fullseye

brdf_microfacet — SPECULAR reflectance op

• データ種: normalmap → image2d
• 呼び出し: import fullseye as fs; fs.ledger.brdf_microfacet(normals, light=(0.0, 0.0, 1.0), view=(0.0, 0.0, 1.0), roughness=0.3, f0=0.04) (実装を直接呼ぶなら 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)、台帳から引くなら opsspecular.get("brdf_microfacet"))

使い方

GGX / Trowbridge-Reitz microfacet specular BRDF. → (H, W), units 1/sr.

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].

詳しい使い方ガイド

• specular_photometric ファミリ ガイド

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• poc_solder_fillet_aoi — py -3.11 examples/poc_solder_fillet_aoi.py
• specular_photometric — py -3.11 examples/specular_photometric.py

型が繋がる次の op(image2d を入力に取れる)

polarization_render

同カテゴリ(reflectance)

brdf_blinn_phong · dichromatic_render

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Provenance: specularity.py — SPECULAR operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.

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