Does it ever make sense to do ray intersection testing when the form of the implicit surface doesn't admit a simple algebraic solution for t? Or is it the case that in practice you always model implicit surfaces in such a way that guarantees intersections can be easily computed when doing ray tracing?

Does it ever make sense to approximate an implicit surface in a form that doesn't naturally admit simple algebraic solutions for ray intersection to a form that does admit simple algebraic solutions for ray intersection?

What would t be for a ray that lies directly a plane?

^ I guess t can be any value in that case

If we are trying to find the intersections of a ray with a mesh with many surfaces, is there a way to filter out some surfaces and speed up our search, since solving for intersections with every surface seems inefficient.

What if we have an explicit surface instead?

For "uglier" implicit surfaces, solving the equation could be much harder. Are there any other solutions for these situations?

Isn't it more effective to use explicit surfaces than implicit surfaces for more general cases?

Solving some hard equations is time-consuming. Are there any ways to solve that?

If the answer ends up being imaginary, is there some nice geometric explanation based on our discussion with imaginary numbers?

Is there a way to search for only a select few surface? How long does this operation take in practice?