appearance op• Data kinds: normalmap → image2d
• Call: import matappear; matappear.ward_anisotropic(normals, light=(0.0, 0.0, 1.0), view=(0.0, 0.0, 1.0), tangent=(1.0, 0.0, 0.0), alpha_x=0.3, alpha_y=0.03) -> 'np.ndarray' (or opsoptics.get("ward_anisotropic"))
Ward's anisotropic reflection (an elliptical-Gaussian microfacet). The stretched highlight of a hairline finish.
> The detailed description below is the original text — the summary and the headings are translated.
normals: (H, W, 3) 法線マップ。
light / view: 面から光源 / 視点への方向(3,)。
tangent: 研磨の筋の方向(3,)。面内へ射影して使う。
alpha_x / alpha_y: 筋方向 / 直交方向の粗さ。この比がハイライトの伸びになる
(等方なら円、alpha_x >> alpha_y なら筋に沿って伸びた線)。
返り値: (H, W) の鏡面反射強度(非負)。背景は 0。
式: ρ = exp(−tan²δ·(cos²φ/αx² + sin²φ/αy²)) / (4π αx αy √(cosθi cosθo)) で、
δ はハーフベクトルと法線の角、φ は接線からの方位角(Ward 1992)。
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.
• colorimetry — 測色と分光の知識 — 色は「分光 × 光源 × 観測者」でしか決まらない
• mv_illumination_practice — 照明の実務知識 — 波長・偏光・点灯方式・外光・安全
• 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.
• appearance_structural_colour — py -3.11 examples/appearance_structural_colour.py
image2d as input)fraunhofer_pattern · psf_to_mtf · illumination_uniformity · render_through_lens · surface_defect · defocus_blur
appearance)cie_xyz_from_wavelength · spectrum_to_srgb · thin_film_reflectance · grating_wavelengths · grating_rgb · thin_film_rgb
*Provenance: matappear.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.