Equations
x = D·e^(θ cot α)·[A sinβ cosθ
+ R cos(s+φ) cos(θ+Ω)
− R sinμ sin(s+φ) sin(θ+Ω)]
y = e^(θ cot α)·[−A sinβ sinθ
− R cos(s+φ) sin(θ+Ω)
− R sinμ sin(s+φ) cos(θ+Ω)]
z = e^(θ cot α)·[−A cosβ + R sin(s+φ) cosμ]
R(s,θ) = 1/√(cos²s/a² + sin²s/b²) + k(s,θ)
k(s,θ) = L·exp(−(2(s−P)/W₁)² − (2ℓ(θ)/W₂)²)
ℓ(θ) = (2π/N)·frac(Nθ/2π)
Inner wall: R_in = R − t·R_ellipse
θ runs along the growth spiral (aperture at θ = 0), s runs around the aperture. Wall thickness t is a fraction of the local aperture radius, so the wall scales with the shell and growth stays self-similar. Preset values come from Cortie (1989, 1993) as tabulated by Picado and the pst-shell package.