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" Topological Data Analysis for Scientific Visualization. "
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BL
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| Record Number
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553045
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| Doc. No
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b381487
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| Main Entry
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Julien Tierny
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| Title & Author
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Topological Data Analysis for Scientific Visualization.
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| Publication Statement
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Cham : Springer,, 2018.
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| Series Statement
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Mathematics and Visualization Ser.
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| Page. NO
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(158 pages).
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| ISBN
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3319715070
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: 9783319715070
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| Notes
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Preliminary Results.
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| Contents
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Intro Preface Acknowledgements Contents Notations 1 Introduction 2 Background 2.1 Data Representation 2.1.1 Domain Representation Preliminary Notions Domain Formalization Topological Invariants 2.1.2 Range Representation Piecewise Linear Scalar Fields Related Geometrical Constructions 2.2 Topological Abstractions 2.2.1 Critical Points 2.2.2 Notions of Persistent Homology 2.2.3 Reeb Graph 2.2.4 Morse-Smale Complex 2.3 Algorithms and Applications 2.3.1 Persistent Homology 2.3.2 Reeb Graph 2.3.3 Morse-Smale Complex 3 Abstraction. 3.1 Efficient Topological Simplification of Scalar Fields3.1.1 Preliminaries General Simplification of Scalar Fields on Surfaces Closed Surfaces Surfaces with Boundary Surface Scalar Field Constrained Topology Minima Regular Vertices Interior Saddles Boundary Saddles Maximum 3.1.2 Algorithm Algorithm Description Sub-level Set Constrained Reconstruction Sur-level Set Constrained Reconstruction Overall Algorithm Convergence From Symbolic to Numerical Perturbation Algorithm Properties 3.1.3 Results and Discussion Time Requirement Discussion Limitations Application. Concluding Remarks3.2 Efficient Reeb Graph Computation for Volumetric Meshes 3.2.1 Preliminaries Loops in Reeb Graphs on PL 3-Manifolds in R3 Loop Surgery Loop Free Reeb Graph Computation 3.2.2 Algorithm Loop Surgery Genus Diagnostic Loop Saddles Cutting Surfaces Loop Free Reeb Graph Computation Inverse Cuts 3.2.3 Results and Discussion Time Complexity Performance Comparison Asymptotic Stress Tests Limitations Concluding Remarks 4 Interaction 4.1 Topological Simplification of Isosurfaces 4.2 Interactive Editing of Topological Abstractions 4.2.1 Morse-Smale Complex Editing. Conforming Discrete GradientAlgorithm Editable Morse-Smale Complexes Identity Map Termination Map Boundary Map User Edits A Histological Example Concluding Remarks 4.2.2 Reeb Graph Editing Harmonic Scalar Fields Reeb-Graph Based Surface Segmentation and Parameterization Editing Operations Chart Boundary Chart Number Chart Corners Preliminary Results Concluding Remarks 5 Analysis 5.1 Exploration of Turbulent Combustion Simulations 5.1.1 Applicative Problem 5.1.2 Algorithm Data Segmentation Feature Tracking Tracking Graph Simplification 5.1.3 Results. Interactive Exploration InterfaceQuantitative Analysis Concluding Remarks 5.2 Quantitative Analysis of Molecular Interactions 5.2.1 Applicative Problem Interactions in Molecular Systems Input Data 5.2.2 Algorithm Feature Definition Technical Challenges Interaction Sites Bonding Graph Repulsive Bond-Cycles 5.2.3 Results Validation Quantitative Analysis and Visual Exploration Concluding Remarks 6 Perspectives 6.1 Emerging Constraints 6.1.1 Hardware Constraints Preliminary Results 6.1.2 Software Constraints Research Directions 6.1.3 Exploration Constraints.
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Electronic books
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