I would randomly sample a frequency, calculate its color and use it to modulate ray color. I would have to scale the result by 3 to account for the pure refracted color being 1/3 brightness.
I think the term “distribution ray tracing” was a bit of a mid-point on the timeline of evolution from Whitted ray tracing to today’s path tracing? IIRC distribution ray tracing came from one of Rob Cook’s Siggraph papers. It’s probably worth moving toward path tracing as a more general and unified concept, and also because when googling & researching, it’ll be easier to find tips & tricks.
Yes when combining spectral rendering with refraction, you’ll need to pick a frequency by sampling the distribution. This can get tricky in general, good to build it in incremental steps. True of reflections as well, but up to you whether you want to have frequency-dependent materials in both cases. There are still reasons to use spectral even if you choose to use simplified materials.
I would randomly sample a frequency, calculate its color and use it to modulate ray color. I would have to scale the result by 3 to account for the pure refracted color being 1/3 brightness.