I'm contemplating writing a version of asteroids on Klein's quartic---a three-holed torus constructed by identifying certain edges of 24 hyperbolic heptahedrons---rather than the usual one-holed torus we get by identifying opposite edges of a square. I've chosen to use Poincare's disk for my model of hyperbolic space, so the path an undisturbed asteroid takes on the screen will be an arc that meets the disk at right angles. I've worked through the algebra for calculating the next position of a particle moving at a constant velocity per timestep, but it's pretty ugly: given a particle's position and velocity vectors, I solve a quadratic to find the center of the circular arc defining the geodesic, then another to find the endpoints where it intersects the unit disc, then a mobius transformation to map the geodesic to the imaginary axis, then a mobius transformation to move it forward along the geodesic according to its velocity, then inverting everything to get back to the original point of view. Does geometric algebra give a nicer description? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com