lissajous curves

#!/usr/bin/perl

use warnings; use strict;

sub pie() {
    2 * atan2(1, 0);
}
sub asin {
    atan2($_[0], sqrt(1 - $_[0]**2));
}

sub liss {
    my($p_m, $p_n, $p_d) = @_;
    my($ht, $wd) = (24, 60);
    my $ou;
    for my $l (0 .. 2 * $ht - 1) {
        0 == $l % 2 and $ou = " " x ($wd + 1);
        my($y0, $y1) = (2 * $l / (2 * $ht) - 1, 2 * ($l + 1) / (2 * $ht) - 1);
        my($su0, $su1) = (asin($y0), asin($y1));
        for my $br (0 .. $p_m - 1) {
            for my $sgn (0, 1) {
                my($u0, $u1) = 
                    ($br * 2 * pie + $sgn * pie + $su0 * ($sgn?-1:1), $br * 2 * pie + $sgn * pie + $su1 * ($sgn?-1:1));
                my($v0, $v1) = ($u0 / $p_m * $p_n + $p_d, $u1 / $p_m * $p_n + $p_d);
                my($x0, $x1) = (sin($v0), sin($v1));
                $x1 < $x0 and ($x0, $x1) = ($x1, $x0);
                int(($v0 - pie / 2) / 2 / pie) == int(($v1 - pie / 2) / 2 / pie) or
                    $x1 = 1;
                int(($v0 + pie / 2) / 2 / pie) == int(($v1 + pie / 2) / 2 / pie) or
                    $x1 = -1;
                my($p0, $p1) = (($x0 + 1) / 2 * $wd, ($x1 + 1) / 2 * $wd);
                my ($ps, $pd) = 
                    int($p0) < int($p1) ?
                        (int($p0), int($p1) - int($p0)) :
                        (int(($p0 + $p1 + 1) / 2), 1);
                my $repl = \substr($ou, $p0, $pd); 
                0 == $l % 2 ?
                    $$repl =~ y/ /'/ :
                    $$repl =~ y/ '/,;/;
            }
        }
        1 == $l % 2 and print $ou, "\n";
    }
}

for (0 .. 19) {
    print "\n" x 4;
    my $r = sub { int(1 - log(1-rand(0.999)) / $_[0]) };
    my($m, $n) = (&$r(0.7), &$r(0.9));
    liss $m, $n, rand(2*pie);
    sleep 3;
}

__END__