radiosity op• Data kinds: table × signal → table
• Call: import fullseye as fs; fs.ledger.radiosity_progressive_3d(patches, emission, form_factors=None, albedo=None, tol=1e-06, max_shots=None, n_quad=3) (to call the implementation directly, import radiosity3d; radiosity3d.radiosity_progressive_3d(patches, emission, form_factors=None, albedo=None, tol=1e-06, max_shots=None, n_quad=3); from the registry, opsoptics.get("radiosity_progressive_3d"))
Progressive-refinement radiosity (Cohen et al. 1988, shooting, eqs. 7–8) on a 3-D patch set, with the evidence that it converged.
Solves B = E + diag(ρ) F̃ B (F̃_ji = F_ij A_i/A_j, eq. 8) by shooting: all patches start with B = ΔB = E (the emitted, or first-reflected, radiosity); repeatedly the patch with the largest unshot energy ΔB_i A_i shoots — every patch j gains ΔRad = ρ_j ΔB_i F_ij A_i/A_j in both B_j and ΔB_j — and its ΔB_i is reset to 0. Ties (equal after rounding to 1e-12 relative) go to the lower index; nothing is random.
Stopping rule — our choice, not Cohen's: the paper stops "when the solution converges to within the desired tolerance" without a number. Here the shooting stops when the residual unshot energy Σ ΔB_i A_i falls to tol times the initial energy Σ E_i A_i (a bound on the energy still missing from the solution). max_shots (default 200 × N) caps the work; hitting it returns converged=False.
*emission* E is (N,) or (N, C) (C colour channels), non-negative. *albedo* defaults to the patches' (RGB when *emission* has 3 channels, else the channel mean). *form_factors* defaults to form_factor_matrix (n_quad).
Returns a dict (table) with kind = "rad_solution", radiosity (N, C), unshot_history (the residual energy before each shot), n_shots, converged, tol, residual_energy (relative), initial_energy and the stop_rule text.
Raises ValueError: an empty or unmarked table (not radiosity_patches); emission or albedo of the wrong shape, negative or non-finite; an albedo outside [0, 1]; *tol* not in (0, 1]; a form-factor matrix of the wrong shape. (An albedo of 1 in a closed enclosure never loses energy: the shooting then stops at *max_shots* with converged=False instead of raising.)
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
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
radiosity)form_factor_parallel_rects · form_factor_perpendicular_rects · form_factor_polygons · radiosity_patches · form_factor_matrix · 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.