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Topology-Based Methods in Visualization II

:	Gerald Farin, Hans-Christian Hege, David Hoffman, Christopher R. Johnson, Konrad Polthier, Martin Ru
:	Hans-Christian Hege, Konrad Polthier, Gerik Scheuermann
:	Topology-Based Methods in Visualization II
:	Springer-Verlag
:	9783540886068
:	1
:	CHF 47.50
:

:	Sonstiges
:	English

:	190
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years,interest in topology-basedvisualization has grown andsigni?cantinnovationhasled o newconceptsandsuccessfulappli ations. The latest trends adapt basic topological concepts to precisely express user interests in topological properties of the data. This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4-6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbr ughttogethermorethan40interna ional researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization. Two inspiring invited talks by George Haller, MIT, and Nelson Max, LLNL, were accompanied by 14 presentations by participants and two panel discussions on current and future trends in visualization research. This book contains thirteen research papers that have been peer-reviewed in a two-stage review process. In the ?rst phase, submitted papers where peer-reviewed by the international program committee. After the workshop accepted papers went through a revision and a second review process taking into account comments from the ?rst round and discussions at the workshop. Abouthalfthepapersconcerntopo ogy-basedanalysisandvisualiza ionof ?uid?owsimulations;twopapersc ncernmoregeneraltopologicalal orithms, while the remaining papers discuss topology-based visualization methods in application areas like biology, medical imaging and electromagnetism.

	Preface	5
	Contents	7
	Visualization of Coherent Structures in Transient 2D Flows	9
	1 Introduction	9
	2 The Finite-Time Lyapunov Exponent	10
	3 Previous Work	11
	4 Visualization of Coherent Structures	12
	5 Results	15
	6 Discussion	19
	References	21
	Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology	22
	1 Introduction	22
	2 Lagrangian Coherent Structures	23
	3 Results	26
	4 Conclusion	35
	References	35
	Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections	37
	1 Introduction	37
	2 Related Work	39
	3 Extracting Separation Manifolds	40
	4 Results	44
	5 Conclusion	47
	References	48
	Topology Based Selection and Curation of Level Sets	50
	1 Introduction	50
	2 Preliminary	55
	3 Algorithm	57
	4 Results	60
	5 Conclusion	61
	References	61
	Representing Interpolant Topology for Contour Tree Computation	64
	1 Introduction	64
	2 The Contour Tree	65
	3 Join and Split Graphs	68
	4 Graph Widgets for Standard Interpolants	68
	5 Finite State Machines for Split Graphs	70
	6 Marching (Hyper)Cubes and Digital Images	73
	7 Implementation and Results	75
	8 Conclusions and Future Work	76
	References	77
	Path Line Attributes - an Information Visualization Approach to Analyzing the Dynamic Behavior of 3D Time- Dependent Flow Fields	79
	1 Introduction	79
	2 Related Work	81
	3 Path Line Attributes	81
	4 System overview	83
	5 Applications	85
	6 Conclusions	90
	References	91
	Flow Structure based 3D Streamline Placement	93
	1 Introduction	93
	2 Related Work	94
	3 Construction of Flow Structures	95
	4 Flow Structure Examples	95
	5 Streamline Seeding	97
	6 Sparse Seeding	99
	7 Results	100
	8 Conclusion	103
	References	103
	Critical Points of the Electric Field from a Collection of Point Charges	105
	1 Introduction	105
	2 Electric Potential and Field	106
	3 Octree Method for Finding Critical Points	106
	4 Finding a Sphere Containing all the Critical Points	108
	5 Results	114
	References	118
	Visualizing global manifolds during the transition to chaos in the Lorenz system	119
	1 Introduction	119
	2 Global manifolds as a collection of geodesic level sets	120
	3 Visualizing the Lorenz manifold	123
	4 Transition through the homoclinic explosion	125
	5 Intersections of two-dimensional manifolds	127
	6 Conclusions	128
	References	129
	Streamline and Vortex Line Analysis of the Vortex Breakdown in a Confined Cylinder Flow	131
	1 Introduction	131
	2 Numerical Experiment of the Lid Driven Cylinder Flow	134
	3 Phenomenological Description Of Vortex Breakdown	135
	4 Topological Analysis	137
	5 Local Flow Analysis	140
	6 Conclusion	145
	References	146
	Flow Topology Beyond Skeletons: Visualization of Features in Recirculating Flow	149
	1 Introduction	149
	2 Topology of vortex rings	151
	3 Analytical vortex ring model	153
	4 Visualization techniques for vortex rings	155
	5 Results	158
	6 Conclusion	162
	References	162
	Bringing Topology-Based Flow Visualization to the Application Domain	165
	1 Introduction	165
	2 Application: Simulation of In-Cylinder Flow	167
	3 Application: Heat Transfer	168
	4 Application: Spinning Missile	170
	5 Application Independent Directions	175
	6 Summary and Conclusions	176
	References	177
	Computing Center-Lines: An Application of Vector Field Topology	181
	1 Introduction	181
	2 Related Work	182
	3 Methodology	183
	4 Results	187
	5 Conclusions and Future Work	191
	References	192