I started out trying to explain why the math is so hairy and this post got very long.
In essence, in the simplest case you need to solve a VERY complicated simultaneous equation to determine the intersection of two splines (even quadratic splines which are the simplest case you'd care about).
Then it occurred to me that there's a very simple solution: allow spline shaped segments of road, but force them to snap to right-angled intersections. Sure it's a restriction, but most traffic engineers avoid strange intersections like the plague (for good reasons).
In essence, in the simplest case you need to solve a VERY complicated simultaneous equation to determine the intersection of two splines (even quadratic splines which are the simplest case you'd care about).
Then it occurred to me that there's a very simple solution: allow spline shaped segments of road, but force them to snap to right-angled intersections. Sure it's a restriction, but most traffic engineers avoid strange intersections like the plague (for good reasons).