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# Trigonometric functions, mostly inherited from Math::Complex.
# -- Jarkko Hietaniemi, since April 1997
# -- Raphael Manfredi, September 1996 (indirectly: because of Math::Complex)
#
package Math::Trig;
{ use 5.006; }
use strict;
use Math::Complex 1.59;
use Math::Complex qw(:trig :pi);
require Exporter;
our @ISA = qw(Exporter);
our $VERSION = 1.23;
my @angcnv = qw(rad2deg rad2grad
deg2rad deg2grad
grad2rad grad2deg);
my @areal = qw(asin_real acos_real);
our @EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}},
@angcnv, @areal);
my @rdlcnv = qw(cartesian_to_cylindrical
cartesian_to_spherical
cylindrical_to_cartesian
cylindrical_to_spherical
spherical_to_cartesian
spherical_to_cylindrical);
my @greatcircle = qw(
great_circle_distance
great_circle_direction
great_circle_bearing
great_circle_waypoint
great_circle_midpoint
great_circle_destination
);
my @pi = qw(pi pi2 pi4 pip2 pip4);
our @EXPORT_OK = (@rdlcnv, @greatcircle, @pi, 'Inf');
# See e.g. the following pages:
# http://www.movable-type.co.uk/scripts/LatLong.html
# http://williams.best.vwh.net/avform.htm
our %EXPORT_TAGS = ('radial' => [ @rdlcnv ],
'great_circle' => [ @greatcircle ],
'pi' => [ @pi ]);
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.
#
sub _remt ($$) {
# Oh yes, POSIX::fmod() would be faster. Possibly. If it is available.
$_[0] - $_[1] * int($_[0] / $_[1]);
}
#
# Angle conversions.
#
sub rad2rad($) { _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 ($;$) { my $d = _DR * $_[0]; $_[1] ? $d : rad2rad($d) }
sub grad2deg ($;$) { my $d = _GD * $_[0]; $_[1] ? $d : deg2deg($d) }
sub deg2grad ($;$) { my $d = _DG * $_[0]; $_[1] ? $d : grad2grad($d) }
sub rad2grad ($;$) { my $d = _RG * $_[0]; $_[1] ? $d : grad2grad($d) }
sub grad2rad ($;$) { my $d = _GR * $_[0]; $_[1] ? $d : rad2rad($d) }
#
# acos and asin functions which always return a real number
#
sub acos_real {
return 0 if $_[0] >= 1;
return pi if $_[0] <= -1;
return acos($_[0]);
}
sub asin_real {
return &pip2 if $_[0] >= 1;
return -&pip2 if $_[0] <= -1;
return asin($_[0]);
}
sub cartesian_to_spherical {
my ( $x, $y, $z ) = @_;
my $rho = sqrt( $x * $x + $y * $y + $z * $z );
return ( $rho,
atan2( $y, $x ),
$rho ? acos_real( $z / $rho ) : 0 );
}
sub spherical_to_cartesian {
my ( $rho, $theta, $phi ) = @_;