Rotation-Minimizing Space Deformations for the Analysis of Lagrangian Vortex Corelines

Julio Rey Ramirez, Xingdi Zhang, Markus Hadwiger and Peter Rautek

IEEE Transactions on Visualization and Computer Graphics, Vol.33, No.1 (Proceedings IEEE VIS 2026), to appear , 2027

Visualizing and verifying unsteady 3D vortex structures remains a fundamental challenge in flow visualization. While recent advancements enable the extraction of objective Lagrangian vortex corelines, visually verifying whether these candidate curves accurately represent the true center of swirling motion remains difficult. Standard visualization techniques, such as instantaneous streamlines, lack Galilean invariance and are highly dependent on the chosen frame of reference, often yielding misleading depictions. Conversely, while Lagrangian pathlines offer a physical ground truth, the local rotational component of particle motion is typically occluded by the convective motion of the flow. To address this, we propose a novel visualization technique that associates objective space-time pathlines with evolving Lagrangian corelines. Our method applies a space deformation induced by the deformation of the coreline that guarantees that no rotation component around the core’s tangent is introduced. By applying this deformation to the tubular neighborhood of the coreline, we transform pathlines into the vortex-centric reference frame, effectively decoupling the local swirl of particles from the global drift and deformation. A primary application of this technique is the visual evaluation of vortex coreline candidates. By explicitly visualizing inversely transformed pathlines in context with the coreline curves, we directly reveal the swirling motion of the surrounding particles. Because this swirling motion is the physical ground truth for validating a vortex coreline, our method provides the first pathline-based visual assessment of candidate curves. We demonstrate our approach on multiple unsteady 3D flow datasets and methods for coreline extraction, revealing vortex-relative particle dynamics that are otherwise hidden by bulk transport.

@article{Rey2026RotationMinimizingSpaceDeformations,
  title = {Rotation-Minimizing Space Deformations for the Analysis of Lagrangian Vortex Corelines},
  author = {Rey Ramirez, Julio and Zhang, Xingdi and Hadwiger, Markus and Rautek, Peter},
  journal = {IEEE Transactions on Visualization and Computer Graphics (Proceedings IEEE VIS 2026)},
  year = {2027},
  volume = {33},
  number = {1},
  pages = {to appear}
}