Authors: Wenbin He, Hanqi Guo, Han-Wei Shen, and Tom Peterka
Abstract: We propose surface density estimate (SDE) to model the spatial distribution of surface features—isosurfaces, ridge surfaces, and streamsurfaces—in 3D ensemble simulation data. The inputs of SDE computation are surfaces represented as polygon meshes, and no field datasets are required. The SDE is defined as the kernel density estimate of the infinite set of points on the input surfaces and is approximated by accumulating the surface densities of triangular patches. We also propose an algorithm to guide the selection of a proper kernel bandwidth for SDE computation. An ensemble Feature Exploration method based on Surface densiTy EstimAtes (eFESTA) is then proposed to extract and visualize the major trends of ensemble surface features. For an ensemble of surface features, each surface is first transformed into a density field based on its contribution to the SDE, and the resulting density fields are organized into a hierarchical representation based on the pairwise distances between them. The hierarchical representation is then used to guide visual exploration of the density fields as well as the underlying surface features. We demonstrate the application of our method using isosurface in ensemble scalar fields, Lagrangian coherent structures in uncertain unsteady flows, and streamsurfaces in ensemble fluid flows.