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Details
Table of Contents
Intro
Preface
Contents
Part I: Scalar Field Topology
Algorithms and Applications
W-Structures in Contour Trees
1 Introduction
2 Background
2.1 Contour Trees
2.2 Contour Tree Algorithms
2.3 Contour Tree Simplification
3 W-Structures in Contour Trees
3.1 Spatial Characterization
3.2 W-Diameter Algorithms
3.3 Algorithm 1-Multi BFS
3.4 Algorithm 2-Double BFS
3.5 Algorithm 3-Dynamic
4 Empirical Study
4.1 Results
5 W-Structure Simplification
5.1 Persistent Homology Overview
5.2 Comparison of Critical Point Pairs
6 Conclusion
3.2 Histogram Distribution
4 Analysis and Visualization of Percolation Curve Ensembles
4.1 Analysis of a Single Percolation Curve
4.2 Analysis of Percolation Curve Ensembles
5 Experiments
5.1 Randomness and Structure: Gaussian Random Fields
5.2 Turbulent Flow: Duct Data Set
6 Conclusions and Future Work
References
Distributed Task-Parallel Topology-Controlled Volume Rendering
1 Introduction
2 Related Work
3 System Design
4 Implementation
4.1 Merge
4.2 Simplify
4.3 Update
4.4 Branch Decomposition Assembly
4.5 Transfer Function Assignment
4.6 Rendering
5 Results
5.1 Experimental Design
5.2 General Observations
5.3 Algorithm Validation
5.4 Strong Scaling
5.5 Weak Scaling
6 Conclusion
References
Topology-Based Feature Design and Tracking for Multi-center Cyclones
1 Introduction
2 Background
3 Full Tracking Graph Computation
4 Feature Definition and Tracking of Cyclonic Systems
5 Implementation Details
6 Case Study
7 Conclusion and Discussion
References
Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes
1 Introduction
2 Science Case
3 Technical Background
4 Application Development Process
4.1 Designing to Serve the ALMA Community
5 Software Design
5.1 Visual Elements
5.2 Interaction Process
6 Case Studies
6.1 Ghost of Mirach Galaxy Data Set
6.2 CMZ Data Set
7 Discussion
References
Part II: Topological Methods in Complex Fields
Flow Fields, Tensor Fields, and Multi-fields
Objective Finite-Time Flow Topology from Flowmap Expansion and Contraction
1 Introduction
2 Related Work
2.1 Classic Steady Vector Field Topology
2.2 Streamlines vs. Pathlines
2.3 Reference Frames
Preface
Contents
Part I: Scalar Field Topology
Algorithms and Applications
W-Structures in Contour Trees
1 Introduction
2 Background
2.1 Contour Trees
2.2 Contour Tree Algorithms
2.3 Contour Tree Simplification
3 W-Structures in Contour Trees
3.1 Spatial Characterization
3.2 W-Diameter Algorithms
3.3 Algorithm 1-Multi BFS
3.4 Algorithm 2-Double BFS
3.5 Algorithm 3-Dynamic
4 Empirical Study
4.1 Results
5 W-Structure Simplification
5.1 Persistent Homology Overview
5.2 Comparison of Critical Point Pairs
6 Conclusion
3.2 Histogram Distribution
4 Analysis and Visualization of Percolation Curve Ensembles
4.1 Analysis of a Single Percolation Curve
4.2 Analysis of Percolation Curve Ensembles
5 Experiments
5.1 Randomness and Structure: Gaussian Random Fields
5.2 Turbulent Flow: Duct Data Set
6 Conclusions and Future Work
References
Distributed Task-Parallel Topology-Controlled Volume Rendering
1 Introduction
2 Related Work
3 System Design
4 Implementation
4.1 Merge
4.2 Simplify
4.3 Update
4.4 Branch Decomposition Assembly
4.5 Transfer Function Assignment
4.6 Rendering
5 Results
5.1 Experimental Design
5.2 General Observations
5.3 Algorithm Validation
5.4 Strong Scaling
5.5 Weak Scaling
6 Conclusion
References
Topology-Based Feature Design and Tracking for Multi-center Cyclones
1 Introduction
2 Background
3 Full Tracking Graph Computation
4 Feature Definition and Tracking of Cyclonic Systems
5 Implementation Details
6 Case Study
7 Conclusion and Discussion
References
Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes
1 Introduction
2 Science Case
3 Technical Background
4 Application Development Process
4.1 Designing to Serve the ALMA Community
5 Software Design
5.1 Visual Elements
5.2 Interaction Process
6 Case Studies
6.1 Ghost of Mirach Galaxy Data Set
6.2 CMZ Data Set
7 Discussion
References
Part II: Topological Methods in Complex Fields
Flow Fields, Tensor Fields, and Multi-fields
Objective Finite-Time Flow Topology from Flowmap Expansion and Contraction
1 Introduction
2 Related Work
2.1 Classic Steady Vector Field Topology
2.2 Streamlines vs. Pathlines
2.3 Reference Frames