What are the mathematical constraints required for a polyline, i.e., a piecewise linear curve, to appear as a smooth curve to human vision? I've discovered one document that specifies only that the change of direction at each vertex must be less than 3°. It seems to me that there also needs to be a limit on degrees turned per curve length, but that's a simple enhancement.
My main question is about how the maximum direction change angle is affected by segment length. If you have two long segments connected at 3° then the change will be (to my eye anyway) much more visible than a 3° angle between short segments. Is anyone aware of any studies in this area?
In case it matters, my application is in polyline generalization for GIS.