radiosity op• Data kinds: points × points → measurement
• Call: import fullseye as fs; fs.ledger.form_factor_polygons(poly_i, poly_j, n_quad=8, occluders=None) (to call the implementation directly, import radiosity3d; radiosity3d.form_factor_polygons(poly_i, poly_j, n_quad=8, occluders=None); from the registry, opsoptics.get("form_factor_polygons"))
View factor F_ij between two flat convex polygons (triangles or quads) in 3-D, numerically.
F_ij = (1/A_i) ∫_{A_i} F_{dA→A_j} dA: the inner factor from a point to the polygon j is Lambert's closed contour sum (1/2π) Σ_k n·Γ_k (exact, no quadrature), the outer integral over i an n_quad × n_quad Gauss–Legendre rule on the (bilinearly mapped) polygon. A polygon that straddles the receiver's plane is integrated by points with the cosine clipped at 0 instead. Each polygon is (3, 3) or (4, 3) vertices (x, y, z) in order around its edge; the sides that face each other count (the vertex order does not matter).
*occluders* is None (nothing in between — true inside a convex cavity) or an optscene scene (list of scene_* dicts): each quadrature point is then tested with one ray to the centre of j.
Gates: Howell's C-11 (0.199825) and C-14 (0.200044) to the quadrature accuracy, reciprocity A_i F_ij = A_j F_ji.
Returns F_ij (measurement).
Raises ValueError: an empty polygon, or one that is not (3|4, 3), non-finite, degenerate, non-planar or non-convex; *n_quad* not an integer in [1, 64]; *occluders* that are not optscene primitives.
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
measurement as input)—
radiosity)form_factor_parallel_rects · form_factor_perpendicular_rects · radiosity_patches · form_factor_matrix · 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.