use constant X => 0;
use constant Y => 1;

my @points1   = ( [1,1], [2,2], [3,3] );     # a line like /
my @points2   = ( [2,1], [3,2], [4,3] );     # a line like / displaced R
my @points3   = ( [1,1], [2.41,1], [3.82,1]);# a line like -
my @template  = ( [1,3], [2,2], [3,1] );     # a line like \

my $vp1 = vector(\@points1,2);
my $vp2 = vector(\@points2,2);
my $vp3 = vector(\@points3,2);
my $vt  = vector(\@template,2);
print "@$vp1\n@$vp2\n@$vp3\ntemplate\n@$vt\n";

sub vector {
    my ($points, $precision) = @_;
    $precision ||= 10;
    # calculate the geometric centroid
    my ( $cx, $cy ) = (0,0);
    for (@$points) {
        $cx += $_->[X];
        $cy += $_->[Y];
    }
    $cx /= @$points;
    $cy /= @$points;
    
    # map the 1 dimensional distance of all points from centroid
    # using simple pythagorean geometry
    my @vector = map{ sqrt(($cx-$_->[X])**2 + ($cy-$_->[Y])**2) } @$points;
    
    # fuzzify to desired precision and sort to create finished vector
    my $template = "%.${precision}f";
    @vector = map{ sprintf $template, $_ } sort { $a <=> $b } @vector;
  return \@vector;
}
__DATA__
0.00 1.41 1.41
0.00 1.41 1.41
0.00 1.41 1.41
template
0.00 1.41 1.41