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The various attenuation sliders can be used (partially in combination with the distance sliders) to make lights that either illuminate near and far objects*, or which only illuminate near ones.
*Good for light sources with a very large area or which are supposed to be very far away - while, for examples, light from the sun technically falls off via the inverse square law, it's already so far away that the small distances within a scene are negligible. Given we can't put our "sun" 150 million kilometres away in SFM to simulate this, constant attenuation is a good fake.
Now, if any of the constant, linear or quadratic sliders are used on their own, their effect is largely equivalent to the intensity slider.
The overall equation looks something like this, or so I believe: (This simplifies out things like FarZ attenuation that only take effect after a certain distance)
Brightness at a point = Intensity * ((Constant Attenuation) + (Linear Attenuation / Distance) + (Quadratic Attenuation / (Distance ^ 2)))
So if Constant and Linear Attenuation are zero, then these terms have no effect, and therefore doubling either Intensity or Quadratic attenuation will double the brightness of the light.
However, if Constant or Linear Attenuation is not zero, then Intensity will multiply that term as well and the two sliders will operate differently.
You can use this to make lights fall off in very specific ways, particularly if you remap sliders to allow negative attenuation.
Lights that fall off very rapidly* (but a lot less sharply than using the MaxDistance slider) or even which get brighter further you are from them**
* A low negative Constant or Linear attenuation, combined with a positive Linear or Quadratic attenuation.
** A low positive Constant or Linear attenuation, combined with a negative Linear or Quadratic attenuation.