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# 5.2 Linear projection with polar () coordinates (-Jp -JP)

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:

1. 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 .
2. 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]
- 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