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Figure 5.6:
Polar (Cylindrical) transformation of
(
) coordinates.
|
This transformation converts polar coordinates (angle
and radius
)
to positions on a plot. Now
and
, hence it is similar
to a regular map projection because
and
are coupled and
(i.e.,
) has a 360° periodicity.
With input and output points both in the plane it is a two-dimensional projection.
The transformation comes in two flavors:
- Normally,
is understood to be directions counter-clockwise from the horizontal axis, but we may choose
to specify an angular offset [whose default value is zero]. We will call this offset
.
Then,
and
.
- Alternatively,
can be interpreted to be azimuths clockwise from the vertical axis, yet we may again
choose to specify the angular offset [whose default value is zero].
Then,
and
.
Consequently, the polar transformation is defined by providing
- scale in inches/unit (-Jp) or full width of plot in inches (-JP)
- Optionally, insert a after p
P to indicate CW azimuths rather than CCW directions
- Optionally, append /
in degrees to indicate an angular offset [0]
- Optionally, append r to reverse the radial direction (here, south and north must be elevations in 0-90° range).
- Optionally, append z to annotate depths rather than radius.
As an example of this projection we will create a gridded data set
in polar coordinates
using grdmath, a RPN calculator that operates on or
creates grid files.
grdmath -R0/360/2/4 -I6/0.1 X 4 MUL PI MUL 180 DIV COS Y 2 POW MUL = $$.grd
grdcontour $$.grd -JP3i -B30Ns -P -C2 -S4 --PLOT_DEGREE_FORMAT=+ddd > GMT_polar.ps
rm -f $$.grd
We used grdcontour to make a contour map of this data. Because
the data file only contains values with
, a donut
shaped plot appears in Figure 5.6.
Next: 6. GMT Map Projections
Up: 5. GMT Coordinate Transformations
Previous: 5.1.3 Cartesian power projection
Contents
Index
Paul Wessel
2008-05-15