I probably won't do multiplayer. I have an idea to make it work, but it only really works if you play against each other, and I've never seen a shoot 'em up that does that.
Time dilation being a challenge depends on the paths used. I tried using Bezier curves, but it turns out that it's impossible to calculate how much apparent time has passed between two events on the curve. I would just calculate it numerically for each enemy, but that wouldn't work for any enemy that follows the player, since its path would be procedural.
Length contraction is easy. Terrell rotation is not. I have yet to find an equation for a first approximation matrix.
Also, there is a problem with stuff red- and blue-shifting out of the visible spectrum.
Can't you just make your game objects radiate a realistic Boltzmann spectrum, perhaps arbitrarily declaring that they all have a fairly high temperature? Then they won't go invisible; their infrared or ultraviolet parts will shift into the visible spectrum to compensate.
This is the bimonthly 'What are you working On?' thread. Previous threads are here. So here's the question:
What are you working on?
Here are some guidelines: