radiosity op• 資料種類:table × table × table → table
• 呼叫: import fullseye as fs; fs.ledger.render_optscene_gi(scene, camera, lights, bounces=None, patch_mm=2.0, outer_mm=None, tol=1e-06, n_quad=3, supersample=1, study_bounces=8, study_tol=0.01)(要直接呼叫實作,import radiosity3d; radiosity3d.render_optscene_gi(scene, camera, lights, bounces=None, patch_mm=2.0, outer_mm=None, tol=1e-06, n_quad=3, supersample=1, study_bounces=8, study_tol=0.01);從台帳取用則 opsoptics.get("render_optscene_gi"))
含相互反射的檢測用渲染:在 render_optscene 的光度之上加上朗伯面片之間的 n 次反射(或收斂解)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The same scene (optscene.scene_*), camera (optical_camera) and lights (illumdesign.light_source results) as optscene.render_optscene. The direct part is computed with the very same irradiance function, so bounces=0 reproduces render_optscene exactly (a test gate). On top of it the surfaces are cut into patches (radiosity_patches, at most *patch_mm* inside pockets and *outer_mm* (default *patch_mm*) elsewhere on a side), their view factors computed with occlusion (form_factor_matrix), and the light reflected between them added:
• bounces=None — converged, by progressive shooting (radiosity_progressive_3d, stop at residual energy tol);
• bounces=k — the Neumann partial sum: light that bounced at most k times between surfaces before reaching the camera (0 = direct only, 1 = one interreflection).
Each pixel's interreflected irradiance is gathered from the patch radiosities with the point-to-polygon closed form at the pixel's own surface point (final gather, one visibility ray per patch), so it is smooth inside a patch. Pixel radiance = ρ/π (E_direct + E_interreflected) in the same linear units as render_optscene. Light intensity enters linearly (the geometry is cached by a SHA-256 of the scene's shapes, camera and patch size — materials and light intensity are read on every call, so a calibration loop that varies albedo or intensity re-solves only the radiosity).
*study_bounces* K > 0 adds a bounce study: the images after 0..K bounces, the increment of each (max abs change / image peak), the observed ratio of successive increments g (the geometric analogue of an observed order of convergence), a GCI-style estimate 1.25 · Δ_k g/(1 − g) of what the remaining bounces still add, whether k is in the asymptotic range (g moved by at most 5 % at k and at k − 1; before it the estimate can be optimistic), the actual error against the converged image, and bounces_needed = the first k in the asymptotic range whose GCI estimate is below *study_tol*.
Returns a dict (table) with kind = "gi_render", image (H, W, 3), direct (H, W, 3, identical to render_optscene), difference (H, W, 3) = image − direct (the interreflection map), indirect_share (H, W), bounces, converged, n_shots, unshot_history, n_patches, patch_radiosity (N, 3), bounce_study (list of rows, or None), bounces_needed and notes.
Raises ValueError: an empty scene, or an unsupported one (see radiosity_patches:
Lambertian boxes, box-minus-box pockets, finite planes; an infinite plane only black); no lights; *bounces* not None or an integer in [0, 1000]; bad *patch_mm*, *tol*, *n_quad*, *supersample*, *study_bounces* or *study_tol*; an all-zero image (as render_optscene).
optics 的每個運算子都先檢驗輸入再計算(不讓任何東西無聲通過):
• 單位寫進參數名 —— _mm / _um / _deg / _mrad。把 mm 和 µm 弄混不會當掉,而是給出「看似合理卻是錯的答案」,所以用命名來防。這裡絕不從數值大小去猜單位。
• 字串一律 ValueError —— float('50') 會成功,於是未解析的設定值會被當成長度混進來(實測:thin_lens('50', '200') 曾回傳看似合理的 66.667 mm)。bool 也按 True == 1 的隱式提升拒絕。
• complex / masked array 一律 ValueError(僅接受實數槽位;拒絕無聲丟棄虛部或剝掉遮罩)。所有輸入中的 NaN/Inf 一律 ValueError。
• 逐項點名拒絕除零及其近親:焦距 0、曲率半徑 0、折射率 <= 0、全不透明光闌(全為 0,正規化變成 0/0)、總和 <= 0 的 PSF、S0 = 0 的 Stokes 向量、物體位於前焦點(像在無窮遠)。
• 只有兩個運算子會回傳非有限值,而且都寫進了契約:depth_of_field 在超焦距以外回傳 far_mm = inf(這正是超焦距的定義),gaussian_beam 在束腰處回傳 wavefront_radius_mm = inf(平面波前的曲率半徑)。兩者都同時回傳一個有限的夥伴(far_is_infinite / curvature_per_mm)。除此之外的無聲 NaN/Inf 都在內部檢出並 ValueError ——「float64 溢位了」和「答案是無窮大」是兩種不同的主張,不能拿後者的臉去交付前者。
• 尺寸上限:生成網格受 optics.MAX_GRID(4096)限制,傳入的場/PSF/光闌受 optics.MAX_FIELD_ELEMENTS(2^24),ABCD 元件序列受 optics.MAX_SYSTEM_ELEMENTS(1024),Zernike 受 MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。以 fail-closed 堵住「小參數引發巨大內部配置」的路徑(實測:n_max=40 × 4096² 需要 108 GB)。
• 物理上不可能的狀態同樣拒絕:偏振度 > 1 的 Stokes 向量、負穿透率、負強度、n-|m| 為奇數等非法 Zernike 指標。
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• poc_pocket_interreflection — py -3.11 examples/poc_pocket_interreflection.py
table 作為輸入)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
radiosity)form_factor_parallel_rects · form_factor_perpendicular_rects · form_factor_polygons · radiosity_patches · form_factor_matrix · radiosity_progressive_3d
*Provenance: radiosity3d.py — OPTICS 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.