require Exporter;
package Math::Trig;
+use 5.005_64;
use strict;
use Math::Complex qw(:trig);
-use vars qw($VERSION $PACKAGE
- @ISA
- @EXPORT @EXPORT_OK %EXPORT_TAGS);
+our($VERSION, $PACKAGE, @ISA, @EXPORT, @EXPORT_OK, %EXPORT_TAGS);
@ISA = qw(Exporter);
%EXPORT_TAGS = ('radial' => [ @rdlcnv ]);
-use constant pi2 => 2 * pi;
-use constant pip2 => pi / 2;
-use constant DR => pi2/360;
-use constant RD => 360/pi2;
-use constant DG => 400/360;
-use constant GD => 360/400;
-use constant RG => 400/pi2;
-use constant GR => pi2/400;
+sub pi2 () { 2 * pi }
+sub pip2 () { pi / 2 }
+
+sub DR () { pi2/360 }
+sub RD () { 360/pi2 }
+sub DG () { 400/360 }
+sub GD () { 360/400 }
+sub RG () { 400/pi2 }
+sub GR () { pi2/400 }
#
# Truncating remainder.
# Angle conversions.
#
-sub rad2deg ($) { remt(RD * $_[0], 360) }
+sub rad2rad($) { remt($_[0], pi2) }
+
+sub deg2deg($) { remt($_[0], 360) }
+
+sub grad2grad($) { remt($_[0], 400) }
+
+sub rad2deg ($;$) { my $d = RD * $_[0]; $_[1] ? $d : deg2deg($d) }
-sub deg2rad ($) { remt(DR * $_[0], pi2) }
+sub deg2rad ($;$) { my $d = DR * $_[0]; $_[1] ? $d : rad2rad($d) }
-sub grad2deg ($) { remt(GD * $_[0], 360) }
+sub grad2deg ($;$) { my $d = GD * $_[0]; $_[1] ? $d : deg2deg($d) }
-sub deg2grad ($) { remt(DG * $_[0], 400) }
+sub deg2grad ($;$) { my $d = DG * $_[0]; $_[1] ? $d : grad2grad($d) }
-sub rad2grad ($) { remt(RG * $_[0], 400) }
+sub rad2grad ($;$) { my $d = RG * $_[0]; $_[1] ? $d : grad2grad($d) }
-sub grad2rad ($) { remt(GR * $_[0], pi2) }
+sub grad2rad ($;$) { my $d = GR * $_[0]; $_[1] ? $d : rad2rad($d) }
sub cartesian_to_spherical {
my ( $x, $y, $z ) = @_;
=head1 SYNOPSIS
use Math::Trig;
-
+
$x = tan(0.9);
$y = acos(3.7);
$z = asin(2.4);
-
+
$halfpi = pi/2;
$rad = deg2rad(120);
details like for example how to display complex numbers. For example:
print asin(2), "\n";
-
+
should produce something like this (take or leave few last decimals):
1.5707963267949-1.31695789692482i
$radians = deg2rad($degrees);
$radians = grad2rad($gradians);
-
+
$degrees = rad2deg($radians);
$degrees = grad2deg($gradians);
-
+
$gradians = deg2grad($degrees);
$gradians = rad2grad($radians);
The full circle is 2 I<pi> radians or I<360> degrees or I<400> gradians.
+The result is by default wrapped to be inside the [0, {2pi,360,400}[ circle.
+If you don't want this, supply a true second argument:
+
+ $zillions_of_radians = deg2rad($zillions_of_degrees, 1);
+ $negative_degrees = rad2deg($negative_radians, 1);
+
+You can also do the wrapping explicitly by rad2rad(), deg2deg(), and
+grad2grad().
=head1 RADIAL COORDINATE CONVERSIONS
$km = great_circle_distance(@L, @T, 6378);
The answer may be off by few percentages because of the irregular
-(slightly aspherical) form of the Earth.
+(slightly aspherical) form of the Earth. The used formula
+
+ lat0 = 90 degrees - phi0
+ lat1 = 90 degrees - phi1
+ d = R * arccos(cos(lat0) * cos(lat1) * cos(lon1 - lon01) +
+ sin(lat0) * sin(lat1))
+
+is also somewhat unreliable for small distances (for locations
+separated less than about five degrees) because it uses arc cosine
+which is rather ill-conditioned for values close to zero.
=head1 BUGS
=head1 AUTHORS
Jarkko Hietaniemi <F<jhi@iki.fi>> and
-Raphael Manfredi <F<Raphael_Manfredi@grenoble.hp.com>>.
+Raphael Manfredi <F<Raphael_Manfredi@pobox.com>>.
=cut