[project page]

This repo provides implementation of several advection methods mentioned in the paper.

• run_efm.py: Eulerian Flow Maps (EFM)
• run_ed8.py: 8-Point Epsilon Differnece Method
• run_ed4.py: 4-Point Epsilon Differnece Method.
• run_ge.py: Gradient Evolution Method, inspired by Gradient-Augmented Reference Maps (referred to as garm in the code)
• run_edge.py: Epsilon-Difference Gradient Evolution Method (EDGE)

The code has been tested on Windows 11 with CUDA 12.8, Python 3.9.23, and Taichi 1.7.3. Other dependencies are listed in requirement.txt.

To set up the environment, run:

conda create -n edge python=3.9
conda activate edge

pip install taichi
pip install matplotlib
pip install vtk
pip install pyevtk
pip install trimesh
pip install scipy

python run_efm.py [-c 0]

Available cases:

• case 0: Leapfrogging Vortices
• case 1: Four Vortices Collision
• case 2: Delta Wing
• case 3: Ink Torus
• case 4: Dye Drift

Results would be saved in the logs\ directory. We use ParaView for data visualization.

Note: Taichi may take a while to compile kernels. Please be patient.

If you find our work useful in your research, please consider citing:

@article{li2025edge,
title = {EDGE: Epsilon-Difference Gradient Evolution for Buffer-Free Flow Maps},
author = {Li, Zhiqi and Wang, Ruicheng and Li, Junlin and Chen, Duowen and Wang, Sinan and Zhu, Bo},
year = {2025},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {44},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/3731193},
doi = {10.1145/3731193},
journal = {ACM Trans. Graph.},
articleno = {96},
numpages = {11}
}