QUINTIC-SPLINE OPTION TO GRID COMMAND

The "quintic splines" gridding algorithm used in MOSS is based on
a public domain algorithm written by Hiroshi Akima and published
by the Association for Computing Machinery (see bibliography).  It
covers the area to be gridded with a mesh of triangles, using the
original data points as vertices.  Next, it examines each data point
and determines the nearest two to ten other data points.  It uses
these nearest neighbors to estimate the slope and gradient at each
data point. The slope and gradient data is then used to calculate
a fifth degree interpolating polynomial over each triangle.  Finally,
each cell in the output grid is examined to determine in which tri-
angle its center lies, and the cell value is calculated based on
the polynomial over this triangle.

Quintic splines is a very fast method of gridding a point map, but
it is not very accurate when there are grid cells far from any data
points.







The SPLINE option is described as follows:

    (number of closest data points)*

     where (number of closest data points)* is a required parameter
     which is input in response to the prompt:

     ENTER NUMBER OF CLOSSEST DATA POINTS TO USE IN
     COMPUTATION (MAX=10):

The response to this prompt determines the number of nearest neighbors
the program will use in determining slope and gradient data, as explain-
ed above.  A large value will produce a smoother grid, but some detail
will be lost.  A small value will produce a rougher grid, but it will
do a better job of preserving local anomalies in the data.  Experience
seems to indicate that a value of 7 or 8 gives good results for most
applications.







While the QUINTIC SPLINES program is running, messages like the follow-
ing will appear on the screen:

     400  TRIANGULATING
     722  TRIANGLES FORMED
     400  SEARCHING FOR 7 NEAREST NEIGHBORS
          SORTING GRID CELLS BY TRIANGLE
     400  CALCULATING GRID CELL VALUES

The numbers at the left of these messages will overprint, so if
you are entering this command from a non-refresh terminal such as
a Tektronix 4014, they may become illegible.  To monitor progress,
simply clear the screen while the program is running.

Limitations of quintic-splines:

1)There must be at least three points in the input data set.
2)The maximum number of points in the input data set is currently
  set to 300 (16 bit version) or 5000 (32 bit version).
3)Points in the input data set cannot all be collinear.




BIBLIOGRAPHY

Akima, Hiroshi, 1978.  "Bivariate Interpolation and Smooth Surface
     Fitting of Irregularly Distributed Data Points," No. 526 in
     Collected Algorithms of the ACM.
Akima, Hiroshi, 1978.  "A Method of Bivariate Interpolation and
     Smooth Surface Fitting for Irregularly Distributed Data Points,"
     ACM Trans. Math. Software 4,2, pp. 148-159.
