# Extrapolation

In general, extrapolation is
not very reliable and the results so obtained are to be viewed with
some lack of confidence. In order for extrapolation to be at all
reliable, the original data must be very consistent.
Natgrid does extrapolation
by least squares
fitting a plane to the original data and using that
plane to produce pseudo data values at some distance from the
convex hull. These pseudo
data points are added to the input data points when
natural neighbors
are calculated. The result of this is that
extrapolated data will asymptote to the least squares fitted plane.
Natgrid allows you to turn off extrapolation and set the interpolated
functional values to a constant outside of the convex hull.
If the control parameter
ext is set to 1 (the default),
extrapolation is allowed; if ext is set to 0, extrapolation is not
allowed.
The parameter
nul specifies the value to be
assigned to the interpolated function outside of the convex hull
when extrapolation
is not allowed; by default nul is 0. .

Example 4
uses the same function as
Example 3, but expands the output region
to allow for extrapolation.
As provided, the code for Example 4 allows for extrapolation. For
an example that disallows extrapolation, change the setting of
ext in the code
for Example 4 from 1 to 0.
Notice that in the
plot that allows extrapolation,
the function values tend toward the least squares
fitted plane outside of the convex hull. The
plot where extrapolation is not allowed
uses the same function and illustrates turning extrapolation off
and setting
the function values to -1.0 outside of the convex hull.
The only difference between the code that produced these plots is
the setting of the value of the ext
parameter.

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