Interactive Visualization for Singular Fibers of Functions f: R3 → R2

Daisuke Sakurai, Osamu Saeki, Hamish Carr, Hsiang Yun Wu, Takahiro Yamamoto, David Duke, Shigeo Takahashi

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Article number7192700
Pages (from-to)945-954
Number of pages10
JournalIEEE Transactions on Visualization and Computer Graphics
Volume22
Issue number1
DOIs
Publication statusPublished - Jan 31 2016

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

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