Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Visualization of scalar topology for structural enhancement
Proceedings of the conference on Visualization '98
An open graph visualization system and its applications to software engineering
Software—Practice & Experience - Special issue on discrete algorithm engineering
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets
VIS '04 Proceedings of the conference on Visualization '04
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Topological Landscapes: A Terrain Metaphor for Scientific Data
IEEE Transactions on Visualization and Computer Graphics
A Topological Framework for the Interactive Exploration of Large Scale Turbulent Combustion
E-SCIENCE '09 Proceedings of the 2009 Fifth IEEE International Conference on e-Science
Visualization of High-Dimensional Point Clouds Using Their Density Distribution's Topology
IEEE Transactions on Visualization and Computer Graphics
Drawing Contour Trees in the Plane
IEEE Transactions on Visualization and Computer Graphics
Fast edge-routing for large graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
Multi-core and many-core shared-memory parallel raycasting volume rendering optimization and tuning
International Journal of High Performance Computing Applications
Topological landscape ensembles for visualization of scalar-valued functions
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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We propose a novel technique for building geometry-preserving topological landscapes. Our technique creates a direct correlation between a scalar function and its topological landscape. This correlation is accomplished by introducing the notion of geometric proximity into the topological landscapes, reflecting the distance of topological features within the function domain. Furthermore, this technique enables direct comparative analysis between scalar functions, as long as they are defined on the same domain. We describe a construction technique that consists of three stages: contour tree computation, contour tree layout, and landscape construction. We provide a detailed description for the latter two steps. For the contour tree layout stage, we discuss dimension reduction and edge routing techniques that produce a drawing of the contour tree on the plane that preserves the geometric proximity. For the landscape construction stage, we develop a contour construction algorithm that takes the contour tree layout as an input, adds contours at heights that correspond to saddles of the contour tree, and produces a contour map. After an additional triangulation step, this construction method results in the landscape that has the same contour tree as the original function.