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Solid angle weighting for hemispherical projection

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I'm projecting points onto the upper half of the unit sphere and end up with [-1, 1] values. Then I map these values to the [0, 1] range and onto a render target. What I want to know is how to weight the samples to take the increasing solid angle of the parameterization towards the edge of the render target into account.
I found a formula that does this for cube map faces. But I suppose this is slightly different because a smaller area is projected onto a plane.

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