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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...) 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?

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I'm not sure which post included this document or who authored it, but they misspoke when they said that the hemispherical projection is an equi-solid-angle projection. It is in fact an equal projected solid angle projection, meaning that it includes the cosine factor needed for illuminance and irradiance calculations. Thus, the average over the circular area with "-vth -vh 180 -vv 180" times pi gives you irradiance.

The equi-solid angle projection is not directly provided in Radiance, due to its visual similarity to the original equi-angular projection (-vta). You can however convert between the two using the pcomb program and the provided "fisheye_corr.cal" definitions in ray/src/cal/cal. The usage is explained in the header of the file, but it is basically a warping function that operates on a Radiance picture file to go between mappings.

-Greg

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