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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