[Radiance-general] Pixel to solid angle transformation

[John Mardaljevic]

Just to round this out.

Me:  For a hemispherical fish-eye view the total should of course be 2pi.  Now I expected a little shortfall as things get 'wonky' towards the horizon, but not quite as big as this -

pcomb -e 'lo=S(1)' del.hdr | pvalue -H -h -o -b -d | total

on various size images gives:

256 sq	5.73709888
512 sq	5.90116727
1024 sq	6.01635629
4096 sq	6.14755086

Greg: The solid angle calculation in pcomb relies on being able to compute the neighboring pixel ray directions.  For one side of the hemispherical view, these pixels fall off the image and so the returned solid angle is zero when it should not be.  On the other side of the view, the solid angle is non-zero but still underestimated as the area isn't taken around the pixel center as it should be.

For normal views, this isn't a big deal, but since so much solid angle is packed into the rim of a hemispherical fisheye, the errors really add up!  The accuracy anywhere away from the rim is probably fine.

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Marija, I was mindful of your comment "to see how calculation is exactly done".  As Greg indicates, solid angle in these instances is really, really hard to get right.  Expect similar errors with hemispherical images depending on the image size.

Cheers
John 

John Mardaljevic PhD FSLL
Professor of Building Daylight Modelling
School of Civil & Building Engineering
Loughborough University
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LE11 3TU, UK

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