Given a continuous scalar field ƒ: X → where X is a topological space, a level set of ƒ is a set {x ∈ X : ƒ (x) = α} for some value α ∈ IR. The level sets of ƒ can be subdivided into connected components. As α changes continuously, the connected components in the level sets appear, disappear, split and merge. The Reeb graph of ƒ encodes these changes in connected components of level sets. It provides a simple yet meaningful abstraction of the input domain. As such, it has been used in a range of applications in fields such as graphics and scientific visualization.

Abstract Visual representation techniques enable perception and exploration of scientific data. Following the topological landscapes metaphor of Weber et al., we provide a new algorithm for visualizing scalar functions defined on simply connected domains of arbitrary dimension. For a potentially high dimensional scalar field, our algorithm produces a collection of, in some sense complete, two‐dimensional terrain models whose contour trees and corresponding topological persistences are identical to those of the input scalar field. The algorithm exactly preserves the volume of each region corresponding to an arc in the contour tree. We also introduce an efficiently computable metric on terrain models we generate. Based on this metric, we develop a tool that can help the users to explore the space of possible terrain models.