=begin comment
say "Waxing, f < 0.5, radius = $r:";
@f = 0, .25, .5;
for @f -> $f {
    my $a = $r - (2 * $r * $f);
    say "  frac = $f, a = $a";
}
=end comment
=begin comment
say "Waxing, f > 0.5, radius = $r:";
@f = .5, .75, 1;
for @f -> $f {
    my $a = (2 * $r * $f) - $r;
    say "  frac = $f, a = $a";
}
=end comment
=begin comment
say "Waning, f > 0.5, radius = $r:";
@f = 1, .75, .5;
for @f -> $f {
    my $a = (2 * $r * $f) - $r;
    say "  frac = $f, a = $a";
}
=end comment
=begin comment
say "Waning, f < 0.5, radius = $r:";
@f = .5, .25, 0;
for @f -> $f {
    my $a = $r - (2 * $r * $f);
    say "  frac = $f, a = $a";
}
=end comment