field op• Data kinds: flow2d → image2d
• Call: import fullseye as fs; fs.ledger.piv_q_criterion(flow, spacing=1.0) (to call the implementation directly, import pivops; pivops.piv_q_criterion(flow, spacing=1.0); from the registry, opspiv.get("piv_q_criterion"))
Q criterion -tr(J^2)/2. It is positive where rotation exceeds strain.
Looking at vorticity alone, shear layers light up too (the near-wall region of a laminar flow looks like a vortex), so for extracting vortices use this. Closed form (measured with analytic fields given directly):
• rigid-body rotation ω=0.01 → +1.0e-4 (= ω^2)
• uniform expansion s=0.01 → -1.0e-4 (= -s^2)
• simple shear g=0.02 → 0.0 (shear is not a vortex is the point)
★ It is a quantity that requires a threshold. Q > 0 alone picks up even faint regions, so a vortex visualisation that does not state how the threshold was chosen hides the possibility that the beauty of the picture is a product of the threshold. Report the change in area when the threshold is varied alongside.
• piv_displacement family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• piv_field_analysis_tour — py -3.11 examples/piv_field_analysis_tour.py
image2d as input)piv_cross_correlate · piv_multipass · piv_deform_pass · strain_from_displacement · correlation_quality · speckle_quality
field)piv_vorticity · piv_divergence · piv_flow_magnitude · piv_to_velocity · piv_velocity_gradient · piv_swirling_strength · piv_strain_rate
*Provenance: pivops.py — PIV operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.