## Abstract

Flow fields are usually visualized relative to a global observer, i.e., a single frame of reference. However, often no global frame can depict all flow features equally well. Likewise, objective criteria for detecting features such as vortices often use either a global reference frame, or compute a separate frame for each point in space and time. We propose the first general framework that enables choosing a smooth trade-off between these two extremes. Using global optimization to minimize specific differential geometric properties, we compute a time-dependent observer velocity field that describes the motion of a continuous field of observers adapted to the input flow. This requires developing the novel notion of an observed time derivative. While individual observers are restricted to rigid motions, overall we compute an approximate Killing field, corresponding to almost-rigid motion. This enables continuous transitions between different observers. Instead of focusing only on flow features, we furthermore develop a novel general notion of visualizing how all observers jointly perceive the input field. This in fact requires introducing the concept of an observation time, with respect to which a visualization is computed. We develop the corresponding notions of observed stream, path, streak, and time lines. For efficiency, these characteristic curves can be computed using standard approaches, by first transforming the input field accordingly. Finally, we prove that the input flow perceived by the observer field is objective. This makes derived flow features, such as vortices, objective as well.

Original language | English (US) |
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Article number | 8440037 |

Pages (from-to) | 1257-1266 |

Number of pages | 10 |

Journal | IEEE Transactions on Visualization and Computer Graphics |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2019 |

### Bibliographical note

Publisher Copyright:© 2018 IEEE.

## Keywords

- Flow visualization
- Killing vector fields
- Lie derivatives
- infinitesimal isometries
- objectivity
- observer frames of reference

## ASJC Scopus subject areas

- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Computer Graphics and Computer-Aided Design