Universe Engine

UNIVERSE ENGINE

— fps

drag — orbit · pinch / scroll — zoom · double-tap — hide UI

g_μν = η_μν + f·k_μk_ν , f = 2Mr³/(r⁴+a²y²) — Kerr–Schild form

ẋ = ∂H/∂p , ṗ = −∂H/∂x , H = ½ g^μνp_μp_ν = 0

Hamiltonian null geodesics integrated per pixel (RK2) — frame-dragging included, nothing painted

r₊ = M + √(M²−a²) , ISCO from Bardeen–Press–Teukolsky

g = −p_t / (p·u) — exact Doppler ⊕ gravitational ⊕ frame-drag shift , I_obs = g³·I_em

Ω = √M/(r^3/2+a√M) , T(r) ∝ r^−3/4

χ 0.90 · r₊ 0.72 rₛ · ISCO 1.16 rₛ · r_cam 12 rₛ · incl 7° · steps 140

v(r) = v₀ ⇒ ω(r) = v₀/r — flat rotation curve (dark-matter halo)

arms: θ(r) = θ₀ + ln(r/r₀)/tan p , p = 13°

stars — · arms 2 · GPU point sprites, additive HDR

linear HDR (RGBA16F) → bright-pass → separable Gaussian bloom (¼ res ×2) → chromatic aberration → ACES tonemap