Lagrangian Simulation Volume-Based Contour Tree Simplification

2025-08-19

AI Summary

To address the problem of data inflation and interpolation errors caused by remeshing in topological analysis of scalar fields for Lagrangian particle simulations, this paper proposes a volume-driven contour tree simplification method tailored to unstructured particle data. Our approach constructs a topological carrier via Delaunay tetrahedralization and generalizes the conventional area-based metric to a volume-based metric for arbitrary integrable attributes—enabling direct simplification without remeshing for the first time. Leveraging the VTK-m graph adapter and a prefix-sum–style parallel hyperscan algorithm, we achieve efficient and scalable attribute computation. Experiments demonstrate that our method constructs and simplifies contour trees on particle data orders of magnitude faster than traditional remeshing-based approaches, while achieving higher segmentation accuracy. This significantly improves both the efficiency and reliability of multiscale structure extraction—e.g., convective clouds—in particle-based simulations.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Segmentation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Extends volume-based contour tree simplification to Lagrangian particle simulations
• Avoids data explosion from resampling irregular parcel data to uniform grids
• Enables direct topological analysis on particle data without interpolation artifacts

Innovation

• Delaunay tetrahedralization for parcel centroids
• Adapted 2D area splines for volume approximation
• Parallel hypersweeps for integrable property computation