lattice op• Data kinds: कोई नहीं → table (केवल arguments से तय होने वाला op — यह कोई image या data input नहीं लेता)
• Call: 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)) (implementation को सीधे call करना हो तो 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)), registry से लेना हो तो opsflyvision.get("fly_vogel_lattice"))
Fibonacci (Vogel spiral) compound eye — hexagonal आँख जितनी ही ommatidia और औसत दूरी, पर कोई lattice नहीं।
> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।
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 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 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* (fly_t4t5_field, fly_flow_from_directions) refuse it; the ops that need only directions (fly_view_plane_texture, fly_expansion_readout, lattice_moire_peak, fly_matched_filter, 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).
• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।
• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।
• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।
• poc_print_registration — py -3.11 examples/poc_print_registration.py
• poc_zebra_stripes_fly_eye — py -3.11 examples/poc_zebra_stripes_fly_eye.py
table को input के रूप में लेते हैं)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. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.