I like that this page gives 1-dimensional examples. Visualizing in 1D is orders of magnitude easier than in 2D (let alone 3D). What I like most about this is that it involves actual passage through hyperspace on a trajectory
. A lot of FTL proposals come down to different ways of justifying teleportation. This system treats hyperspace as an extension of real space, which leads to some interesting possibilities for the player's experience.
For example - and bear with me here, I haven't thought through the math - if warp-travel in 3D space is equivalent to trajectories in higher-dimensional space, then the "exit" and "re-entry" will have some interesting visual artifacts. Imagine the star system turning itself inside out as you leave: http://www.youtube.com/watch?v=MDvlO9q6qWk
. Now imagine the visual chaos of missing
on the return. Let's say you oscillate in and out of real-space, trying to settle back into cononical spacetime.. the effect would be that the stars and planets around you appear to morph and twist (where in reality your hyperdimensional point of view is shifting)
Implementation of all this is likely prohibitively difficult. Fun to think about, though!