that is called spherical illuminance. As an approximation, you could calculate 6 illuminance values (up, down, East, West, North, South) and average them. Christopher Cuttle wrote a few papers on spherical illuminance.
From: Giovanni Betti [mailto:firstname.lastname@example.org]
Sent: Tuesday, May 08, 2012 1:42 PM
To: Radiance general discussion
Subject: [Radiance-general] integral of radiation in one point
I have question that I hope you'll help get my head around.
I want to calculate the overall illuminance on a point in space that is, regardless of directionality.
I have made some simplified 2d sketches for clarity.
As I understand a radiance sensor point in rtrace will have cosine related sensitivity (image01)
If I am to place two coincident with opposing normals (image2) I'll miss on contributions from the sides.
Rotating the normals by 90 degrees at a time (figure 3) and summing contributions might not work either because will overestimate diagonal contributions (figure 4 ).
So I'm not getting too much closer to the solution...
Is there something that I am missing here?
Any light on this will be appreciated,