Featurizing Relative Positioning of Isosurface Components from Two Scalar Fields
Abstract
When analyzing multiple scalar fields (known as multi-fields), relative positioning of isosurface components can be of interest, e.g. when a warm region in the air causes cloud formation above it. Exploring relative positions, however, introduces a challenge in parameter tuning, in the sense that the combinations of isovalues for the scalar fields amount to an enormous number. To overcome this issue, we propose to summarize the relative positioning as a feature associated with the space of combinations of isosurface components, by turning this information into a novel partitioning of the recently proposed Reeb product. As a starting point, the present work considers a simple case, where there are only two scalar fields. The partitioning becomes what we call phase diagrams, whose horizontal and vertical axes correspond to the two isovalues. The phase diagrams are indeed similar to liquid-gas-solid phase diagrams used in the study of physics. In each partition, the relative positioning of isosurfaces are equivalent, and by moving from one partition to another, there is a phase change, where the relative positioning changes – a temperature isosurface component above a cloud changes its position relatively downwards to lie below it, say. Although a similar concept of phase diagram, called the Reeb complement, has appeared in a separate work, it captured a different feature in the data. There, the partitions captured how isosurface component lied another (and without regard to their geometrical coordinates). In other words, the present work captures a different feature from the data, and doing so required a novel algorithm. While we define the location of an isosurface component using the centroid, the definition can be customized by the user to depending on the use cases.