Mesh distance for dimension reduction and visualization of numerical simulation data

Abstract

Computational modeling frequently generates sets of related simulation runs, known as ensembles. These simulations often output 3D surface mesh data, where the geometry and variable values of the mesh are changing with each time step. Comparing these ensembles depends on comparing not only geometric properties, but also associated field data. In this paper, we propose a new metric for comparing mesh geometry combined with field data variables. Our measure is a generalization of the well-known Metro algorithm used in mesh simplification. The Metro algorithm can compare two meshes but doesn't consider field variables. Our metric evaluates a single variable in combination with the mesh geometry. Combining our metric with multidimensional scaling, we visualize a low dimensional representation of all the time steps from a set of example ensembles to demonstrate the effectiveness of this approach.