Post History

The best route is a straight connection between the two points being connected.  Of course that's not always possible due to other objects being in the way, or to be able to route other connections.

I think most auto-routing software uses 45° bends because that's a reasonable tradeoff between electrically good enough and keeping the software simple.  I use Eagle, and that's what its auto-router does even when a direct path between points is available.

45° corners are shallow enough so that there isn't much inductance due to the corner, nor possibility to trap chemicals.  Remember that inductance goes with the square of the number of turns.  45° is half the "turns" of 90°, so ¼ the inductance due to the bend.  Since even 90° isn't a problem in most cases, 45° is "good enough" for the vast majority.  The increase over a straight line isn't that much.

Routers are one of the few remaining pieces of software that take significant time on a human scale, even on today's computers.  It can take over 10 minutes to route a decent size board on a reasonably modern machine.  Therefore algorithm efficiency is still important.  I'm not privy to the internals of any auto-router, but it's easy to imagine that having only 7 possible directions to go from any existing end simplifies things considerably compared to being able to head off in any direction, let alone in a curve.

The fixed grid architecture of most existing routers isn't well suited to arbitrary angles and curves.  The overall grid size goes up with the square of the fineness, and of course the algorithm has more grids to look at, so gets slower too.