Just spit-balling here, but it seems to me that you could probably get away with just using the endpoints and maybe the control points. There might be some odd

Just spit-balling here, but it seems to me that you could probably get away with just using the endpoints and maybe the control points. There might be some odd cases where this falls apart, but in general I suspect it would work pretty well and in the edge cases it probably wouldn't be too confusing; you'd still get a point to rotate around in the vicinity of the curve at the centre of a line between the endpoints. If you included the control points, it would still end up roughly close to the centre of the visual curve.