nx_henyey_greenstein.nx

nx_henyey_greenstein.nx -- anisotropic single-scatter phase function in Q10. Epoch 2 FIRMAMENT primitive per nxc2/docs/NISHI_GAME_ENGINE_ROADMAP.md. The Henyey-Greenstein phase function approximates light scattering off small particles (atmospheric aerosols, water droplets, fog, pigment). Published in Henyey & Greenstein 1941 "Diffuse Radiation in the Galaxy" (Astrophysical Journal 93, 70-83) -- pre-1970 astrophysics, public-domain math. Formula: P(cos θ, g) = (1 - g^2) / (4π · (1 + g^2 - 2g·cos θ)^1.5) where: cos θ in [-1, 1]: scattering angle cosine (1 = forward, -1 = backward) g in [-1, 1]: asymmetry parameter g > 0 = forward-scattering (atmospheric haze ~ 0.8) g = 0 = isotropic g < 0 = backward-scattering (some pigments) Output: probability density. Normalized so ∫P dΩ = 1 over sphere. Range can exceed 1.0 when |g| near 1 and cos θ near sign(g) (forward/backward peaking). Capped at NX_HG_SATURATED to keep downstream arithmetic well-behaved. Fixed-point strategy: keep numerator and denominator in raw integer space and defer all divisions to a single final step. Avoids the Q10 precision starvation that would otherwise hit the (1 + g^2 - 2gc) term as it approaches 0. Loss audit: the only information-discarding ops are (a) integer sqrt (_isqrt) which truncates the fractional part, introducing ~1% error at typical g values; (b) clamp at |g| >= NX_HG_G_MAX to avoid singularity; (c) final integer division. All three are inherent to fixed-point evaluation of a singular function and are named here per cardinal rule 25. genealogy_id: henyey_greenstein_1941_phase lineage_id: nx_henyey_greenstein_q10