Dsgrid is a package in the ngmath library
that implements a simple
inverse distance weighted interpolation
algorithm. The input for the
interpolation is a set of randomly-spaced three-dimensional
coordinates with functional values at those coordinates;
the output is a set of interpolated function values at coordinates
in a user-specified grid.
The coordinates in the output
grid must
be
monotone increasing in each coordinate direction, but need not
be uniformly spaced.
See the comparative
analysis of the ngmath packages for details
on which ngmath package is most appropriate for your problem.
Computational interpolation methods can be divided into two
basic classes: fitted function methods and weighted average
methods.
The fitted function, or fitted surface, methods
fit an algebraic
surface to the known data and then pick the interpolated
values from the fitted surface. The weighted average
methods calculate interpolated values as
weighted averages
of known values.
Among the weighted average methods, the simplest are known as
the inverse distance weighted average methods. Dsgrid uses one
of these methods.
Dsgrid uses a simple
weighted
average method to do its interpolation.
For interpolation at a coordinate,
weights are computed for input
coordinates, the values of such weights being inversely
proportional to the distance an input coordinate is from the point
where an interpolated value is desired.
In the default situation in the Dsgrid package, the influence of
an input datum on a calculated value at an interpolation point
varies as the inverse cube of the distance between the interpolated point
and the input datum. The sum of the weights is normalized to unity and
an interpolated value is the sum of the products of the known functional values
and the calculated weights.
The capability exists in Dsgrid
to vary the power of the distances used to compute the weights.
For powers of the distances greater than one, the interpolated
surface is flat at the input data; the size of the flat spot increases
with increasing values of the power.
If the power of the distances is one, then
the weights are computed simply as linear inverse distances and the
areas around input data are cone shaped. If the power is less than
one, then the areas around input data form a cusp at the data points.
Example 2 illustrates the effects
of modifying the exponent of the
distances used in computing the weights. For full details on
interpolation methods, consult
Dave Watson's
book Contouring.
- Functionally equivalent Fortran
and C interfaces are provided in both
single and double precision versions.
- Interfaces exist for two-dimensional interpolation as well as 3D.
- Interfaces exist for interpolation at individual points.
- The capability exists to specify that only input data points
within a specified distance from an interpolated point be considered
in the calculation of weights.
In the default case, all input data are used in the calculation of the
weights.
- The package has a shadowing option which, when in effect,
reduces the effect that a cluster of points might have in
skewing interpolated values. This shadowing feature is based on
original work of Bob Lackman.
Example 4 illustrates the
shadowing feature.
You should now proceed to the module on
learning how to use Dsgrid.
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