Search NASA⌕ Search

SEARCH · Search NASA

Results for “reeb graph”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

GASP: Gradient-Aware Shortest Path Algorithm for Boundary-Confined 2-Manifold Reeb Graph Visualization

Reeb graphs are an important tool for abstracting and representing the topological structure of a function defined on a manifold. We have identified three properties for faithfully representing Reeb graphs in a visualization: they should be constrained to the boundary, compact, and aligned with the function gradient. Existing algorithms for drawing Reeb graphs are agnostic to or violate these properties. In this paper, we introduce an algorithm to generate Reeb graph visualizations, called GASP, that is cognizant of these properties, thereby producing visualizations that are more representative of the underlying data. To demonstrate the improvements, the resulting Reeb graphs are evaluated both qualitatively and quantitatively against the geometric barycenter algorithm, using its implementation available in the Topology ToolKit (TTK), a widely adopted tool for calculating and visualizing Reeb graphs.

Rahman, Sefat [University of Utah]↗
DOE OSTI2023

A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations

Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data. Topology-based visualizations reveal and explicitly communicate structures underlying data. Although our understanding of what types of features are captured by topological visualizations is good, our understanding of people's perception of those features is not. Further, this paper evaluates the sensitivity of topology-based isocontour, Reeb graph, and persistence diagram visualizations compared to a reference color map visualization for synthetically generated scalar fields on 2-manifold triangular meshes embedded in 3D. In particular, we built and ran a human-subject study that evaluated the perception of data features characterized by Gaussian signals and measured how effectively each visualization technique portrays variations of data features arising from the position and amplitude variation of a mixture of Gaussians. For positional feature variations, the results showed that only the Reeb graph visualization had high sensitivity. For amplitude feature variations, persistence diagrams and color maps demonstrated the highest sensitivity, whereas isocontours showed only weak sensitivity. These results take an important step toward understanding which topology-based tools are best for various data and task scenarios and their effectiveness in conveying topological variations as compared to conventional color mapping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an essential role in capturing the shape of scalar field data. Herein we present a state–of–the–art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time–varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Hybrid Parallel Contour Trees, Version 1.0

A common operation in scientific visualization is to compute and render a contour of a data set. Given a function of the form f : R^d -> R, a level set is defined as an inverse image f^-1(h) for an isovalue h, and a contour is a single connected component of a level set. The Reeb graph can then be defined to be the result of contracting each contour to a single point, and is well defined for Euclidean spaces or for general manifolds. For simple domains, the graph is guaranteed to be a tree, and is called the contour tree. Analysis can then be performed on the contour tree in order to identify isovalues of particular interest, based on various metrics, and render the corresponding contours, without having to know such isovalues a priori. This code is intended to be the first data-parallel algorithm for computing contour trees. Our implementation will use the portable data-parallel primitives provided by Nvidia’s Thrust library, allowing us to compile our same code for both GPUs and multi-core CPUs. Native OpenMP and purely serial versions of the code will likely also be included. It will also be extended to provide a hybrid data-parallel / distributed algorithm, allowing scaling beyond a single GPU or CPU.

Sewell, Christopher↗
DOE OSTI2017

Hybrid Parallel Contour Trees, Version 1.0

A common operation in scientific visualization is to compute and render a contour of a data set. Given a function of the form f : R^d -> R, a level set is defined as an inverse image f^-1(h) for an isovalue h, and a contour is a single connected component of a level set. The Reeb graph can then be defined to be the result of contracting each contour to a single point, and is well defined for Euclidean spaces or for general manifolds. For simple domains, the graph is guaranteed to be a tree, and is called the contour tree. Analysis can then be performed on the contour tree in order to identify isovalues of particular interest, based on various metrics, and render the corresponding contours, without having to know such isovalues a priori. This code is intended to be the first data-parallel algorithm for computing contour trees. Our implementation will use the portable data-parallel primitives provided by Nvidia’s Thrust library, allowing us to compile our same code for both GPUs and multi-core CPUs. Native OpenMP and purely serial versions of the code will likely also be included. It will also be extended to provide a hybrid data-parallel / distributed algorithm, allowing scaling beyond a single GPU or CPU.

Sewell, Christopher↗
DOE OSTI2016

Topological Methods for Visualization

This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

58 GEOSCIENCES↗