| Subject: | great_circle_direction is inaccurate when points are close together |
| Date: | Sat, 30 Oct 2010 03:20:35 +1000 |
| To: | <bug-Math-Complex [...] rt.cpan.org> |
| From: | Daniel Burr <dburr [...] topcon.com> |
The current implementation of <Math::Trig::great_circle_direction> is
incorrect when the points are very close together (and can trigger a
divide-by-zero error in extreme cases). This better implementation is
based on the formula at http://williams.best.vwh.net/avform.htm#Crs
Also note that the documentation for
<Math::Trig::great_circle_direction> is incorrect - it returns a value
in the range (0, 2*pi) not (-pi, pi) as stated.
sub great_circle_direction {
my ($theta0, $phi0, $theta1, $phi1) = @_;
$phi0 = pi / 2 - $phi0;
$phi1 = pi / 2 - $phi1;
my $tc = -atan2(sin($theta0-$theta1)*cos($phi1),
cos($phi0)*sin($phi1)-sin($phi0)*cos($phi1)*cos($theta0-$theta1));
$tc += 2*pi while($tc < 0);
$tc -= 2*pi while($tc > 2*pi);
return $tc;
}
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