Lagrangian Simulation Volume-Based Contour Tree Simplification

TL;DR

This paper introduces a novel volume-based contour tree simplification method for parcel-in-cell simulations, significantly improving efficiency and quality over traditional grid-based approaches by leveraging Delaunay tetrahedralization and hypersweep parallelization.

Contribution

It extends volume-based contour tree simplification to parcel data using Delaunay tetrahedralization and hypersweep parallelization, avoiding resampling artifacts and enhancing computational efficiency.

Findings

Contour trees on parcels are much faster to compute than on resampled grids.

The method improves segmentation quality by avoiding interpolation artifacts.

Parallel implementation achieves high efficiency in processing large datasets.

Abstract

Many scientific and engineering problems are modelled by simulating scalar fields defined either on space-filling meshes (Eulerian) or as particles (Lagrangian). For analysis and visualization, topological primitives such as contour trees can be used, but these often need simplification to filter out small-scale features. For parcel-based convective cloud simulations, simplification of the contour tree requires a volumetric measure rather than persistence. Unlike for cubic meshes, volume cannot be approximated by counting regular vertices. Typically, this is addressed by resampling irregular data onto a uniform grid. Unfortunately, the spatial proximity of parcels requires a high sampling frequency, resulting in a massive increase in data size for processing. We therefore extend volume-based contour tree simplification to parcel-in-cell simulations with a graph adaptor in Viskores (VTK-m), using Delaunay tetrahedralization of the parcel centroids as input. Instead of relying on a volume approximation by counting regular vertices -- as was done for cubic meshes -- we adapt the 2D area splines reported by Bajaj et al. 10.1145/259081.259279, and Zhou et al. 10.1109/TVCG.2018.2796555. We implement this in Viskores (formerly called VTK-m) as prefix-sum style hypersweeps for parallel efficiency and show how it can be generalized to compute any integrable property. Finally, our results reveal that contour trees computed directly on the parcels are orders of magnitude faster than computing them on a resampled grid, while also arguably offering better quality segmentation, avoiding interpolation artifacts.