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


Scalar topology in the form of Morse theory has provided computational tools that analyze and visualize information from scientific and engineering tasks. Contracting isocontours to single points encapsulates variations in isocontour connectivity in the Reeb graph. For multivariate information, isocontours generalize to fibers—inverse images of points in the vary, and this space is therefore known as fiber topology. However, fiber topology is less totally developed than Morse theory, and current efforts depend upon manual visualizations. This paper presents a way 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 additionally introduces a 3D read based mostly on the extension of Reeb graphs to Reeb spaces. Using the Joint Contour Web, a quantized approximation of the Reeb area, this accelerates topological visualization and permits online perturbation to scale back or remove degeneracies in functions below study. Validation of the interface is performed by assessing whether or not the interface supports the mathematical workflow each of specialists and of less experienced mathematicians.

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