curves and Surfaces . . . . . . . . . . 18
1.2.2 Di erential Equation Systems . . . . . . . . . . . . . . . 35
1.3 Mesh-based Geometry . . . . . . . . . . . . . . . . . . . . . . . 40
1.3.1 Marching Cubes . . . . . . . . . . . . . . . . . . . . . . 42
1.3.2 Di erential Geometry Properties of Discretised Curves
and Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 44
2 Mesh-based Geometries in the Application of Finite Element Model-
ling 47
2.1 Introduction to Finite Element Methods . . . . . . . . . . . . . 50
2.1.1 General Method of Finite Elements . . . . . . . . . . . . 51
2.1.2 Mesh Property Prerequisites for Simulation . . . . . . . 53
2.2 Generation of Mesh Variants via Volumetrical Representation . 54
2.2.1 Related Work on Voxelization and Isosurface Reconstruc-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.2.2 Voxelization of the Model . . . . . . . . . . . . . . . . . 56
2.2.3 Surface Reconstruction . . . . . . . . . . . . . . . . . . . 58
2.2.4 Quad Element Adjustment . . . . . . . . . . . . . . . . 61
2.2.5 Discussion on Quad Mesh Generation via Voxelization . 62
2.3 Optimization of Finite Element Meshes . . . . . . . . . . . . . 62
2.3.1 Warping Removal . . . . . . . . . . . . . . . . . . . . . 63
2.3.2 Mesh Relaxation . . . . . . . . . . . . . . . . . . . . . . 65
2.4 Filling Arbitrary Holes in Finite Element Models . . . . . . . . 71
2.4.1 Related Work on Hole Filling in Meshes . . . . . . . . . 73
2.4.2 Preliminaries in the Application Case . . . . . . . . . . 75
2.4.3 De nition of Semantic Holes . . . . . . . . . . . . . . . 76
2.4.4 Filling Holes Using an Advancing Front Algorithm . . . 784 Contents
2.4.5 Results on Filling Arbitrary Holes in FE Meshes . . . . 86
3 Beyond Meshes { Applications in Biochemistry and Live Science 89
3.1 Introduction to Protein-Solvent Systems . . . . . . . . . . . . . 90
3.2 Related Work on Visualization of Protein-Solvent Systems . . . 95
3.3 Protein Representations . . . . . . . . . . . . . . . . . . . . . . 95
3.3.1 Atom-Based Representations . . . . . . . . . . . . . . . 96
3.3.2 Secondary-Structure-Based Representation . . . . . . . 98
3.3.3 Surface Representations . . . . . . . . . . . . . . . . . . 103
3.4 Dynamic Data for Time-Based Molecular Visualization Methods 117
3.5 Time-Based Haptic Analysis of Protein Dynamics . . . . . . . . 118
3.5.1 Related Work on Haptics for Protein Dynamics . . . . . 120
3.5.2 Haptic Interaction with Protein Trajectory . . . . . . . 121
3.5.3 Results on Haptics Analysis of Protein Dynamics . . . . 123
3.6 Solvent Visualization . . . . . . . . . . . . . . . . . . . . . . . . 124
3.6.1 Filtering of Solvent Molecules . . . . . . . . . . . . . . . 125
3.6.2 Visual Abstractions of Solvent Pathlines . . . . . . . . . 127
3.7 Hyperstreamlines for Di usion Tensor Imaging . . . . . . . . . 139
3.7.1 Related Work on Di usion Tensor Imaging . . . . . . . 140
3.7.2 DTI Data . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.7.3 Tubelets . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
3.7.4 Sphere Tracing on the GPU . . . . . . . . . . . . . . . . 147
3.7.5 Results on Hyperstreamlines . . . . . . . . . . . . . . . 150
4 Discussion 153List of Abbreviations
h:;:i the scalar product
I the rst fundamental formp
II the secondtal formp
n
C the n times continuously di erentiable functions
c_ derivative with respect to parameter t
0c derivative with respect to arc length parameter s
0f derivative with respect to the function
(n)
f n-th derivative with respect to the function parameter
i if and only if
lin(:::) the linear hull
T M the tangent spacep
AFM advancing front method
CAE computer-aided engineering
DTI di usion tensor imaging
GPU graphic processing unit
FE nite element
FEA nitet analysis
MLS moving least-squares
MR magnetic resonance
MRI imaging
ODE ordinary dierential equationAbstract
The fast increase of computational power not only enables the simulation of
complex non-linear and highly dynamic processes but also allows for further
increase of the problem sizes and makes parameter studies with numerous
simulation runs a ordable. One of the often underrated consequences of this
development is the resulting rampant amount of simulation data that has to
be processed, analysed and evaluated accordingly. Therefore, the develop-
ment of powerful and capable analysis tools likewise gains in importance with
visualization playing an increasingly crucial role.
The visual conditioning of data { both in simulation pre- and post-processing
{ provides intuitive and fast insight. Hence, appropriate visualizations have
to be developed and, where required, tailored to the speci c needs of the
particular application. As in visualization applications the principal purpose
is not a visually pleasing appearance itself { although marvellous visual quality
of course is preferable { but to provide an ideal blend of data compensation
and emphasis on relevant features in order to enable and support intuitive
data handling and analysis.
In many application elds, geometry plays a crucial role in analysis. The
major contributions of this work are on the geometric aspects of visualization
methods in the application elds of virtual prototyping in car industry on one
hand and molecular dynamics on the other hand. In both, the challenge is
to comply with needs while satisfying the required correctness of
the shape, geometry and topology in order to ensure reliable analysis support,
while providing superior visual quality in interactive methods, elaborating the
data characteristics without concealing relevant features. But still the focus
with respect to geometry is di erent in both application elds.
On one hand, as in the area of car prototyping, reliable geometric models are of
superior importance for both robust simulation set-ups and trustable results,
since the evaluation of the geometric properties of the model is the principal
purpose of simulation. The simulations in this eld are usually based on nite
element (FE) methods, thus the visualization is mesh-based accordingly. In
this thesis newds for processing, customization and (re-)construction of
geometry and geometric characteristics are presented, tailored to the speci c
needs of automotive pre-processing.
On the other hand, as in the application eld of molecular dynamics, the
geometric shape of the simulation entities often is not relevant but dictates8 Abstract
the simulation constraints and, thus, still plays an essential role in analysis
tasks. Therefore, the work presented in this eld emphasises the power of
geometric concepts as essential foundation for data structuring and intuitive
evaluation during simulation data analysis. Since the molecules themselves do
not have an intrinsic shape, geometric molecular representations always entail
abstraction up to a certain extent. This fact, in turn, can be exploited to
create semantically expressive molecular visualizations based on very di erent
intrinsic and geometric properties of the data.
Being developed in close collaboration with scientists in the dedicated applic-
ation elds, the methods presented in this thesis found their way into recent
research in the case of molecular dynamics as well as into commercial applic-
ation tools in the case of the nite element analysis methods.Zusammenfassung
Der inzwischen sprunghafte Anstieg an verfugbarer Rechenleistung ermoglicht
nicht nur die Simulation komplexer nicht-linearer und hochdynamischer Pro-
zesse an sich, sondern erlaubt auch den weiteren Anstieg der Problemgro en
und macht Parameterstudien mit zahlreichen Simulationslaufen handhabbar.
Eine der dabei hau g untersch atzten Folgen ist die daraus resultierende starke
Zunahme an Simulationsergebnissen, welche anschlie end entsprechend weiter
verarbeitet, analysiert und ausgewertet werden mussen. Aus diesem Grund ist
die Entwicklung leistungsfahiger und machtiger Analysewerkzeuge von immer
gro erer Bedeutung, wobei die Visualisierung eine zunehmend entscheidende
Rolle spielt.
Die visuelle Aufbereitung von Daten, sowohl in der Vor- als auch in der Nach-
bearbeitung, bietet einen intuitiven und direkten Einblick in die Ergebnisse.
Darum mussen passende Visualisierungen entwickelt und gegebenenfalls auf
die speziellen Bedurfnisse der Anwendung angepasst werden. Sinn und Zweck
von Visualisierungsanwendungen ist letztlich nicht allein die visuell anspre-
chende Darstellung an sich, sondern die Tatsache, eine ideale Mischung aus