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.
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:
- Run program and print out resulting pdf.
- Carefully cut out disks.
- 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.