Shortnote

The perl script below uses the BV4141 display controller in order to draw the current time onto the BV4141 display. The image shows the time 2:50.

Calculations

The equation of the circle gives us any mobile point on the perimeter of a circle centered in $O(a,b)$ and radius $r$ . The equations to obtain the points on the perimeter of the circle are as follows:

$\begin{eqnarray*} x &=& a + r * \cos{\theta} \\ y &=& b + r * \sin{\theta} \end{eqnarray*}$

where $\theta$ represents an angle, measured counter-clockwise on the circle (following trigonometric rules).

We know that, for clocks, the hours divide the clock-face into $12$ equal angles, such that every $\theta$ , when divided corresponds to $\frac{360}{12}=30^\circ$ . Conversely, for hours, the clock-face is divided into $60$ equal angles, such that every $\theta$ , when divided corresponds to $\frac{360}{60}=6^\circ$ .

We also know that the starting point of the clock is at 12 hours sharp and continues to grow, clockwise, to 1, 2 and so on. Thus, every clock-wise step can be considered as an addition of $\theta$ angles, such that hour 1 represents $90^\circ-30$ , hour 2 represents $90^\circ-60$ .

The problem is when we reach hour 4, because $90^\circ-120$ gives us a negative angle $-30$ . For that, we use modulo arithmetic: $-30mod(360)=330$ in order to wrap the value back to positive values.

Code

The code requires that the BV4141 display controller is copied into the $PATH of the user running this script. This can be done by just copying vacctl.pl to /usr/local/bin (preferably) or /usr/bin.

vacclock.pl

#!/usr/bin/perl
###########################################################################
##  Copyright (C) Wizardry and Steamworks 2012 - License: GNU GPLv3      ##
##  Please see: http://www.gnu.org/licenses/gpl.html for legal details,  ##
##  rights of fair usage, the disclaimer and warranty conditions.        ##
###########################################################################
 
 
# Returns the angles that correspond to the current 
# number of hours and minutes. It does that by using 
# clock arithmetic and wrapping the angles into a circle.
# For hours, the clock face divides into 12 equal 
# angles.For minutes, the clock face divides into 60 
# equal angles.
sub angles {
  my @time = split(/:/, shift);
  return %a = (
    'h' => (90-$time[0]*360/12) % 360,
    'm' => (90-$time[1]*360/60) % 360
  );
}
 
my $pi = 3.14159265358979;
sub deg_to_rad { ($_[0]/180) * $pi }
sub rad_to_deg { ($_[0]/$pi) * 180 }
 
# Get hour and minutes.
@time = ((localtime)[2],(localtime)[1]);
 
# If military time, change to conventional time.
if($hour > 12) { $hour -= 12; }
 
# Get the angles corresponding to the current time.
%a = &angles("$time[0]:$time[1]");
 
# x,y for hours.
@xy_h=(int(62+32*cos(deg_to_rad($a{'h'}))), int(62+32*sin(deg_to_rad($a{'h'}))));
# x,y for minutes.
@xy_m=(int(62+62*cos(deg_to_rad($a{'m'}))), int(62+62*sin(deg_to_rad($a{'m'}))));
 
# Clear display.
`vacctl.pl --clear`;
# Draw clock face.
`vacctl.pl --circle=62,62,62`;
# Draw hours.
`vacctl.pl --line=62,62,$xy_h[0],$xy_h[1]`;
# Draw minutes.
`vacctl.pl --line=62,62,$xy_m[0],$xy_m[1]`;

Table of Contents

Shortnote

Calculations

Code