Mapping Hacks

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Chapter 3, Mapping Your World

#30 Plot a Great Circle on a Flat Map

HACK

Great Circles of Perl

In practice, great-circle routes are hard to navigate precisely, because the

bearing of a great circle relative to True North changes continually, unlike

that of a rhumb line. In fact, the conventional way to navigate a great-circle

route is to approximate it with a series of short rhumb lines. We can use this

same technique to draw the path of a great-circle arc on a flat map in Perl:

#!/usr/bin/perl

use Math::Trig qw(great_circle_direction deg2rad);

use Imager;

use strict;

my ($mapfile, $lon1, $lat1, $lon2, $lat2) = @ARGV;

my @origin = ($lon1, $lat1);

my @dest = ($lon2, $lat2);

my $step = .1;

my @position = @origin;

my @points;

until (abs($position[0] - $dest[0]) < $step

and abs($position[1] - $dest[1]) < $step) {

my $bearing = great_circle_direction(

deg2rad( $position[0] ),

Figure 3-33. Great-circle arc from San Francisco to London on a Gnomonic projection

Plot a Great Circle on a Flat Map #30

Chapter 3, Mapping Your World

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145

HACK

deg2rad( 90 - $position[1] ),

deg2rad( $dest[0] ),

deg2rad( 90 - $dest[1] )

);

$position[0] += sin($bearing) * $step / cos(deg2rad($position[1])) ;

$position[1] += cos($bearing) * $step;

$position[0] += 360 if $position[0] < -180;

$position[0] -= 360 if $position[0] > 180; ...