--- /dev/null
+package Math::Trig::Radial;
+
+use strict;
+use vars qw(@ISA @EXPORT);
+@ISA = qw(Exporter);
+
+@EXPORT =
+ qw(
+ cartesian_to_cylindrical
+ cartesian_to_spherical
+ cylindrical_to_cartesian
+ cylindrical_to_spherical
+ spherical_to_cartesian
+ spherical_to_cylindrical
+ great_circle_distance
+ );
+
+use Math::Trig;
+
+sub pip2 { pi/2 }
+
+=pod
+
+=head1 NAME
+
+Math::Trig::Radial - spherical and cylindrical trigonometry
+
+=head1 SYNOPSIS
+
+ use Math::Trig::Radial;
+
+ ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z);
+ ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z);
+ ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z);
+ ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);
+ ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi);
+ ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);
+
+=head1 DESCRIPTION
+
+This module contains a few basic spherical and cylindrical
+trigonometric formulas. B<All angles are in radians>, if needed
+use C<Math::Trig> angle unit conversions.
+
+=head2 COORDINATE SYSTEMS
+
+B<Cartesian> coordinates are the usual rectangular I<xyz>-coordinates.
+
+Spherical coordinates are three-dimensional coordinates which define a
+point in three-dimensional space. They are based on a sphere surface.
+The radius of the sphere is B<rho>, also known as the I<radial>
+coordinate. The angle in the I<xy>-plane (around the I<z>-axis) is
+B<theta>, also known as the I<azimuthal> coordinate. The angle from
+the I<z>-axis is B<phi>, also known as the I<polar> coordinate. The
+`North Pole' is therefore I<0, 0, rho>, and the `Bay of Guinea' (think
+Africa) I<0, pi/2, rho>.
+
+Cylindrical coordinates are three-dimensional coordinates which define
+a point in three-dimensional space. They are based on a cylinder
+surface. The radius of the cylinder is B<rho>, also known as the
+I<radial> coordinate. The angle in the I<xy>-plane (around the
+I<z>-axis) is B<theta>, also known as the I<azimuthal> coordinate.
+The third coordinate is the I<z>.
+
+=head2 CONVERSIONS
+
+Conversions to and from spherical and cylindrical coordinates are
+available. Please notice that the conversions are not necessarily
+reversible because of the equalities like I<pi> angles equals I<-pi>
+angles.
+
+=over 4
+
+=item cartesian_to_cylindrical
+
+ ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z);
+
+=item cartesian_to_spherical
+
+ ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z);
+
+=item cylindrical_to_cartesian
+
+ ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z);
+
+=item cylindrical_to_spherical
+
+ ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);
+
+Notice that when C<$z> is not 0 C<$rho_s> is not equal to C<$rho_c>.
+
+=item spherical_to_cartesian
+
+ ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi);
+
+=item spherical_to_cylindrical
+
+ ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);
+
+Notice that when C<$z> is not 0 C<$rho_c> is not equal to C<$rho_s>.
+
+=back
+
+=head2 GREAT CIRCLE DISTANCE
+
+ $distance = great_circle_distance($x0, $y0, $z0, $x1, $y1, $z1 [, $rho]);
+
+The I<great circle distance> is the shortest distance between two
+points on a sphere. The distance is in C<$rho> units. The C<$rho> is
+optional, it defaults to 1 (the unit sphere), therefore the distance
+defaults to radians. The coordinates C<$x0> ... C<$z1> are in
+cartesian coordinates.
+
+=head EXAMPLES
+
+To calculate the distance between London (51.3N 0.5W) and Tokyo (35.7N
+139.8E) in kilometers:
+
+ use Math::Trig::Radial;
+ use Math::Trig;
+
+ my @L = spherical_to_cartesian(1, map { deg2rad $_ } qw(51.3 -0.5));
+ my @T = spherical_to_cartesian(1, map { deg2rad $_ } qw(35.7 139.8));
+
+ $km = great_circle_distance(@L, @T, 6378);
+
+The answer may be off by up to 0.3% because of the irregular (slightly
+aspherical) form of the Earth.
+
+=head2 AUTHOR
+
+Jarkko Hietaniemi F<E<lt>jhi@iki.fiE<gt>>
+
+=cut
+
+sub cartesian_to_spherical {
+ my ( $x, $y, $z ) = @_;
+
+ my $rho = sqrt( $x * $x + $y * $y + $z * $z );
+
+ return ( $rho,
+ atan2( $y, $x ),
+ $rho ? acos( $z / $rho ) : 0 );
+}
+
+sub spherical_to_cartesian {
+ my ( $rho, $theta, $phi ) = @_;
+
+ return ( $rho * cos( $theta ) * sin( $phi ),
+ $rho * sin( $theta ) * sin( $phi ),
+ $rho * cos( $phi ) );
+}
+
+sub spherical_to_cylindrical {
+ my ( $x, $y, $z ) = spherical_to_cartesian( @_ );
+
+ return ( sqrt( $x * $x + $y * $y ), $_[1], $z );
+}
+
+sub cartesian_to_cylindrical {
+ my ( $x, $y, $z ) = @_;
+
+ return ( sqrt( $x * $x + $y * $y ), atan2( $y, $x ), $z );
+}
+
+sub cylindrical_to_cartesian {
+ my ( $rho, $theta, $z ) = @_;
+
+ return ( $rho * cos( $theta ), $rho * sin( $theta ), $z );
+}
+
+sub cylindrical_to_spherical {
+ return ( cartesian_to_spherical( cylindrical_to_cartesian( @_ ) ) );
+}
+
+sub great_circle_distance {
+ my ( $x0, $y0, $z0, $x1, $y1, $z1, $rho ) = @_;
+
+ $rho = 1 unless defined $rho; # Default to the unit sphere.
+
+ my ( $r0, $theta0, $phi0 ) = cartesian_to_spherical( $x0, $y0, $z0 );
+ my ( $r1, $theta1, $phi1 ) = cartesian_to_spherical( $x1, $y1, $z1 );
+
+ my $lat0 = pip2 - $phi0;
+ my $lat1 = pip2 - $phi1;
+
+ return $rho *
+ acos(cos( $lat0 ) * cos( $lat1 ) * cos( $theta0 - $theta1 ) +
+ sin( $lat0 ) * sin( $lat1 ) );
+}
+
+1;
+
projects / p5sagit/p5-mst-13.2.git / commitdiff