lattice opなし → table(引数だけで決まる op —— 画像やデータの入力を取らない)import fullseye as fs; fs.ledger.fly_vogel_lattice(radius=15, dphi_deg=4.63, az0_deg=0.0, el0_deg=0.0, density_power=0.5, angle_deg=np.float64(137.50776405003785)) (実装を直接呼ぶなら import flyvision; flyvision.fly_vogel_lattice(radius=15, dphi_deg=4.63, az0_deg=0.0, el0_deg=0.0, density_power=0.5, angle_deg=np.float64(137.50776405003785))、台帳から引くなら opsflyvision.get("fly_vogel_lattice"))A Fibonacci (Vogel-spiral) compound eye: the same ommatidia count and the same mean spacing as the hexagonal eye, no lattice at all.
Point k sits at the angular radius rho_k = rho_max ((k + 1/2)/n)^p from
the optical axis and at the position angle k * angle_deg around it — the
arrangement of sunflower florets (Vogel 1979), here on the sphere. The
ommatidia count is the hexagon’s n = 3 radius (radius + 1) + 1 and
rho_max is solved so that the mean nearest-neighbour angle equals
dphi_deg, which makes the two eyes directly comparable: same number of
samples, same average density, and only the arrangement differs. The
reciprocal of a hexagonal lattice is six sharp points, so a texture past its
Nyquist limit folds into one sharp false stripe (moire); the Vogel spiral
has no reciprocal lattice, so the same texture folds into a ring of weak
noise — the question the zebra PoC asks is which an eye would rather have.
radius / dphi_deg / az0_deg / el0_deg: as :func:fly_hex_lattice.
density_power: p in (0, 1]. 0.5 is uniform density; above it the
centre is denser (a fovea / acute zone: density ∝ k^(1 - 2p)), below it
the rim is.
angle_deg: the divergence angle, the golden angle by default.
Returns a lattice dict with the keys of :func:fly_hex_lattice — "uv"
holds (k, 0), the spiral index, so (0, 0) is still the ommatidium
nearest the axis — plus "geometry": "vogel", "rho_rad" (the angular
radius of each ommatidium), "nn_rad" (its nearest-neighbour angle) and
"density_power". The ops that need a hexagonal neighbour
(:func:fly_t4t5_field, :func:fly_flow_from_directions) refuse it; the
ops that need only directions (:func:fly_view_plane_texture,
:func:fly_expansion_readout, :func:lattice_moire_peak,
:func:fly_matched_filter, :func:fly_egomotion_from_flow) take it.
Ground truth (pinned in the tests): n == 3 radius (radius + 1) + 1, every
direction is a unit vector, mean(nn_rad) == dphi to 1e-6, the
coefficient of variation of the nearest-neighbour angle at p = 0.5 is
0.012 (below 0.03; a hexagon’s is 0, and p = 0.65 gives 0.14), and the
Delaunay triangulation of the gnomonic projection has a mean degree within
0.5 of 6 (5.85 for 721 ommatidia; the deficit is the rim).
Raises ValueError: a radius outside [2, MAX_LATTICE_RADIUS], a
non-positive dphi_deg, a density_power outside (0, 1], a non-finite
angle, and a divergence angle that is a multiple of 360 (all points on one
ray).
py -3.11 examples/poc_print_registration.pypy -3.11 examples/poc_zebra_stripes_fly_eye.pytable を入力に取れる)fly_t4t5_field · fly_flow_from_directions · fly_matched_filter · fly_egomotion_from_flow · fly_eye_merge · fly_view_plane_texture · fly_hex_resample · fly_expansion_readout
lattice)Provenance: flyvision.py — FLYVISION operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.