reflectance op• Datenarten: normalmap → image2d
• Aufruf: import specularity; specularity.brdf_microfacet(normals, light=(0.0, 0.0, 1.0), view=(0.0, 0.0, 1.0), roughness=0.3, f0=0.04) (oder opsspecular.get("brdf_microfacet"))
GGX-/Trowbridge-Reitz-Mikrofacetten-BRDF für Glanz. → (H, W), Einheit 1/sr.
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
`f_s = D * G * F / (4 (n.l) (n.v))` with
• `D` the Trowbridge-Reitz (1975) / GGX normal distribution,
`a^2 / (pi * ((n.h)^2 (a^2 - 1) + 1)^2) for a = roughness^2`, which
integrates to 1 against `(n.h) dw` over the hemisphere — measured by
20000-point midpoint quadrature in `tests/test_specularity.py` at
relative errors 3.2e-07, 6.3e-08 and 4.0e-09 for roughness 0.2, 0.3 and
0.6, all of it quadrature error (the 200000-point rule gives 3.2e-09,
6.3e-10, 4.0e-11, exactly the 100x a midpoint rule predicts);
• `G` the separable Smith (1967) masking-shadowing term with the GGX
lambda;
• `F` Schlick's (1994) Fresnel approximation,
`f0 + (1 - f0) (1 - v.h)^5`. *f0* is the normal-incidence reflectance:
about 0.04 for common dielectrics, 0.5 to 1.0 for metals. When the exact
Fresnel curve matters, use `match3d.fresnel_reflectance` instead — this
is the approximation the microfacet literature specifies, and it is named
rather than hidden.
Exact ground truth it reproduces: at normal incidence with light, view and
normal aligned, every geometric factor is 1 and the value collapses to
`f0 / (4 pi roughness^4)` in closed form — reproduced bit for bit at
roughness 0.3, 0.5 and 1.0 and to 3.3e-16 relative at roughness 0.1, which
took rewriting the GGX denominator to avoid a cancellation (see the comment
at the code; the textbook arrangement was off by 2.2e-13 relative at the
peak). The lobe is reciprocal in light and view to machine precision
(measured 1.7e-16), and its maximum sits at the half-vector.
`roughness` is the perceptual parameter, squared once to reach the GGX
`alpha` — the convention that makes a linear slider feel linear. A
perfectly smooth surface (`roughness = 0`) is a delta function, not a
finite BRDF, so it is refused rather than returned as an infinity.
Raises `ValueError`: geometry problems as in
:func:brdf_blinn_phong; *roughness* outside `(0, 1]`; *f0* outside
`[0, 1]`.
• Leitfaden zur Familie specular_photometric
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• specular_photometric — py -3.11 examples/specular_photometric.py
image2d als Eingabe)reflectance)brdf_blinn_phong · dichromatic_render
*Provenance: specularity.py — SPECULAR Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.