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Hi!

Maybe you already bumped into the problem of projecting a cubemap into spherical harmonics and found this page to help you out: http://www.rorydriscoll.com/2012/01/15/cubemap-texel-solid-angle/ ?

But maybe you need the solution of another, similar problem that consists in finding the solid angle of a pixel lying in the z=0 plane and orthogonally projected onto the hemisphere, like shown here:

OrthoProjection.png