How often are implicit surfaces used? There is a convenience in reuse of the same triangle mesh algorithm; however, to get the same effects and detail as an implicit surface, I do imagine that an extremely fine mesh would be required. On the other hand, such a high detail implicit surface may have a very high number of roots; this could become an intractable problem when using our ray tracing algorithm?
In practice they're not used often; another challenge with them is that it's not always easy to edit an implicit surface to match a desired shape. With an explicit representation like a triangle mesh, that is much easier. However, at the start of lecture tomorrow we'll talk a bit about the second assignment, which is based on ray tracing implicit surfaces, and see some other examples of impressive things people have done with them.
I may be a bit too inspired by 3Blue1Brown's fourier-transform animations (https://www.youtube.com/watch?v=-qgreAUpPwM), but I'm curious about the difficulty of generating an implicit or a parametric surface. While I can see why editing an implicit surface might be difficult, is it still possible to create an implicit surface from a sketched-out drawing (or make a large mesh into one defined by a set of parametric equations)? It seems to me that parametric surfaces might allow for a quicker intersection check, as opposed to barycentric interpolation for triangles, potentially?