Table of Contents

Topological Methods in Data Analysis and Visualization; Preface; Geometric Topology & Visualizing 1-Manifolds; Stripe Parameterization of Tubular Surfaces; The Stability of the Apparent Contour of an Orientable 2-Manifold; Reconstructing Cell Complexes From Cross-sections; Substructure Topology Preserving Simplification of Tetrahedral Meshes; Practical Considerations in Morse-Smale Complex Computation; Modeling and Simplifying Morse Complexes in Arbitrary Dimensions; Simplification of Jacobi Sets; Combinatorial 2D Vector Field Topology Extraction and Simplification. Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data an.