OrcaFlex Manual - Orcina

Theory, Interpolation Methods
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� Cubic Bessel (also known as Parabolic Blending). Cubic Bessel interpolation is similar to cubic spline in that it
is also piecewise cubic. But for this method the cubics are chosen so that the only the first derivative is
continuous at each X data point. The second derivative is not, in general, continuous at the data points, which
can be a drawback for some purposes. However cubic Bessel interpolation has the advantage that it gives 'local'
interpolation – i.e. the (X,Y) values at any given data point only affects the interpolated curve over the intervals
near that point.
Choosing interpolation method
Sometimes OrcaFlex provides a choice of interpolation method. In general we would recommend that you use the
default interpolation method, but in some cases it may be appropriate to use a different method. To decide you need
to take into account what the interpolated data is used for and the different properties of the interpolation methods.
If continuity of first derivative is not required then linear interpolation is often appropriate. It has the advantage
that it is very simple. The other 2 methods are piecewise cubic and they both produce a smooth curve, i.e. one with
continuous first derivative. Cubic spline interpolation gives a curve that also has a continuous second derivative,
whereas cubic Bessel does not, but in many cases this is not important.
Both cubic spline and cubic Bessel produce curves that often have overshoots. For example the following graphs
show how each method interpolates a particular set of data. Although the greatest Y value specified in the data is 8,
the interpolated curves for cubic spline and cubic Bessel both exceed this value. How serious this overshoot is
depends on the data – it can be much more serious than illustrated here or sometimes there can be no problem at
all. The amount of overshoot is generally less with cubic Bessel than with cubic spline. But if you are using either of
the piecewise cubic interpolation methods then you should always check whether the interpolated curve gives an
appropriate fit to the data. If it does not then you usually need to supply more data points.