Tetrahedron-Tetrahedron Intersection and Volume Computation Using Neural Networks
Loading...
Date
2026
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
Narrow-phase collision detection is a critical bottleneck in physics-based simulation, traditionally relying on exact but sequential CPU-bound algorithms that struggle to exploit massive GPU parallelism. In this work, we reframe the tetrahedron-tetrahedron intersection as a learned inference problem. We leverage principles of hierarchical permutation invariance—derived from DeepSets and PointNet—to construct a neural architecture that jointly predicts intersection status and volumetric overlap directly from vertex coordinates. We generate a large dataset of 12 million pairs covering five distinct tetrahedron pair configurations, ensuring the model learns robust geometric decision boundaries. Our most accurate model achieves 99.3% mean classification accuracy across five contact configurations and predicts overlap volume with MAE ≈ 2.88×10−3 (for positive volumes) while remaining entirely GPU-resident. On consumer-grade GPU, our pipeline outperforms the exact CGAL library by 93× in detection speed and over 16,821× when volume computation is included. This “volume-for-free” paradigm offers a transformative trade-off for real-time applications where approximate is acceptable but ultra-fast geometric reasoning is paramount.
Description
@inproceedings{10.2312:egs.20261016,
booktitle = {Eurographics 2026 - Short Papers},
editor = {Musialski, Przemyslaw and Lim, Isaak},
title = {{Tetrahedron-Tetrahedron Intersection and Volume Computation Using Neural Networks}},
author = {Pedro, Erendiro and Meißenhelter, Hermann and Zachmann, Gabriel},
year = {2026},
publisher = {The Eurographics Association},
ISSN = {2309-5059},
ISBN = {978-3-03868-299-8},
DOI = {10.2312/egs.20261016}
}