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Mapping from view height ® and zenith cos angle (mu) to UV coordinates in the transmittance LUT
Assuming r between ground and top atmosphere boundary, and mu= cos(zenith_angle)
Chosen to increase precision near the ground and to work around a discontinuity at the horizon
See Bruneton and Neyret 2008, “Precomputed Atmospheric Scattering” section 4
Simplified ray-sphere intersection
where:
Ray origin, o = [0,0,r] with r <= atmosphere.top_radius
mu is the cosine of spherical coordinate theta (-1.0 <= mu <= 1.0)
so ray direction in spherical coordinates is [1,acos(mu),0] which needs to be converted to cartesian
Direction of ray, u = [0,sqrt(1-mu*mu),mu]
Center of sphere, c = [0,0,0]
Radius of sphere, r = atmosphere.top_radius
This function solves the quadratic equation for line-sphere intersection simplified under these assumptions
Mapping from view height ® and zenith cos angle (mu) to UV coordinates in the transmittance LUT Assuming r between ground and top atmosphere boundary, and mu= cos(zenith_angle) Chosen to increase precision near the ground and to work around a discontinuity at the horizon See Bruneton and Neyret 2008, “Precomputed Atmospheric Scattering” section 4