Appreciated your thanks. I leave "what is better" up to you.

#! perl -slw
use strict;

printf "%s", scalar <DATA>;
my @points = map[ split ' ', $_ ], <DATA>;

my $i=0;
while ($i < @points-2)  #quit when there aren't 2 points left
{   
   my ($x1,$y1) = @{$points[$i]};
   my ($x2,$y2) = @{$points[$i+1]};
   
   if ( ($y2 - $y1 ) / ( $x2 - $x1 ) < 0 )
   {
      splice @points,$i,2; #remove both points
      $i--;                #backup a point to restart
      $i=0 if $i<0;        #boundary condition at index 0
   }
   else
   {
      $i++;
   }
}
print join ' ', @$_ for @points;
[download]