#!/usr/bin/perl -w
use strict;

# This takes two 2-dimensional points (A and B)
# and a width, and returns 4 points that are the
# counter-clockwise perimeter of a "thick line"
# (box) of the specified width around the line.

sub line2box
{
    my $w= pop @_;
    die 'Usage: line2box($ax,$ay,$bx,$by,$width)'
        if  $w <= 0  ||  4 != @_;
    # We just keep our 4 coordinates in a single array
    # so we don't have to repeat ourselves much below.

    $w /= 2;    # Length of offset vector is $width/2

    my @d;      # Differences between X and Y coord.s
    my $l= 0;
    for( 0, 1 ) {
        my $d= $_[$_] - $_[2+$_];
        $l += $d*$d;
        push @d, $d;
    }

    # Now $l is length**2, so we want to scale our
    # perpendicular vectors by $width / $length so:
    $l= sqrt( $w*$w / $l );
    $_ *= $l   for  @d;

    my @box;
    my @s= ( -1, 1 );   # Sign to apply (- or +)
    for my $s ( 0, 1 ) {         # Index into @s
        # $p==0 for A, $p==1 for B
        for my $p ( $s, !$s ) {  # Which point
            for my $c ( 0, 1 ) { # Which coordinate
                # Push the selected coordinate
                push @box,
                    $_[2*$p+$c] + $s[$s^$c]*$d[!$c];
            }
        }
    }
    return @box;
}

while(  <DATA>  ) {
    last if !/\S/;
    my @line= split ' ';
    $line[-1] **= 0.5;
    my @box= line2box( @line );
    printf qq[A line from A( %5.1f, %5.1f )$/]
        .  qq[       to   B( %5.1f, %5.1f )$/]
        .  qq[of width sqrt( %5.1f )$/]
        .  qq[is a box, counter-clock-wise:$/]
        .  qq[            W( %5.1f, %5.1f )$/]
        .  qq[            X( %5.1f, %5.1f )$/]
        .  qq[            Y( %5.1f, %5.1f )$/]
        .  qq[            Z( %5.1f, %5.1f )$/]
        .  $/
        ,  @line[0..3], $line[4]**2,
        ,  @box;
}

##</code><code>##

__END__
 1  0 1 5 4
 1  1 6 1 16
-1 -2 2 1 8

A line from A(   1.0,   0.0 )
       to   B(   1.0,   5.0 )
of width sqrt(   4.0 )
is a box, counter-clock-wise:
            W(   2.0,   0.0 )
            X(   2.0,   5.0 )
            Y(   0.0,   5.0 )
            Z(   0.0,   0.0 )

          w=2
        |<--->|

        |
       (Y)(B)(X)
        |  #
       4+  #
        |  #
       3+  #
        |  #
       2+  #
        |  #
       1+  #
        |  #
--+--+-(Z)(A)(W)-+--
 -2 -1  0  1  2


A line from A(   1.0,   1.0 )
       to   B(   6.0,   1.0 )
of width sqrt(  16.0 )
is a box, counter-clock-wise:
            W(   1.0,  -1.0 )
            X(   6.0,  -1.0 )
            Y(   6.0,   3.0 )
            Z(   1.0,   3.0 )

     |
    4+
     |
    3+ (Z)            (Y)   ---
     |                       ^
    2+                       |
     |                       |
    1+ (A)############(B)   w=4
     |                       |
--+--+--+--+--+--+--+--+--+- |
 -1  0  1  2  3  4  5  6  7  v
   -1+ (W)            (X)   ---
     |
   -2+
     |

A line from A(  -1.0,  -2.0 )
       to   B(   2.0,   1.0 )
of width sqrt(   8.0 )
is a box, counter-clock-wise:
            W(   0.0,  -3.0 )
            X(   3.0,   0.0 )
            Y(   1.0,   2.0 )
            Z(  -2.0,  -1.0 )

           |
          3+     /
           |      \
          2+ (Y)   w=2*(2**.5)
           |         \
          1+    (B)    /
           |   //
--+--+--+--+--+--+-(X)-+--
 -3 -2 -1  0//1  2  3  4
    (Z)  -1+
         //|
       (A) -2
           |
        -3(W)
           |
         -4+
           |

##</code><code>##

        for my $p ( $s, !$s ) {  # Which point