Interactive visualization for singular fibers of functions :

Sakurai, Daisuke; Saeki, Osamu*; Carr, H.*; Wu, H.-Y.*; Yamamoto, Takahiro*; Duke, D.*; Takahashi, Shigeo*

IEEE Transactions on Visualization and Computer Graphics, 22(1), p.945 - 954, 2016/01

https://doi.org/10.1109/TVCG.2015.2467433

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 therefore shows how to accelerate and semi-automate this task through an interface for visualizing fiber singularities of multivariate functions : . This interface exploits existing conventions of fiber topology, but also introduces a 3D view based on the extension of Reeb graphs to Reeb spaces. Validation of the interface is performed by assessing whether the interface supports the mathematical workflow both of experts and of less experienced mathematicians.