Math-PlanePath

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devel/dragon.pl  view on Meta::CPAN

    }

    # shift @values; shift @values; shift @values; shift @values;
    require Math::OEIS::Grep;
    Math::OEIS::Grep->search(array=>\@values);
  }
  exit 0;
}

{
  # convex hull iterations
  #
  require Math::Geometry::Planar;
  my $points = [ [0,0], [1,0], [1,1] ];
  my $nx = 1;
  my $ny = 1;
  foreach my $k (1 .. 20) {
    ($nx,$ny) = ($nx-$ny, $ny+$nx); # add rotate +90
    my $num_points = scalar(@$points);
    print "k=$k  nxy=$nx,$ny  count=$num_points\n";

devel/lib/Math/PlanePath/WythoffLines.pm  view on Meta::CPAN

      1  |   1
    Y=0  |
         +-----------------------------------------------------
           X=0   1   2   3   4   5   6   7   8   9  10  11  12

A coordinate pair Y and X are the start of a Fibonacci style recurrence,

    F[1]=Y, F[2]=X    F[i+i] = F[i] + F[i-1]

Any such sequence eventually becomes a row of the Wythoff array
(L<Math::PlanePath::WythoffArray>) after some number of initial iterations.
The N value at X,Y is the row number of the Wythoff array containing
sequence beginning Y and X.  Rows are numbered starting from 1.  Eg.

    Y=4,X=1 sequence:       4, 1, 5, 6, 11, 17, 28, 45, ...
    row 7 of WythoffArray:                  17, 28, 45, ...
    so N=7 at Y=4,X=1

Conversely a given N is positioned in the triangle according to where row
number N of the Wythoff array "precurses" by running the recurrence in
reverse,

examples/c-curve-wx.pl  view on Meta::CPAN

  my ($prev_x,$prev_y) = $to01->transform($x_lo,$y_lo);
  ### origin: "$prev_x, $prev_y"

  undef $dc;

  my $bitmap = Wx::Bitmap->new ($width, $height);
  my $scale = 0.5;
  # $scale = sqrt(3)/2;

  my $iterations = 100;
  my $n = $n_lo+1;
  $idle_drawing = sub {
    my ($event) = @_;
    ### idle_drawing: $event

    my $time = Time::HiRes::time();
    # my $client_dc = Wx::ClientDC->new($draw);
    # my $dc = Wx::BufferedDC->new($client_dc, $bitmap);
    my $dc = Wx::ClientDC->new($draw);

    my $remaining = $iterations;
    for ( ; $n <= $n_hi; $n++) {
      if ($remaining-- < 0) {
        # each took time/iterations, want to take .25 sec so
        # new_iterations = .25/(time/iterations)
        # new_iterations = iterations * .25/time
        my $time = Time::HiRes::time() - $time;
        $iterations = int(($iterations+1) * .25/$time);
        # print "$iterations cf time $time\n";

        if ($event) { $event->RequestMore(1); }
        return;
      }

      my ($x,$y) = $path->n_to_xy($n);
      ($x,$y) = $to01->transform($x,$y);
      ### point: "$x, $y"

      my $c = 0;

lib/Math/PlanePath/ArchimedeanChords.pm  view on Meta::CPAN

#      f(x) / sub = f'(x)
#      sub = f(x) / f'(x)
#
#
# _chord_angle_inc() takes $t is a polar angle around the Archimedean spiral.
# Returns an increment polar angle $u which may be added to $t to move around
# the spiral by a chord length 1 unit.
#
# The loop is Newton's method, $f=f(u), $slope=f'(u) so $u-$f/$slope is a
# better $u, ie. f($u) closer to 0.  Stop when the subtract becomes small,
# usually only about 3 iterations.
#
sub _chord_angle_inc {
  my ($t) = @_;
  # ### _chord_angle_inc(): $t

  my $u = 2*_PI/$t; # estimate

  foreach (0 .. 10) {
    my $shu = sin($u/2); $shu *= $shu;   # sin^2(u/2)
    my $tu = ($t+$u);

lib/Math/PlanePath/WythoffPreliminaryTriangle.pm  view on Meta::CPAN

        1 = 6 - 5
        4 = 5 - 1
    stop on reaching 4,1 which is Y=4,X=1 with Y>=1 and 0<=X<Y

Conversely a coordinate pair X,Y is reckoned as the start of a Fibonacci
style recurrence,

    F[i+i] = F[i] + F[i-1]   starting F[1]=Y, F[2]=X       

Iterating these values gives a row of the Wythoff array
(L<Math::PlanePath::WythoffArray>) after some initial iterations.  The N
value at X,Y is the row number of the Wythoff array which is reached.  Rows
are numbered starting from 1.  For example,

    Y=4,X=1 sequence:       4, 1, 5, 6, 11, 17, 28, 45, ...
    row 7 of WythoffArray:                  17, 28, 45, ...
    so N=7 at Y=4,X=1

=cut

# =head2 Phi Slope Blocks

t/MyTestHelpers.pm  view on Meta::CPAN

# Don't want to load Exporter here since that could hide a problem of a
# module missing a "use Exporter".  Though Test.pm and Test::More (via
# Test::Builder::Module) both use it anyway.
#
# use Exporter;
# use vars qw(@ISA @EXPORT_OK %EXPORT_TAGS);
# @ISA = ('Exporter');
# @EXPORT_OK = qw(findrefs
#                 main_iterations
#                 warn_suppress_gtk_icon
#                 glib_gtk_versions
#                 any_signal_connections
#                 nowarnings);
# %EXPORT_TAGS = (all => \@EXPORT_OK);

sub DEBUG { 0 }


#-----------------------------------------------------------------------------

t/MyTestHelpers.pm  view on Meta::CPAN

    MyTestHelpers::diag ("search ", $proberef);
    MyTestHelpers::findrefs($proberef);
  }
}

#-----------------------------------------------------------------------------
# Gtk/Glib helpers

# Gtk 2.16 can go into a hard loop on events_pending() / main_iteration_do()
# if dbus is not running, or something like that.  In any case limiting the
# iterations is good for test safety.
#
sub main_iterations {
  my $count = 0;
  if (DEBUG) { MyTestHelpers::diag ("main_iterations() ..."); }
  while (Gtk2->events_pending) {
    $count++;
    Gtk2->main_iteration_do (0);

    if ($count >= 500) {
      MyTestHelpers::diag ("main_iterations(): oops, bailed out after $count events/iterations");
      return;
    }
  }
  MyTestHelpers::diag ("main_iterations(): ran $count events/iterations");
}

# warn_suppress_gtk_icon() is a $SIG{__WARN__} handler which suppresses spam
# from Gtk trying to make you buy the hi-colour icon theme.  Eg,
#
#     {
#       local $SIG{'__WARN__'} = \&MyTestHelpers::warn_suppress_gtk_icon;
#       $something = SomeThing->new;
#     }
#

t/MyTestHelpers.pm  view on Meta::CPAN

    # in Gtk 2.0 gdk_flush() is a sync actually
    Gtk2::Gdk->flush;
  }

  my $count = 0;
  while (! $done) {
    if (DEBUG >= 2) { MyTestHelpers::diag ("wait_for_event()   iteration $count"); }
    Gtk2->main_iteration;
    $count++;
  }
  MyTestHelpers::diag ("wait_for_event(): '$signame' ran $count events/iterations\n");

  $widget->signal_handler_disconnect ($sig_id);
  Glib::Source->remove ($timer_id);
}


#-----------------------------------------------------------------------------
# X11::Protocol helpers

sub X11_chosen_screen_number {