Exploring 3D Unsteady Flow using 6D Observer Space Interactions

Xingdi Zhang, Amani Ageeli, Thomas Theußl, Markus Hadwiger and Peter Rautek

IEEE Transactions on Visualization and Computer Graphics, Vol.32, No.1 (Proceedings IEEE VIS 2025), to appear , 2026

Visualizing and analyzing 3D unsteady flow fields is a very challenging task. We approach this problem by leveraging the mathematical foundations of 3D observer fields to explore and analyze 3D flows in reference frames that are more suitable to visual analysis than the input reference frame. We design novel interactive tools for determining, filtering, and combining reference frames for observer-aware 3D unsteady flow visualization. We represent the space of reference frame motions in a 3D spatial domain via a 6D parameter space, in which every observer is a time-dependent curve. Our framework supports operations in this 6D observer space by separately focusing on two 3D subspaces, for 3D translations, and 3D rotations, respectively. We show that this approach facilitates a variety of interactions with 3D flow fields. Building on the interactive selection of observers, we furthermore introduce novel techniques such as observer-aware streamline- and pathline-filtering as well as observer-aware isosurface animations of scalar fluid properties for the enhanced visualization and analysis of 3D unsteady flows. We discuss the theoretical underpinnings as well as practical implementation considerations of our approach, and demonstrate the benefits of its 6+1D observer-based methodology on several 3D unsteady flow datasets.

@article{Zhang2025ObserverSpaces,
  title = {Exploring 3D Unsteady Flow using 6D Observer Space Interactions},
  author = {Zhang, Xingdi and Ageeli, Amani and Theu{\ss}l, Thomas and Hadwiger, Markus and Rautek, Peter},
  journal = {IEEE Transactions on Visualization and Computer Graphics (Proceedings IEEE VIS 2025)},
  year = {2026},
  volume = {32},
  number = {1},
  pages = {to appear}
}