(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 arrival [1]. 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.

The script produces the plot in Figure; 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) Global distribution of antipodes).

#!/usr/bin/env bash
#		GMT EXAMPLE 23
#
# Purpose:	Plot distances from Rome and draw shortest paths
# GMT modules:	grdmath, grdcontour, coast, plot, text, grdtrack
# Unix progs:	echo, cat
#
gmt begin ex23
	# 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
	gmt grdmath -Rg -I1 $lon $lat SDIST = dist.nc

	# Location info for 5 other cities + label justification
	cat <<- END > cities.txt
	105.87	21.02	LM	HANOI
	282.95	-12.1	LM	LIMA
	178.42	-18.13	LM	SUVA
	237.67	47.58	RM	SEATTLE
	28.20	-25.75	LM	PRETORIA
	END
	gmt coast -Rg -JH90/25c -Glightgreen -Sblue -A1000 -Bg30 -B+t"Distances from $name to the World" -Wthinnest

	gmt grdcontour dist.nc -A1000+v+u" km"+fwhite -Glz-/z+ -S8 -C500 -Wathin,white -Wcthinnest,white,-

	# For each of the cities, plot great circle arc to Rome with gmt plot
	gmt plot -Wthickest,red -Fr$lon/$lat cities.txt

	# Plot red squares at cities and plot names:
	gmt plot -Ss0.5c -Gred -Wthinnest cities.txt
	gmt text -Dj10p/0 -F+f12p,Courier-Bold,red+j -N cities.txt
	# Place a yellow star at Rome
	echo "$lon $lat" | gmt plot -Sa0.5c -Gyellow -Wthin

	# Sample the distance grid at the cities and use the distance in integer km for labels
	gmt grdtrack -Gdist.nc cities.txt -o0:2 --FORMAT_FLOAT_OUT=0:%g,1:%g,2:%.0f \
		| gmt text -D0/-12p -N -Gwhite -W -C2p -F+f12p,Helvetica-Bold+jCT

	# Clean up after ourselves:
	rm -f cities.txt dist.nc
gmt end show
../_images/ex23.png

All great-circle paths lead to Rome.

Footnote

[1]Pedants who wish to argue about the “other” arc going the long way should consider using it.