Enabling insight into large and complex datasets is a prevalent theme in visualization research for which different approaches are pursued.

Topology-based methods are built on the idea of abstracting characteristic structures such as the topological skeleton from the data and to construct the visualizations accordingly. There are currently new demands for and renewed interest in topology-based visualization solutions. This book presents 13 peer-reviewed papers as written results from the 2005 workshop Topology-Based Methods in Visualization that was initiated to enable additional stimulation in this field. It contains a longer chapter dedicated to a survey of the state-of-the-art, as well as a great deal of original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in topology-based visualization research.

Topology-Based Flow Visualization, The State of the Art.- Topology-guided Visualization of Constrained Vector Fields.- Scale-Space Tracking of Critical Points in 3D Vector Fields.- Feature Flow Fields in Out-of-Core Settings.- Streamline Predicates as Flow Topology Generalization.- Topology-based versus Feature-based Flow Analysis Challenges and an Application.- Topology Based Flow Analysis and Superposition Effects.- On the Applicability of Topological Methods for Complex Flow Data.- Extraction and Visualization of Swirl and Tumble Motion from Engine Simulation Data.- Simulation Methods for Advanced Design Engineering.- A Practical Approach to Two-Dimensional Scalar Topology.- On the Role of Topology in Focus+Context Visualization.- N-dimensional Data-Dependent Reconstruction Using Topological Changes.