"For example, all surfaces that are shaded with interpolated normal will have an unnatural shadow discontinuity at the silhouette edges with single shadow ray traces."
For some reason I really want to understand what this sentence means. I don't know why it jumped out at me, maybe because it seems both accessible and arcane, I want some path to even just tour the arcane concerns of someone so deep into a (this) particular domain.
In English: if you're only using one ray for shading, then you'll have areas that are completely in shadow directly next to areas that are completely not in shadow; what we call hard shadows. Soft shadows are a better approximation of reality, because they show the shades of grey between "covered" and "uncovered", but they require more ray intersections (unless you're using sphere tracing!).
Sphere tracing is awesome. So many effects can be so easily and cheaply approximated, apart from soft shadows also subsurface scattering, bloom/glare etc. Downside, while great for geometry describable by distance fields, it's quite useless with polygonal assets...
Typically when ray tracing you follow one (or more) rays from the eye through a pixel on the screen until it hits something. Then you have to decide what that point on the surface of thing it hits should look like. Usually this breaks down into a combination of how much ambient light you're simulating, the material properties of the surface, the results of any reflection/refraction rays you fire off, and the effect of light sources on it.
The simplest way to calculate the light sources is to follow another ray to each of your light sources, and if there's nothing in the way, you add the intensity of that light to the pixel.
The problem with this simple approach is that something is either blocking your path to the light source or it isn't, which creates absolutely sharp shadows because it's simulating the lights as if all the light's brightness is emanating from a single infinitesimal point.
In real life, lights tend not to be like that.
To get realistic looking shadows with ray tracing you have to send multiple rays to different parts of each of your lights, adding a portion of the lights brightness each time (you're essentially doing a monte carlo integration over the area of the light). The more you do, the better looking shadow edges you can get, but also the more effort you have to spend in calculating.
Raytracing is rather fun because you can get really interesting results with relatively little code and it's very visual - you actually see your bugs. Some people do simple ray tracers as katas. I did a basic one as a way of learning Scala. If you're interested in having a look it's here (very simple of course - I do treat my light sources as points): https://github.com/kybernetikos/ScalaTrace/wiki/ScalaTrace
For some reason I really want to understand what this sentence means. I don't know why it jumped out at me, maybe because it seems both accessible and arcane, I want some path to even just tour the arcane concerns of someone so deep into a (this) particular domain.