radiosity op• Data kinds: none → measurement (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.form_factor_perpendicular_rects(h=1.0, w=1.0, length=1.0) (to call the implementation directly, import radiosity3d; radiosity3d.form_factor_perpendicular_rects(h=1.0, w=1.0, length=1.0); from the registry, opsoptics.get("form_factor_perpendicular_rects"))
View factor from a rectangle w × l to a rectangle h × l sharing the edge of length l at 90° (Howell's catalogue C-14, closed form).
With H = h/l and W = w/l (surface 1 is the w side, surface 2 the h
side)::
F_12 = 1/(π W) ( W atan(1/W) + H atan(1/H) − √(H²+W²) atan(1/√(H²+W²))
+ ¼ ln{ (1+W²)(1+H²)/(1+W²+H²)
· [W²(1+W²+H²)/((1+W²)(W²+H²))]^(W²)
· [H²(1+H²+W²)/((1+H²)(H²+W²))]^(H²) } )
H = W = 1 (two unit squares on a common edge) gives 0.200044. Reciprocity:
w F_12 = h F_21 (form_factor_perpendicular_rects(w, h, l) is F_21).
Returns the view factor F_12 (measurement).
Raises ValueError: a non-positive or non-finite length.
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_polygons · 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.