@conference {939,
	title = {Topological Subdivision Graphs for Comparative and Multifield Visualization},
	booktitle = {Topological Methods in Data Analysis and Visualization V},
	year = {2020},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {We propose that a topological model of a real-valued function can be employed to define a spatial subdivision of the function{\textquoteright}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.},
	isbn = {978-3-030-43036-8},
	author = {Heine, Christian and Garth, Christoph},
	editor = {Carr, Hamish and Fujishiro, Issei and Sadlo, Filip and Takahashi, Shigeo}
}
