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7.23 All great-circle paths lead to Rome

While motorists recently have started to question the old saying ``all roads lead to Rome'', aircraft pilots have known from the start that only one great-circle path connects the points of departure and arrival7.5. This provides the inspiration for our next example which uses grdmath to calculate distances from Rome to anywhere on Earth and grdcontour to contour these distances. We pick five cities that we connect to Rome with great circle arcs, and label these cities with their names and distances (in km) from Rome, all laid down on top of a beautiful world map. Note that we specify that contour labels only be placed along the straight map-line connecting Rome to its antipode, and request curved labels that follows the shape of the contours.

    #!/bin/sh
    #               GMT EXAMPLE 23
    #
    # Purpose:      Plot distances from Rome and draw shortest paths
    # GMT progs:    grdmath, grdcontour, pscoast, psxy, pstext, grdtrack
    # Unix progs:   echo, cat, awk
    #
    ps=example_23.ps

    # Position and name of central point:

    lon=12.50
    lat=41.99
    name="Rome"

    # Calculate distances (km) to all points on a global 1x1 grid

    grdmath -Rg -I1 $lon $lat SDIST 111.13 MUL = dist.grd

    # Location info for 5 other cities + label justification

    cat << EOF > cities.d
    105.87  21.02   HANOI           LM
    282.95  -12.1   LIMA            LM
    178.42  -18.13  SUVA            LM
    237.67  47.58   SEATTLE         RM
    28.20   -25.75  PRETORIA        LM
    EOF

    pscoast -Rg -JH90/9i -Glightgreen -Sblue -U"Example 23 in Cookbook" -A1000 \
            -B0g30:."Distances from $name to the World": -K -Dc -Wthinnest > $ps

    grdcontour dist.grd -A1000+v+ukm+kwhite -Glz-/z+ -S8 -C500 -O -K -J \
            -Wathin,white -Wcthinnest,white,- >> $ps

    # For each of the cities, plot great circle arc to Rome with psxy

    while read clon clat city; do
            (echo $lon $lat; echo $clon $clat) | psxy -R -J -O -K -Wthickest/red >> $ps
    done < cities.d

    # Plot red squares at cities and plot names:
    psxy -R -J -O -K -Ss0.2 -Gred -Wthinnest cities.d >> $ps
    awk '{print $1, $2, 12, 1, 9, $4, $3}' cities.d | pstext -R -J -O -K -Dj0.15/0 -Gred -N >> $ps
    # Place a yellow star at Rome
    echo "$lon $lat" | psxy -R -J -O -K -Sa0.2i -Gyellow -Wthin >> $ps

    # Sample the distance grid at the cities and use the distance in km for labels

    grdtrack -Gdist.grd cities.d \
            | awk '{printf "%s %s 12 0 1 CT %d\n", $1, $2, int($NF+0.5)}' \
            | pstext -R -J -O -D0/-0.2i -N -Wwhite,o -C0.02i/0.02i >> $ps

    # Clean up after ourselves:

    rm -f cities.d dist.grd .gmt*

Figure 7.23: All great-circle paths lead to Rome.

The script produces the plot in Figure 7.23; note how interesting the path to Seattle appears in this particular projection (Hammer). We also note that Rome's antipode lies somewhere near the Chatham plateau (antipodes will be revisited in Example 25).

Next: 7.24 Data selection based Up: 7. Cook-book Previous: 7.22 World-wide seismicity the Contents Index