A hexidecimal slide-rule in PDF.

[perlmoth]

I wanted a circular slide rule to help me with some hexadecimal calculations. Searching the web came up blank with respect to hexadecimal slide rules so I decided to make my own.

Here is the code I came up with:

use strict;
use warnings;

use PDF::API2;

use constant PAGE_WIDTH      => 595;
use constant PAGE_HEIGHT     => 842;

use constant LINE_WIDTH      =>   0.5;
use constant THIN_LINE_WIDTH =>   0.25;
use constant CM              =>  28.346457;  # 1 cm in points

sub log16 {
  my $n = shift;
  return log($n) / log(16);
}

sub angle {
  my $theta = shift;
  return -360.0 * log16($theta)
}

sub run {
  my $pdf = PDF::API2->new;
  my $font = $pdf->corefont("TimesNewRoman");
  $pdf->mediabox(PAGE_HEIGHT, PAGE_WIDTH);
  my $gfx = $pdf->page->gfx;
  $gfx->strokecolor( '#000' );
  $gfx->linewidth( THIN_LINE_WIDTH );

  my $yc = PAGE_WIDTH / 2.0;
  my $radius = PAGE_HEIGHT / 4.0 - 1 * CM;
  my @tick16 = map( $_ / 16.0, (16 .. 255) );

  my %outerDisk =
    (centre => PAGE_HEIGHT / 4.0,
     dir => +1,
     bigLetter => 0.35 * CM,
     smallLetter => 0.18 * CM
    );
  my %innerDisk =
    (centre => 3.0 * PAGE_HEIGHT / 4.0,
     dir => -1,
     bigLetter => -0.6 * CM,
     smallLetter => -0.3 * CM
    );

  for my $disk ( \%outerDisk, \%innerDisk ) {

    $gfx->save();

    $gfx->translate($$disk{centre}, $yc);

    $gfx->linewidth( LINE_WIDTH );
    $gfx->circle(0, 0, 1);
    $gfx->circle(0, 0, $radius);
    $gfx->circle(0, 0, $radius + 0.75 * CM * $$disk{dir});
    $gfx->stroke();

    $gfx->linewidth( THIN_LINE_WIDTH );
    $gfx->move(0, -0.5 * CM);
    $gfx->line(0, 0.5 * CM);
    $gfx->stroke();
    $gfx->move(-0.5 * CM, 0);
    $gfx->line(0.5 * CM, 0);
    $gfx->stroke();

    for my $i (@tick16) {
      my $angle = angle($i);
      $gfx->rotate($angle);
      if ($i * 16 % 16 == 0) {
        $gfx->move(0, $radius);
        $gfx->line(0, $radius + 0.3 * CM * $$disk{dir});
        $gfx->stroke;
        $gfx->textlabel(0, $radius + $$disk{bigLetter}, $font, 10, spr
+intf("%X", $i), -align => 'center');
      }
      elsif ($i * 16 % 4 == 0) {
        $gfx->move(0, $radius);
        $gfx->line(0, $radius + 0.15 * CM * $$disk{dir});
        $gfx->stroke;
      }
      else {
        $gfx->move(0, $radius);
        $gfx->line(0, $radius + 0.1 * CM * $$disk{dir});
        $gfx->stroke;
      }
      if ($i < 4.0 and $i * 16 % 16 != 0) {
        $gfx->textlabel(0, $radius + $$disk{smallLetter}, $font, 5, sp
+rintf("%X", $i * 16 % 16), -align => 'center');
      }
      if ($i > 4.0 and $i < 8.0 and $i * 16 % 2 == 0 and $i * 16 % 16 
+!= 0) {
        $gfx->textlabel(0, $radius + $$disk{smallLetter}, $font, 5, sp
+rintf("%X", $i * 16 % 16), -align => 'center');
      }
      if ($i > 8.0 and $i * 16 % 4 == 0 and $i * 16 % 16 != 0) {
        $gfx->textlabel(0, $radius + $$disk{smallLetter}, $font, 5, sp
+rintf("%X", $i * 16 % 16), -align => 'center');
      }
      $gfx->rotate(-$angle);
    }

    $gfx->restore();

  }

  $pdf->saveas("hex_slide_rule.pdf");
}

run();

Instructions:

1. Run program and print out resulting pdf.
2. Carefully cut out disks.
3. Put the inner disk over the outer disk with the centres carefully aligned and pin together.

Here are instructions in how to use slide rules. My rule is the equivalent of the C and D scales of a normal slide rule, except in hex. The principle of use is the same.