Interpolating Splines: Which is the fairest of them all?
Abstract
Interpolating splines are a basic primitive for designing planar curves. There is a wide diversity in the literature but no consensus on a "best" spline, or even criteria for preferring one spline over another. For the case of G2-continuous splines, we emphasize two properties that can arguably be expected in any definition of "best" and show that any such spline is made from segments cut from a single generator curve, such as the Euler spiral.
Citation
Raph Levien and Carlo H. Séquin. "Interpolating Splines: Which is the fairest of them all?". Computer-Aided Design and Applications, 6(1):91–102, June 2009.