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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 G 2 -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.

Interpolating Splines: Which is the fairest of them all?