Might also try inlining Determinant and some common sub-expression elimination...

sub SegmentIntersection {
  my @points = @{$_[0]};
  my @p1 = @{$points[0]}; # p1,p2 = segment 1
  my @p2 = @{$points[1]};
  my @p3 = @{$points[2]}; # p3,p4 = segment 2
  my @p4 = @{$points[3]};

  my $a = $p2[0] - $p1[0];
  my $b = $p3[1] - $p4[1];
  my $c = $p2[1] - $p1[1];
  my $d = $p3[0] - $p4[0];
  my $det = $a*$b - $c*$d;
  
  return 0 if (abs($det) < $delta); # parallel

  my $e = $p3[1]-$p1[1];
  my $f = $p3[0]-$p1[0];
  my $n1 = $f*$b - $e*$d
  my $n2 = $a*$e - $c*$f;

  if ($det > 0)
  {
    return $n1 < $det && $n2 < $det && $n1 > 0 && $n2 > 0;
  } 
  else 
  {
    return $n1 > $det && $n2 > $det && $n1 < 0 && $n2 < 0;
  }
}
[download]