Among the various cubic Hermite interpolations, Akima interpolation is a computationally less expensive methodcapable of producing smooth and more natural looking curve fit. It computes slopes at the data points using local procedures which use coordinates of five consecutive data points with the point of interest in the middle. However, the procedure fails to produce slopes at the edge case when slopes of two or more intervals have same slope on either side of the current point. An alternate function was provided for this special case. This limitation of shifting functions is overcome in the proposed method. Unit vectors of the line segments joining the data points are used instead of their slopes (which were used in Akima's method) in weight functions and the derivative formula. This method is also extensible for interpolating 2D open or closed paths (which is not possible using Akima's formulation).
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