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**pP**to indicate CW azimuths rather than CCW directions - Optionally, append / in degrees to indicate an angular offset [0]

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 grdfiles.

grdmath -R0/360/2/4 -I6/0.1 X 4 MUL PI MUL 180 DIV COS Y 2 POW MUL = test.grd grdcontour test.grd -JP3i -B30Ns -P -C2 -S4 --PLOT_DEGREE_FORMAT=+ddd > GMT_polar.ps rm -f test.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.