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#ActualZBethel

Posted 28 November 2012 - 07:52 AM

Isn't the notion of solid angle in this context an abstraction of what we're trying to accomplish? What I mean is, when you're trying to numerically integrate a light source over a hemisphere, a differential solid angle is just basically saying, "perform a one dimentional integral over all of the surface area pieces of the sphere". Well, to do that, we ultimately need spherical coordinates to compute dA via dtheta and dphi, and it turns into a two dimentional integral that is more in line with our actual implementation.

I guess I think of the solid angle representation as a concise theoretical format that can be converted to spherical when I need to actually integrate the thing. Is that an accurate way to think about it?

EDIT: That appears to be what Bacterius observed as well in the above post. I didn't get my coffee yet.

#1ZBethel

Posted 28 November 2012 - 07:47 AM

Isn't the notion of solid angle in this context an abstraction of what we're trying to accomplish? What I mean is, when you're trying to numerically integrate a light source over a hemisphere, a differential solid angle is just basically saying, "perform a one dimentional integral over all of the surface area pieces of the sphere". Well, to do that, we ultimately need spherical coordinates to compute dA via dtheta and dphi, and it turns into a two dimentional integral that is more in line with our actual implementation.

I guess I think of the solid angle representation as a concise theoretical format that can be converted to spherical when I need to actually integrate the thing. Is that an accurate way to think about it?

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