Topological Subdivision Graphs for Comparative and Multifield Visualization

Title	Topological Subdivision Graphs for Comparative and Multifield Visualization
Publication Type	Conference Paper
Year of Publication	2020
Authors	Heine, Christian, and Garth Christoph
Editor	Carr, Hamish, Fujishiro Issei, Sadlo Filip, and Takahashi Shigeo
Conference Name	Topological Methods in Data Analysis and Visualization V
Publisher	Springer International Publishing
Conference Location	Cham
ISBN Number	978-3-030-43036-8
Abstract	We propose that a topological model of a real-valued function can be employed to define a spatial subdivision of the function's domain. When multiple topologically-induced subdivisions for the same or different functions on the same domain are combined, a finer spatial subdivision arises: the topological subdivision complex. The topological subdivision graph then gives adjacency relations among the d-cells of the subdivision complex and can be used to describe similarities among topological models. We apply this idea to give new topological models for multiple real-valued functions (multifields), extending contour trees and Morse-Smale complexes to these problem settings, and we illustrate our idea for piecewise-linear functions. We also discuss how our work relates to joint contour nets.

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