Interstellar Horizons

Rayleigh Only Nishita with Mie scattering disabled — pure molecular scattering baseline

I_{λ} = I_{sun} \int_{0}^{D} β_{R} (λ) ρ_{R} (h) P_{R} (θ) e^{- τ_{R}} d s

Preetham (1999) Analytical — Perez sky luminance/chromaticity model

F (θ, γ) = (1 + A e^{\frac{B}{\cos θ}}) (1 + C e^{D γ} + E \cos^{2} γ)

Nishita (1993) Ray-marching — single-scattering Rayleigh + Mie

I_{λ} = I_{sun} \int_{0}^{D} [β_{R} (λ) ρ_{R} (h) P_{R} (θ) + β_{M} ρ_{M} (h) P_{M} (θ)] e^{- τ (\vec{x}, \vec{s}) - τ (\vec{x}, \vec{v})} d s

Hosek-Wilkie (2012) Enhanced analytical — improved horizon, ground albedo feedback

F (θ, γ) = (1 + A e^{\frac{B}{\cos θ + 0.01}}) (C + D e^{E γ} + F \cos^{2} γ + G χ (H, γ) + I \sqrt{\cos θ})

Nishita + Ozone Adds Chappuis band absorption — deeper blues during twilight

τ = τ_{R} + τ_{M} + τ_{O_{3}}

CIE Standard Clear Sky (Type 12) Empirical luminance model — ISO 15469 architectural standard

\frac{L (θ, γ)}{L_{z}} = \frac{φ (θ) \cdot f (γ)}{φ (0) \cdot f (θ_{s})}

Parameter Matrix

Parameter		Rayleigh	Preetham	Nishita	Hosek-Wilkie	Nishita+O₃	CIE Clear
Geometry
Sun position	$α_{s}$	✓	✓	✓	✓	✓	✓
Viewing elevation	$θ$	ray direction	Perez $\frac{F (θ, γ)}{F (0, θ_{s})}$	ray direction	ray direction	ray direction	$φ (θ)$ gradation
Observer altitude	$h_{0}$	ray origin	—	ray origin	ray origin	ray origin	—
Atmospheric Scattering
Rayleigh coefficient	$β_{R}$	sole scatter term	implicit in Perez fit	per-channel	per-channel	per-channel	—
Mie coefficient	$β_{M}$	$β_{M} = 0$	implicit in Perez fit	$β_{M} \propto T$	$β_{M} \propto T$	$β_{M} \propto T$	—
Rayleigh scale height	$H_{R}$	8 km	—	8 km	8 km	8 km	—
Mie scale height	$H_{M}$	—	—	1.2 km	1.2 km	1.2 km	—
Turbidity	$T$	scales $ρ_{R}$	drives all Perez coeffs	scales $β_{M}$	scales $β_{M}$	scales $β_{M}$	affects CCT
Phase Functions
Rayleigh phase	$P_{R}$	$\frac{3}{16 π} (1 + \cos^{2} θ)$	baked into Perez $E$	$\frac{3}{16 π} (1 + \cos^{2} θ)$	$\frac{3}{16 π} (1 + \cos^{2} θ)$	$\frac{3}{16 π} (1 + \cos^{2} θ)$	—
Mie phase	$P_{M}$	—	baked into Perez $C, D$	Henyey-Greenstein	Cornette-Shanks	Henyey-Greenstein	—
Asymmetry parameter	$g$	—	—	$0.76$ (fixed)	$0.76$ (fixed)	$0.76$ (fixed)	—
Absorption & Ozone
Ozone absorption	$β_{O_{3}}$	—	—	—	—	Chappuis band, 3-ch	—
Ozone density	$ρ_{O_{3}}$	—	—	—	—	$e^{- 2 \frac{\| h - 25 \|}{15}}$ km	—
Ozone column strength	$S_{O_{3}}$	—	—	—	—	slider $(0 - 3)$	—
Surface & Multi-Scatter
Ground albedo	$A$	—	—	—	$I_{g} = A \cdot E_{☉} e^{- τ}$	—	—
Multiple scattering	$I_{ms}$	—	implicit in empirical fit	—	order-2, $k_{ms} = 0.075$	—	implicit in empirical fit
Color & Tone Mapping
Color space		spectral RGB → sRGB	CIE $Y x y$ → sRGB	spectral RGB → sRGB	spectral RGB → sRGB	spectral RGB → sRGB	CCT → $Y x y$ → sRGB
Tone mapping	$k$	Reinhard, $k = 1.0$	Reinhard, $k = 0.04$	Reinhard, $k = 1.0$	Reinhard, $k = 1.0$	Reinhard, $k = 1.0$	Reinhard, $k = 0.15$
Twilight handling		indirect glow	fade to $- 6 °$	indirect glow	indirect glow	indirect glow	fade to $- 6 °$
CIE-Specific
Sky type coefficients	$a - e$	—	—	—	—	—	Type 12 (clear, polluted)
Correlated color temp	$T_{cc}$	—	—	—	—	—	$3500 - 15000$ K
Preetham-Specific
Perez coefficients	$A - E$	—	3 sets $(Y, x, y) \times T$	—	—	—	—
Zenith chromaticity	$x_{z}, y_{z}$	—	polynomial in $T, θ_{s}$	—	—	—	—

Parameter

Rayleigh

Preetham

Nishita

Hosek-Wilkie

Nishita+O₃

CIE Clear

Geometry

Sun position