Topological Subdivision Graphs for Comparative and Multifield Visualization

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.