my $modified = reduce{
    my( $x1, $y1, $x2, $y2 ) = ( @{ @{ $a }[ -1 ] }, @$b );
     $x2 < $x1 ? pop @{ $a } : push @{ $a }, $b;
    $a;
} [ shift @points ], @points;

##</code><code>##

my $i = 1;
while ($i < @points) {
    if ($points[$i-1][0] > $points[$i][0]) {
        splice @points,$i-1,2;
        --$i or $i = 0;
    } else {
        $i++;
    }
}

##</code><code>##

my $modified = [];
for my $point (@points) {
    if (@$modified and $modified->[-1][0] > $point->[0]) {
        pop @$modified;
    } else {
        push @$modified, $point;
    }
}

##</code><code>##

my @m;
@m&&$m[-1][0]>$_->[0]?pop @m:push @m,$_ for @points;