| Description: |
A while back my younger sister asked me to help her with homework from her college trig course. She had to solve a Great Circle Distance problem. After showing her the steps, it got me to thinking, and then reading, and then finally coding. What I found was quite interesting, and from that research spawned an application to find the distances between to corporate locations from their zip codes that I implemented on our intranet.
There are actually a couple of different methods for determining the distance between 2 long/lat pairs and
you need to be aware of the accuracy of each. The Great Circle method is the least accurate IIRC, but is the most accessible, as it is a part of Math::Trig.
I wrote some code to do this using the various methods. As I mentioned, it finds the distances between two zip codes for which the long/lat pairs are known, but I've removed the database interface for brevity and just given the pertinent code.
You should also read:
this, this and (my favorite) this article.
I was pretty explicit in my code so that my non-programming sister could understand it when I showed it too her to explain the different algorithms, but I think it gets the point across.
C-.
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use strict;
use Math::Trig qw(deg2rad pi great_circle_distance asin acos);
############################
## Distances are in Miles ##
############################
my ($lat1, $long1);
my ($lat2, $long2);
print "Haversine : ". &Haversine($lat1, $long1, $lat2, $long2) ."\n"
+;
print "Law Cosines : ". &LawCosines($lat1, $long1, $lat2, $long2)."\n"
+;
print "Flat-Earth : ". &FlatEarth($lat1, $long1, $lat2, $long2) ."\n"
+;
print "Great Circle: ". &GreatCircle($lat1, $long1, $lat2, $long2)."\n
+";
sub LawCosines {
my ($lat1, $long1, $lat2, $long2) = @_;
my $r=3956;
my $dist = acos(sin(deg2rad($lat1))*
sin(deg2rad($lat2))+
cos(deg2rad($lat1))*
cos(deg2rad($lat2))*
cos(deg2rad($long2)- deg2rad($long1)))
* $r;
return $dist;
}
sub FlatEarth {
my ($lat1, $long1, $lat2, $long2) = @_;
my $r=3956;
my $a = (pi/2)- deg2rad($lat1);
my $b = (pi/2)- deg2rad($lat2);
my $c = sqrt($a**2 + $b**2 - 2 * $a *$b
*cos(deg2rad($long2)-deg2rad($long1)));
my $dist = $c * $r;
return $dist;
}
sub Haversine {
my ($lat1, $long1, $lat2, $long2) = @_;
my $r=3956;
$dlong = deg2rad($long1) - deg2rad($long2);
$dlat = deg2rad($lat1) - deg2rad($lat2);
$a = sin($dlat/2)**2 +cos(deg2rad($lat1))
* cos(deg2rad($lat2))
* sin($dlong/2)**2;
$c = 2 * (asin(sqrt($a)));
$dist = $r * $c;
return $dist;
}
sub GreatCircle {
my ($lat1, $long1, $lat2, $long2) = @_;
my $r=3956;
my @zip1 = (deg2rad($long1), deg2rad(90-$lat1));
my @zip2 = (deg2rad($long2), deg2rad(90-$lat2));
my $dist = great_circle_distance(@zip1, @zip2,$r);
return $dist;
}
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