radiosity op• 資料種類:table × signal → table
• 呼叫: import fullseye as fs; fs.ledger.radiosity_progressive_3d(patches, emission, form_factors=None, albedo=None, tol=1e-06, max_shots=None, n_quad=3)(要直接呼叫實作,import radiosity3d; radiosity3d.radiosity_progressive_3d(patches, emission, form_factors=None, albedo=None, tol=1e-06, max_shots=None, n_quad=3);從台帳取用則 opsoptics.get("radiosity_progressive_3d"))
三維面片組上的漸進細化輻射度(Cohen 等 1988,shooting,式 7–8)及其收斂的證據。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Solves B = E + diag(ρ) F̃ B (F̃_ji = F_ij A_i/A_j, eq. 8) by shooting: all patches start with B = ΔB = E (the emitted, or first-reflected, radiosity); repeatedly the patch with the largest unshot energy ΔB_i A_i shoots — every patch j gains ΔRad = ρ_j ΔB_i F_ij A_i/A_j in both B_j and ΔB_j — and its ΔB_i is reset to 0. Ties (equal after rounding to 1e-12 relative) go to the lower index; nothing is random.
Stopping rule — our choice, not Cohen's: the paper stops "when the solution converges to within the desired tolerance" without a number. Here the shooting stops when the residual unshot energy Σ ΔB_i A_i falls to tol times the initial energy Σ E_i A_i (a bound on the energy still missing from the solution). max_shots (default 200 × N) caps the work; hitting it returns converged=False.
*emission* E is (N,) or (N, C) (C colour channels), non-negative. *albedo* defaults to the patches' (RGB when *emission* has 3 channels, else the channel mean). *form_factors* defaults to form_factor_matrix (n_quad).
Returns a dict (table) with kind = "rad_solution", radiosity (N, C), unshot_history (the residual energy before each shot), n_shots, converged, tol, residual_energy (relative), initial_energy and the stop_rule text.
Raises ValueError: an empty or unmarked table (not radiosity_patches); emission or albedo of the wrong shape, negative or non-finite; an albedo outside [0, 1]; *tol* not in (0, 1]; a form-factor matrix of the wrong shape. (An albedo of 1 in a closed enclosure never loses energy: the shooting then stops at *max_shots* with converged=False instead of raising.)
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 · render_optscene_gi
*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.