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 package Geo::Calc::XS;  | 
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 require 5.4.0;  | 
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 use XSLoader;  | 
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 our @ISA = qw( Exporter DynaLoader );  | 
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 our %EXPORT_TAGS = ( 'all' => [ 'new', 'distance_to' ] );  | 
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 our @EXPORT_OK = ( @{ $EXPORT_TAGS{'all'} } );  | 
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 our @EXPORT = ();  | 
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 our $VERSION = '0.33';  | 
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 XSLoader::load 'Geo::Calc::XS', $VERSION;  | 
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 # Copyright 2011-2014 by Sorin Alexandru Pop.  | 
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 # For other contributors see ChangeLog.  | 
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 # See the manual pages for details on the licensing terms.  | 
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 =head1 NAME  | 
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 Geo::Calc::XS - simple geo calculator for points and distances  | 
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 =head1 SYNOPSIS  | 
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31
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  use Geo::Calc::XS;  | 
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32
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33
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  my $gc            = Geo::Calc::XS->new( lat => 40.417875, lon => -3.710205 );  | 
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  my $lan           = $gc->get_lan();  | 
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  my $lon           = $gc->get_lon();  | 
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  my $radius        = $gc->get_radius();  | 
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  my $units         = $gc->get_units();  | 
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  my $distance      = $gc->distance_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
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  my $brng          = $gc->bearing_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
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  my $f_brng        = $gc->final_bearing_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
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  my $midpoint      = $gc->midpoint_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
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  my $destination   = $gc->destination_point( 90, 1, -6 );  | 
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  my $bbox          = $gc->boundry_box( 3, 4, -6 );  | 
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44
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  my $r_distance    = $gc->rhumb_distance_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
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  my $r_brng        = $gc->rhumb_bearing_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
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  my $r_destination = $gc->rhumb_destination_point( 30, 1, -6 );  | 
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  my $point         = $gc->intersection( 90, { lat => 40.422371, lon => -3.704298 }, 180, -6 );  | 
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49
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 =head1 DESCRIPTION  | 
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50
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51
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 B implements a variety of calculations for latitude/longitude points  | 
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52
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53
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 All these formulas are for calculations on the basis of a spherical earth  | 
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54
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 (ignoring ellipsoidal effects), which is accurate enough for most purposes.  | 
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56
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 [ In fact, the earth is very slightly ellipsoidal; using a spherical model  | 
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57
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 gives errors typically up to 0.3% ].  | 
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58
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59
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 Benchmarking this module and L I found out that this module is sometimes  | 
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60
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 more than 8000 times faster.  | 
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61
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62
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 This module is designed to be thread-safe, although, of course,  | 
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63
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 interpreter-based threads are officially discouraged (see  | 
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64
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 L).  | 
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65
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66
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 =head1 CAVEATS  | 
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67
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68
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 This is not a drop-in replacement for L, see the COMPATIBILITY  | 
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69
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 section further down.  | 
| 
70
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71
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 =head1 Geo::Calc::XS->new()  | 
| 
72
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73
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  $gc = Geo::Calc::XS->new( lat => 40.417875, lon => -3.710205 ); # Somewhere in Madrid  | 
| 
74
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  $gc = Geo::Calc::XS->new( lat => 51.503269, lon => 0, units => 'k-m' ); # The O2 Arena in London  | 
| 
75
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76
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 Creates a new Geo::Calc::XS object from a latitude and longitude. The default  | 
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77
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 decimal precision is -6 for all functions => meaning by default it always  | 
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78
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 returns the results with 6 decimals.  | 
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79
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80
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 The default unit distance is 'm' (meter), but you cand define another unit using C.  | 
| 
81
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 Accepted values are: 'm' (meters), 'k-m' (kilometers), 'yd' (yards), 'ft' (feet) and 'mi' (miles)  | 
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82
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| 
83
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 If a C parameter is passed, it is ignored.  | 
| 
84
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| 
85
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 Returns a reference to a C object.  | 
| 
86
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| 
87
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 =head2 Parameters  | 
| 
88
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| 
89
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 Each of these parameters can be accessed after construction using C,  | 
| 
90
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 C, C or C.  | 
| 
91
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| 
92
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 =over 4  | 
| 
93
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| 
94
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 =item lat  | 
| 
95
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96
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 => latitude of the point ( required )  | 
| 
97
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98
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 =item lon  | 
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99
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100
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 => longitude of the point ( required )  | 
| 
101
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102
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 =item radius  | 
| 
103
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| 
104
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 => earth radius in km ( defaults to 6371 )  | 
| 
105
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| 
106
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 =item units  | 
| 
107
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108
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 => the distance unit received and output by this object ( defaults to 'm' )  | 
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109
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110
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 =back  | 
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111
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112
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 =cut  | 
| 
113
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| 
114
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 =head1 METHODS  | 
| 
115
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| 
116
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 =head2 distance_to  | 
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117
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| 
118
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  $gc->distance_to( $point[, $precision] )  | 
| 
119
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  $gc->distance_to( { lat => 40.422371, lon => -3.704298 } )  | 
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120
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  $gc->distance_to( Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ) )  | 
| 
121
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122
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 This uses the "haversine" formula to calculate great-circle distances between  | 
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123
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 the two points - that is, the shortest distance over the earth's surface -  | 
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124
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 giving an `as-the-crow-flies` distance between the points (ignoring any hills!)  | 
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125
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126
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 The haversine formula `remains particularly well-conditioned for numerical  | 
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127
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 computation even at small distances` - unlike calculations based on the spherical  | 
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128
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 law of cosines. It was published by R W Sinnott in Sky and Telescope, 1984,  | 
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129
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 though known about for much longer by navigators. (For the curious, c is the  | 
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130
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 angular distance in radians, and a is the square of half the chord length between  | 
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131
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 the points).  | 
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132
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133
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 Returns with the distance using the precision defined or -6  | 
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134
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 ( -6 = 6 decimals ( eg 4.000001 ) ), in this object's distance unit.  | 
| 
135
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136
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 =cut  | 
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138
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 =head2 bearing_to  | 
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140
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  $gc->bearing_to( $point[, $precision] );  | 
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141
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  $gc->bearing_to( { lat => 40.422371, lon => -3.704298 }, -6 );  | 
| 
142
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  $gc->bearing_to( Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ), -6 );  | 
| 
143
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    | 
| 
144
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 In general, your current heading will vary as you follow a great circle path  | 
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145
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 (orthodrome); the final heading will differ from the initial heading by varying  | 
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146
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 degrees according to distance and latitude (if you were to go from say 35N,45E  | 
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 (Baghdad) to 35N,135E (Osaka), you would start on a heading of 60 and end up on  | 
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 a heading of 120!).  | 
| 
149
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150
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 This formula is for the initial bearing (sometimes referred to as forward  | 
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 azimuth) which if followed in a straight line along a great-circle arc will take  | 
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152
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 you from the start point to the end point  | 
| 
153
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| 
154
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 Returns the (initial) bearing from this point to the supplied point, in degrees  | 
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155
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 with the specified pricision  | 
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156
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| 
157
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 See L  | 
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 =cut  | 
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160
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161
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 =head2 final_bearing_to  | 
| 
162
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    | 
| 
163
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 | 
  my $f_brng = $gc->final_bearing_to( $point[, $precision] );  | 
| 
164
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 | 
  my $f_brng = $gc->final_bearing_to( { lat => 40.422371, lon => -3.704298 } );  | 
| 
165
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  my $f_brng = $gc->final_bearing_to( Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ) );  | 
| 
166
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
167
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns final bearing (in degrees) arriving at supplied destination point from  | 
| 
168
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 this point; the final bearing will differ from the initial bearing by varying  | 
| 
169
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 degrees according to distance and latitude  | 
| 
170
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
    | 
| 
171
 | 
 
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 =cut  | 
| 
172
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    | 
| 
173
 | 
 
 | 
 
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 =head2 midpoint_to  | 
| 
174
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
175
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->midpoint_to( $point[, $precision] );  | 
| 
176
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->midpoint_to( { lat => 40.422371, lon => -3.704298 } );  | 
| 
177
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->midpoint_to( Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ) );  | 
| 
178
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
179
 | 
 
 | 
 
 | 
 
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 | 
 Returns the midpoint along a great circle path between the initial point and  | 
| 
180
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
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 the supplied point.  | 
| 
181
 | 
 
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 | 
    | 
| 
182
 | 
 
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 | 
 
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 See L for derivation  | 
| 
183
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 | 
    | 
| 
184
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 =cut  | 
| 
185
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    | 
| 
186
 | 
 
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 =head2 destination_point  | 
| 
187
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
188
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->destination_point( $bearing, $distance[, $precision] );  | 
| 
189
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->destination_point( 90, 1 );  | 
| 
190
 | 
 
 | 
 
 | 
 
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 | 
 
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 | 
    | 
| 
191
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the destination point and the final bearing using Vincenty inverse  | 
| 
192
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 formula for ellipsoids.  | 
| 
193
 | 
 
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 | 
 
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 | 
 
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    | 
| 
194
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 C<$bearing> must be specified in degrees, where 0 is north and 90 is east, and  | 
| 
195
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 C<$distance> must be specified in this object's distance unit.  | 
| 
196
 | 
 
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    | 
| 
197
 | 
 
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 | 
 
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 =cut  | 
| 
198
 | 
 
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    | 
| 
199
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 boundry_box  | 
| 
200
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
201
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->boundry_box( $width[, $height[, $precision]] );  | 
| 
202
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->boundry_box( 3, 4 ); # will generate a 3x4m box around the point, assuming the object's distance unit is meters  | 
| 
203
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->boundry_box( 1 ); # will generate a 2x2m box around the point (radius), assuming the object's distance unit is meters  | 
| 
204
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
205
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the boundry box min/max having the initial point defined as the center  | 
| 
206
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 of the boundry box, given the width and height.  | 
| 
207
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
208
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 If only one dimension has been specified, than that dimension is considered a  | 
| 
209
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 radius.  | 
| 
210
 | 
 
 | 
 
 | 
 
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    | 
| 
211
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Dimensions should be specified in the object's distance unit.  | 
| 
212
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 
 | 
    | 
| 
213
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 =cut  | 
| 
214
 | 
 
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 | 
 
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 | 
    | 
| 
215
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 rhumb_distance_to  | 
| 
216
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
217
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_distance_to( $point[, $precision] );  | 
| 
218
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_distance_to( { lat => 40.422371, lon => -3.704298 } );  | 
| 
219
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_distance_to( Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ) );  | 
| 
220
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
221
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the distance from this point to the supplied point, in the object's  | 
| 
222
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 distance unit, travelling along a rhumb line.  | 
| 
223
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
224
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A 'rhumb line' (or loxodrome) is a path of constant bearing, which crosses all  | 
| 
225
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 meridians at the same angle.  | 
| 
226
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
227
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Sailors used to (and sometimes still) navigate along rhumb lines since it is  | 
| 
228
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 easier to follow a constant compass bearing than to be continually adjusting  | 
| 
229
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the bearing, as is needed to follow a great circle. Rhumb lines are straight  | 
| 
230
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 lines on a Mercator Projection map (also helpful for navigation).  | 
| 
231
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
232
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Rhumb lines are generally longer than great-circle (orthodrome) routes. For  | 
| 
233
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 instance, London to New York is 4% longer along a rhumb line than along a  | 
| 
234
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 great circle . important for aviation fuel, but not particularly to sailing  | 
| 
235
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 vessels. New York to Beijing . close to the most extreme example possible  | 
| 
236
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 (though not sailable!) . is 30% longer along a rhumb line.  | 
| 
237
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
238
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 See L  | 
| 
239
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
240
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =cut  | 
| 
241
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
242
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 rhumb_bearing_to  | 
| 
243
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
244
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_bearing_to( $point[, $precision] );  | 
| 
245
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_bearing_to( { lat => 40.422371, lon => -3.704298 } );  | 
| 
246
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_bearing_to( Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ) );  | 
| 
247
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
248
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the bearing from this point to the supplied point along a rhumb line,  | 
| 
249
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 in degrees  | 
| 
250
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
251
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =cut  | 
| 
252
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
253
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 rhumb_destination_point  | 
| 
254
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
255
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_destination_point( $brng, $distance[, $precision] );  | 
| 
256
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->rhumb_destination_point( 30, 1 );  | 
| 
257
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
258
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the destination point from this point having travelled the given  | 
| 
259
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 distance (in the object's distance unit) on the given bearing along a rhumb  | 
| 
260
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 line.  | 
| 
261
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
262
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =cut  | 
| 
263
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
264
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 intersection  | 
| 
265
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
266
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->intersection( $brng1, $point, $brng2[, $precision] );  | 
| 
267
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->intersection( 90, { lat => 40.422371, lon => -3.704298 }, 180 );  | 
| 
268
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  $gc->intersection( 90, Geo::Calc::XS->new( lat => 40.422371, lon => -3.704298 ), 180 );  | 
| 
269
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
270
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the point of intersection of two paths defined by point and bearing  | 
| 
271
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
272
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 See L  | 
| 
273
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
274
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =cut  | 
| 
275
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
276
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head2 distance_at  | 
| 
277
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
278
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Returns the distance in meters for 1deg of latitude and longitude at the  | 
| 
279
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 specified latitude.  | 
| 
280
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
281
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  my $m_distance = $self->distance_at([$precision]);  | 
| 
282
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  my $m_distance = $self->distance_at();  | 
| 
283
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
  # at lat 2 with precision -6 returns { m_lat => 110575.625009, m_lon => 111252.098718 }  | 
| 
284
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
285
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Note that this method always returns distances in meters, unlike all the other  | 
| 
286
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 methods which use the object's distance unit. This is kept as it is for backwards  | 
| 
287
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 compatibility.  | 
| 
288
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
289
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 COMPATIBILITY  | 
| 
290
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
291
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A B object does not have the same interface as a L  | 
| 
292
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 object, despite the similarities.  | 
| 
293
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
294
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Here are the currently known differences:  | 
| 
295
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
296
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
297
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
298
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item  | 
| 
299
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
300
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 C is provided by L but not by this module.  | 
| 
301
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
302
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item  | 
| 
303
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
304
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The constructor for L accepts a C parameter, but this module ignores it.  | 
| 
305
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
306
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item  | 
| 
307
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
308
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Methods with identicial names perform similar functions but may return  | 
| 
309
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 different results after a few decimal places.  | 
| 
310
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
311
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item  | 
| 
312
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
313
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 It's undocumented whether L is thread-safe, whereas this module does  | 
| 
314
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 intend to be thread-safe.  | 
| 
315
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
316
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
317
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
318
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 SEE ALSO  | 
| 
319
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
320
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 L is the original implementation, which is abandoned at time of  | 
| 
321
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 writing (Aug 2014).  | 
| 
322
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
323
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 REPOSITORY  | 
| 
324
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
325
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 L  | 
| 
326
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
327
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 BUGS  | 
| 
328
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
329
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 All complex software has bugs lurking in it, and this module is no  | 
| 
330
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 exception.  | 
| 
331
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
332
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Please report any bugs through the web interface at L.  | 
| 
333
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
334
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 AUTHOR  | 
| 
335
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
336
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Sorin Alexandru Pop C<<  >>  | 
| 
337
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
338
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 THANKS  | 
| 
339
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
340
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Marius Crisan C<<  >>  | 
| 
341
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
342
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 David D Lowe C<<  >>  | 
| 
343
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
344
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Chris Hughes C<<  >>  | 
| 
345
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
346
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 LICENSE  | 
| 
347
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
348
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This program is free software; you can redistribute it and/or  | 
| 
349
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 modify it under the same terms as Perl itself.  | 
| 
350
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
351
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 See L  | 
| 
352
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
353
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =cut  | 
| 
354
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
355
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 __END__  |