radiosity op• Data kinds: table → matrix
• Call: import fullseye as fs; fs.ledger.form_factor_matrix(patches, n_quad=3, symmetric=True, far_ratio=8.0) (to call the implementation directly, import radiosity3d; radiosity3d.form_factor_matrix(patches, n_quad=3, symmetric=True, far_ratio=8.0); from the registry, opsoptics.get("form_factor_matrix"))
All patch-to-patch view factors F_ij of a radiosity_patches set (occlusion by the scene's rays).
Each pair is form_factor_polygons (n_quad × n_quad Gauss points on the receiver, Lambert's contour sum to the sender) restricted to pairs that face each other; when the patches came from a scene, each Gauss point tests one ray to the sender's centre against the scene. Pairs farther apart than *far_ratio* times the larger patch's diagonal use the receiver's centroid alone (the sender is still exact); far_ratio=None integrates every pair fully. symmetric=True (default) enforces reciprocity exactly by averaging A_i F_ij and A_j F_ji (the raw values agree to the quadrature accuracy) — the progressive solver's F_ij A_i / A_j is then exactly F_ji.
Returns the (N, N) matrix (matrix), zero diagonal. In a closed enclosure each row sums to 1 (to the quadrature accuracy); an opening shows as a row sum < 1.
Raises ValueError: an empty or unmarked table (not radiosity_patches); *n_quad* not an integer in [1, 16]; *far_ratio* below 1.
Every optics op validates its input before computing (nothing slips through silently):
• Units are baked into the argument name — _mm / _um / _deg / _mrad. Confusing mm with µm does not crash; it yields a plausible-looking wrong answer, so the name prevents it. Nothing here guesses the unit from the magnitude.
• Strings raise ValueError — float('50') succeeds, so an unparsed configuration value would slip through as a length (measured: thin_lens('50', '200') returned a plausible 66.667 mm). bool is refused too, as the implicit promotion True == 1.
• complex / masked arrays raise ValueError (real-valued slots only; silently dropping the imaginary part or peeling off the mask is refused). NaN/Inf raises ValueError on every input.
• Division by zero and its relatives are refused by name: focal length 0, radius of curvature 0, refractive index <= 0, a fully opaque aperture (all zeros, so the normalisation is 0/0), a PSF whose sum is <= 0, a Stokes vector with S0 = 0, and an object sitting at the front focal point (the image is at infinity).
• Only two ops return a non-finite value, and both state it as a contract: depth_of_field returns far_mm = inf beyond the hyperfocal distance (that is what the hyperfocal distance means), and gaussian_beam returns wavefront_radius_mm = inf at the waist (the radius of curvature of a plane wavefront). Both also return a finite companion (far_is_infinite / curvature_per_mm). Any other silent NaN/Inf is detected internally and raises ValueError — "float64 overflowed" and "the answer is infinite" are different claims, so the first is never returned wearing the face of the second.
• Size caps: generated grids are capped by optics.MAX_GRID (4096); supplied fields/PSFs/apertures by optics.MAX_FIELD_ELEMENTS (2^24); ABCD element chains by optics.MAX_SYSTEM_ELEMENTS (1024); Zernike by MAX_ZERNIKE_TERMS (512) / MAX_ZERNIKE_ORDER (40) / MAX_ZERNIKE_BASIS (2^25). This closes, fail-closed, the paths where a small argument triggers a huge internal allocation (measured: n_max=40 × 4096² needs 108 GB).
• Physically impossible states are refused too: a Stokes vector with degree of polarisation > 1, negative transmittance, negative intensity, and invalid Zernike indices such as n-|m| odd.
• 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.
• poc_pocket_interreflection — py -3.11 examples/poc_pocket_interreflection.py
matrix as input)abcd_trace · emva_filter_distortion · mueller_apply · mueller_checks · pixel_shift_capture · pixel_shift_merge · pixel_shift_motion_mask · oct_from_spectra
radiosity)form_factor_parallel_rects · form_factor_perpendicular_rects · form_factor_polygons · radiosity_patches · radiosity_progressive_3d · render_optscene_gi
*Provenance: radiosity3d.py — OPTICS 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.