In many tiled video games, roads, tracks and other paths tend to be designed without the knowledge on 2nd derivative continuity (or ignoring it for aesthetic reasons). So it would consist of straight segments, and rounded segments (and maybe some intersections). The rounded segments will be simply quarters of a circle. The problem with this is that while the path is continuous (no teleportation), and the velocity is continuous (no sudden direction change), the acceleration isn't continuous - there's no acceleration on the straight segments, and then suddenly there is acceleration on the rounded segment, and that acceleration, for an arc, is constant. In real life there's an easing added to the paths of e.g. railways, so that the sudden acceleration doesn't surprise passengers. In tiles you could also design the turns to be C² continuous, but it might be aesthetically displeasing by looking like being handdrawn rather than mathematically constructed.

I'm saying all this, because it seems Hobby's algorithm is something designed precisely to construct splines that maximize this aesthetically pleasing C¹ continuity... However it tends to explode splines by favoring arc connections, so I think some optimization is needed to limit that behavior: https://i.imgur.com/W9ssWTu.png