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Hemispherical projection vs equisolid projection

I would like to confirm whether the hemispherical projection (-vth) of Radiance in functions like rpict has the following projection equation:

r = f * sin(theta)

, where theta is the zenith angle between the ray and the optical axis, r is the distance of the projection from the optical axis, and f is the focal length?

I have this question because the following document from Radiance-online.org (https://discourse.radiance-online.org/uploads/default/original/1X/2796d9e673281d0a0c706180f9dd724acae49b61.pdf) claims that the hemispherical projection in Radiance is the same as the equisolid projection. However, the equisolid projection has the following projection equation:

r = 2f * sin(theta/2)

, which is obviously not the same as the first projection. Is this document wrong?