We talk qualitatively quite a bit about the softness or hardness of light, as it's one of the fundamental qualities and something every photographer and videographer should consider when choosing how to light their subjects. This neat video takes a more scientific approach by asking how we can quantify the softness of light.
Coming to you from Cinematography Database, this fun video examines the idea of measuring just how soft a light source is. The softness of light depends on two things: the distance from the subject (the closer the source, softer it is) and its size (the bigger it is, the softer it is). These two things affect the apparent size of the source relative to the subject, or in more mathematical terms, the solid angle formed by the source. The solid angle is a neat and tidy way of quantifying the apparent size of the source, though we generally still speak of light softness qualitatively. Nonetheless, it's a fun look at what we really mean when we speak about the softness of light and why differently sized light sources placed at correspondingly different distances can still produce the same softness.
It would be interesting to try to quantify the fall-off qualities which also change with distance. The same 'relative' size light sources vary in quality due to their distance. Less fall-off means less highlight to shadow contrast as well as a smoother transition. It's related to the inverse square law but modified due to the non-point source of the light.
nice work it a great start to an eventual app that would cover the issues of light source selection. A good statement to answer or explain would be the reason that a 88 para is better in a larger space while a 330 par is better in a smaller space. I think this is fitting right into you 3D modeling study, I mean its counter intuitive to use a small light source and get better results in a larger room, while using a larger light source in a smaller room makes a little more sense to me.