Geometry and Topology Seminar: Interactive Visualization for Singular Fibers of Functions f : R^3 -> R^2.
11 February 2016 13:00 in CM221
Scalar topology in the form of Morse theory has provided computational tools that analyze and visualize data from sci-entific 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 visualiza-tions. 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. Val-idation of the interface is performed by assessing whether the interface supports the mathematical workflow both of experts and of less experienced mathematicians.