Sakurai, D, Saeki, O, Carr, H et al. (4 more authors) (2016) Interactive Visualization for Singular Fibers of Functions f : R3 → R2. IEEE Transactions on Visualization and Computer Graphics, 22 (1). pp. 945-954. ISSN 1077-2626
Abstract
Scalar topology in the form of Morse theory has provided computational tools that analyze and visualize data from scientific and engineering tasks. Contracting isocontours to single points encapsulates variations in isocontour connectivity in the Reeb graph. For multivariate data, isocontours generalize to fibers—inverse images of points in the range, and this area is therefore known as fiber topology. However, fiber topology is less fully developed than Morse theory, and current efforts rely on manual visualizations.
This paper presents how to accelerate and semi-automate this task through an interface for visualizing fiber singularities of multivariate functions R3 → R2. This interface exploits existing conventions of fiber topology, but also introduces a 3D view based on the extension of Reeb graphs to Reeb spaces. Using the Joint Contour Net, a quantized approximation of the Reeb space, this accelerates topological visualization and permits online perturbation to reduce or remove degeneracies in functions under study. Validation of the interface is performed by assessing whether the interface supports the mathematical workflow both of experts and of less experienced mathematicians.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2015, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
Keywords: | singular fibers; fiber topology; mathematical visualization; design study |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/J013072/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Oct 2015 09:07 |
Last Modified: | 03 Mar 2020 16:44 |
Published Version: | http://dx.doi.org/10.1109/TVCG.2015.2467433 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers |
Identification Number: | 10.1109/TVCG.2015.2467433 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:88921 |