Akima spline

An Akima spline is a piecewise cubic interpolation that sets each interior slope from a weighted difference of the four neighboring secants, giving a fair curve that avoids the overshoot of natural cubic splines near sharp changes in data. Hiroshi Akima introduced it in 1970 (J. ACM 17(4), 589-602). Because the local slope depends only on adjacent points, a single bad offset does not propagate undulations along the whole curve, which is why it is used to fair hull offset tables and section areas where ordinary splines wiggle. It is C1 continuous, not C2, so curvature can be discontinuous at knots.