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
Apple used straight segments and circular arcs on its icons upto iOS 6, and switched to 2nd-order continuous shapes on version 7. Here is a side-by-side comparison :
It's actually much more prominent in 3D reflections, because this 2nd derivative ("acceleration") affects the "flow" of the reflection: https://i.stack.imgur.com/pctnj.png
> Your visual system can actually see those discontinuities.
Because it's also the biggest difference of curvature (actually the radius of curvature, the inverse of the curvature value, which is what is geometrically significant, "what we see") possible, the one between infinity (a line is a circle with an infinite radius) and a "normal" (finite) value.
Which means that the radius of curvature of the "seams" of the spline is the same for both curves in the common point - the spline is "smoother", there is no jump in the curvature. Like C1 means, that each point (except for start and end) of the spline has a tangent (the samé tangent from the left and the right side), no spikes.
And C3 is about the torsion of (3D, as in "not contained in a plane") curves.
Practically speaking, what tiled video games could take advantage of this? I think generally it's important for tracks in these kind of games to be aligned with the grid and to minimize the number of sprites needed. Having discrete straight and curved pieces like a toy train set seems like a good fit for the problem game designers face.
Real world roads and tracks follow the principle that the curvature changes linearly with the curve length. This has the advantage that at constant driving speed the steering wheel has to be turned with constant speed as well.
So, the curve should really be a clothoid, sometimes called Euler spiral, but a cubic Bézier can be a good enough approximation.
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