Quote - It doesn't look any different than a straight inverse square, except within 3 radii.

 

I've been playing with different radii and test scenes with that light shader and... wow. I'm completely surprised that there is barely any difference, no matter what the radius is set to.

One of my first reactions was "Is the formula actually working?" and to test that I set the radius so that it encompassed my entire enclosed scene. There failed to be any light at all, which meant that every polygon in the scene was being calculated correctly as being inside the radius and, because your implementation of the formula is producing negative intensities or is simply bottoming out at zero---either way producing visually black---then it looks like it's working as predicted.

Now, before trying this out, I would have made a (kind of educated) guess that there would be some kind of discernible continuum from constant to inverse linear to inverse square along which all real-world spherical light sources could be placed. In theory, this still holds but really........... the visual differences are so slight from one type of light to another that it's not even worth worrying about; they almost all look like inverse square fall-off!

Perhaps the mistake I was making was in thinking of those points along the continuum as being real-world things but actually, they're theoretical objects. Constant = the light source is an infinite plane; inverse linear = the light source is an infinite one-dimensional line; inverse square = the light source is an infinitessimal point. I guess in the real world, all the possible types of spherical light source we're likely to encounter live in a very tightly grouped spot up near "exponent = 2" where the differences are minutely subtle.

Big thanks for posting the light shader and allowing me to find out and correct my faulty impressions!