I think I have a spline problem, and I would like to implement the
solution in S. There are a lot of spline algorithms and I am looking for
some direction on what is most appropriate. I need a spline that can be
made to extrapolate certain data points as described below. Of course it
needs to happen algorithmically as I have lots of this data. Can a
Bezier be fit to data?

 

Consider a material volume sampled in discrete non-uniform intervals.
There is a continuous trend in properties that is integrated over each
interval. We are aware of the specific form of the continuous trend, but
it is concealed by the interval nature of the data. The specific need is
to identify the 'true' location and value of the minima and maxima of
the function representing the data. Perhaps an example...

 

In the following figure, the numbers represent the sampled layers: the
height of the bars is the value of the sampled property. The x axis is
depth into the material volume. The asterisk represents the true value
and location of the minima and maxima. We know that they are lower and
higher than the interval sampled data, and (critically) that the value
of the maxima or maxima is offset from the center of the sampled volume,
depending on the trajectory of the change between sampled layers.
Perhaps you can imagine a smooth line connecting the asterisks which
preserves the area of the corresponding bars. 

 

          *

          

         33333

         33333

*        33333 *

1111     33333 444

1111 222 33333 444 5*5

1111 2*2 33333 444 555 6*6

1111 222 33333 444 555 666

 


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