Visualizing 2D scalar fields with hierarchical topology

This paper describes an effort to create new visualizations by exploiting hierarchical scalar topology. First, we build a hierarchical topology through synchronously constructing and simplifying Contour Tree (CT) and Morse-Smale (MS) complex of scalar fields. We then introduce three algorithms based on the hierarchical topology: (1) topology-based multi-resolution contouring - an overview provided for a scalar field by extracting iso-values from the simplified CT and tracing approximate contours across the MS complex cells; (2) topology based spaghetti plots for uncertainty - a seeding scheme based on the hierarchical topology for visualizing uncertainty among ensemble scalar data; (3) virtual ribbons - a new scheme for visualizing multivariate data invented by overlapping visual ribbons which encode the scalar variation of a region covered by uniform contours. We compare the new approaches with current alternatives.