great_circle_direction() was broken,

reported by Alexander Becher.

p4raw-id: //depot/perl@19376

diff --git a/lib/Math/Trig.pm b/lib/Math/Trig.pm
index 9e653c8..7560df5 100644 (file)
--- a/lib/Math/Trig.pm
+++ b/lib/Math/Trig.pm
@@ -19,8 +19,8 @@ our($VERSION, $PACKAGE, @ISA, @EXPORT, @EXPORT_OK, %EXPORT_TAGS);
 $VERSION = 1.02;
 
 my @angcnv = qw(rad2deg rad2grad
-            deg2rad deg2grad
-            grad2rad grad2deg);
+               deg2rad deg2grad
+               grad2rad grad2deg);
 
 @EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}},
           @angcnv);
@@ -133,13 +133,17 @@ sub great_circle_distance {
 sub great_circle_direction {
     my ( $theta0, $phi0, $theta1, $phi1 ) = @_;
 
+    my $distance = &great_circle_distance;
+
     my $lat0 = pip2 - $phi0;
     my $lat1 = pip2 - $phi1;
 
     my $direction =
-       atan2(sin($theta0 - $theta1) * cos($lat1),
-             cos($lat0) * sin($lat1) -
-             sin($lat0) * cos($lat1) * cos($theta0 - $theta1));
+       acos((sin($lat1) - sin($lat0) * cos($distance)) /
+            (cos($lat0) * sin($distance)));
+
+    $direction = pi2 - $direction
+       if sin($theta1 - $theta0) < 0;
 
     return rad2rad($direction);
 }

diff --git a/lib/Math/Trig.t b/lib/Math/Trig.t
index 85ff357..5b1f12e 100755 (executable)
--- a/lib/Math/Trig.t
+++ b/lib/Math/Trig.t
@@ -27,10 +27,11 @@ if ($^O eq 'unicos') { # See lib/Math/Complex.pm and t/lib/complex.t.
 
 sub near ($$;$) {
     my $e = defined $_[2] ? $_[2] : $eps;
+    print "# near? $_[0] $_[1] $e\n";
     $_[1] ? (abs($_[0]/$_[1] - 1) < $e) : abs($_[0]) < $e;
 }
 
-print "1..26\n";
+print "1..29\n";
 
 $x = 0.9;
 print 'not ' unless (near(tan($x), sin($x) / cos($x)));
@@ -188,14 +189,30 @@ use Math::Trig ':radial';
 #      unless (near(great_circle_direction(0, 0, pi, pi), -pi()/2));
     print "ok 25\n";
 
-    # London to Tokyo.
-    my @L = (deg2rad(-0.5), deg2rad(90 - 51.3));
-    my @T = (deg2rad(139.8),deg2rad(90 - 35.7));
+    my @London  = (deg2rad(  -0.167), deg2rad(90 - 51.3));
+    my @Tokyo   = (deg2rad( 139.5),   deg2rad(90 - 35.7));
+    my @Berlin  = (deg2rad ( 13.417), deg2rad(90 - 52.533));
+    my @Paris   = (deg2rad (  2.333), deg2rad(90 - 48.867));
 
-    my $rad = great_circle_direction(@L, @T);
-
-    print 'not ' unless (near($rad, -0.546644569997376));
+    print 'not '
+       unless (near(rad2deg(great_circle_direction(@London, @Tokyo)),
+                    31.791945393073));
+    
     print "ok 26\n";
+    print 'not '
+       unless (near(rad2deg(great_circle_direction(@Tokyo, @London)),
+                    336.069766430326));
+    print "ok 27\n";
+
+    print 'not '
+       unless (near(rad2deg(great_circle_direction(@Berlin, @Paris)),
+                    246.800348034667));
+    
+    print "ok 28\n";
+    print 'not '
+       unless (near(rad2deg(great_circle_direction(@Paris, @Berlin)),
+                    58.2079877553156));
+    print "ok 29\n";
 }
 
 # eof