TY - JOUR

T1 - Time-Dependent Flow seen through Approximate Observer Killing Fields

AU - Hadwiger, Markus

AU - Mlejnek, Matej

AU - Theusl, Thomas

AU - Rautek, Peter

N1 - KAUST Repository Item: Exported on 2021-02-19
Acknowledgements: We thank Anna Fruhstuck for the illustrations and for help with the figures and the video, Holger Theisel for helpful discussions, and the anonymous reviewers for helpful comments. This work was supported by King Abdullah University of Science and Technology (KAUST). This research used resources of the Core Labs of King Abdullah University of Science and Technology (KAUST). See App. I (supplementary material) for data set acknowledgments.

PY - 2018/8/20

Y1 - 2018/8/20

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/628778

UR - https://ieeexplore.ieee.org/document/8440037

UR - http://www.scopus.com/inward/record.url?scp=85051767175&partnerID=8YFLogxK

U2 - 10.1109/TVCG.2018.2864839

DO - 10.1109/TVCG.2018.2864839

M3 - Article

AN - SCOPUS:85051767175

SN - 1077-2626

VL - 25

SP - 1257

EP - 1266

JO - IEEE Transactions on Visualization and Computer Graphics

JF - IEEE Transactions on Visualization and Computer Graphics

IS - 1

ER -