Next: Sun raster files
Up: 2-D grdfiles
Previous: Pixel registration
Boundary Conditions for operations on grids
GMT has the option to specify boundary conditions in some programs
that operate on grids (grdsample -–L; grdgradient
-L; grdtrack -L; nearneighbor -L;
grdview -–L). The boundary conditions come into play
when interpolating or computing derivatives near the limits of the
region covered by the grid. The default boundary
conditions used are those which are ``natural'' for the boundary
of a minimum curvature interpolating surface.
If the user knows that the data are periodic in x (and/or
y), or that the data cover a sphere with x,y
representing longitude,latitude, then there are better
choices for the boundary conditions.
Periodic conditions on x (and/or y) are chosen by
specifying x (and/or y) as the boundary condition flags;
global spherical cases are specified using the g (geographical)
flag. Behavior of these conditions is as follows:
-
- Periodic
- conditions on x indicate that the data are
periodic in the distance (
xmax - xmin) and thus repeat
values after every
N = (xmax - xmin)/xinc. Note that
this implies that in a grid-registered file the values in the first
and last columns are equal, since these are located at
x = xminand
x = xmax, and there are N + 1 columns in the file.
This is not the case in a pixel-registered file, where there are only
N and the first and last columns are located at
xmin + xinc/2 and
xmax - xinc/2. If y is
periodic all the same holds for y.
- Geographical
- conditions indicate the following:
- 1.
- If
and also 180 modulo
xinc = 0then a periodic condition is used on x with a period of 360;
else a default condition is used on the x boundaries.
- 2.
- If condition 1 is true and also
ymax = 90 then a
``north pole condition'' is used at ymax, else a default
condition is used there.
- 3.
- If condition 1 is true and also
ymin = -90 then a
``south pole condition'' is used at ymin, else a default
condition is used there.
``Pole conditions'' use a 180o phase-shift of the data,
requiring 180 modulo
xinc = 0.
- Default
- boundary conditions are
on the boundary, where f(x, y) is represented by the values in
the grid file, and
is the derivative in the direction normal to a
boundary, and
is the two-dimensional Laplacian operator.
Next: Sun raster files
Up: 2-D grdfiles
Previous: Pixel registration
Paul Wessel
1999-12-03