Just use sin and cos to determine the Y and X centers of your labels respectively.

Then depending on the size of your labels, determine their position with respect to those points.

A second example below, shows how to do vertical text in case you desire that feature.

#!/usr/bin/perl
use warnings;
use strict;
use Tk;

                           
my $pi = atan2(1,1)*4.0;           # an amusing transcendental number
my $main = MainWindow -> new();    # the primal widget
my ($width, $height );             # canvas geometry
$width = $height = 500;            # change me if you don't like me

my $x = int($width/2);
my $y = int($height/2);
my $r = int($x*0.8) >= int($y*0.8) ? int($x*0.8) : int($y*0.8);  # $ra
+dius
my $c = $main -> Canvas('-width' => $width, '-height' => $height);
$c -> create('oval', $x-$r, $y-$r, $x+$r, $y+$r, -width => 2);
$c -> pack(-expand => 1, -fill => 'both');

 # the following two together _prevent_ resizing:
$main -> maxsize($width,$height);  # fixes size 
$main -> minsize($width,$height);  # fixes size 
my ($outickx, $outicky, $intickx, $inticky, $tickwidth);  
for (0..11) {                      # the tick initialization loop
    $outickx = int($x + sin($_*$pi/6.0)*$r*1.00);
    $outicky = int($y - cos($_*$pi/6.0)*$r*1.00);
    $intickx = int($x + sin($_*$pi/6.0)*$r*0.85);
    $inticky = int($y - cos($_*$pi/6.0)*$r*0.85);
    $tickwidth = $_ % 3 == 0 ? 3 : 1;
    $c->create('line', ($outickx, $outicky, $intickx, $inticky),
               -width => $tickwidth,
              );
} # end tick loop
undef $outickx; undef $outicky;    # cleanup
undef $intickx; undef $inticky;
undef $tickwidth;

# time and date variables:
my ($second,$minute,$hour,$date,$month,$year,$weekday,$yday,$dst);
my ($hourx, $houry, $minutex, $minutey ); # clock hand geometry
# my ($secondx, $secondy );               # (unused) clock hand geomet
+ry

for (;;) {                                # this is the timekeeping lo
+op
       # feel free to make use of some of these variables:
    ($second,$minute,$hour,$date,$month,$year,$weekday,$yday,$dst) =
       localtime();
    $hour = $hour % 12;
    ($hourx, $houry, $minutex, $minutey,  # $secondx, $secondy, 
        ) = ( 
        int($x + sin((($hour+$minute/60.0)/6.0)*$pi) *$r*0.75 ),
        int($y - cos((($hour+$minute/60.0)/6.0)*$pi) *$r*0.75 ),
        int($x + sin( ($minute/30.0)*$pi) *$r*1.00 ), 
        int($y - cos( ($minute/30.0)*$pi) *$r*1.00 ), 
        # int($x + sin( ($second/30.0)*$pi) *$r ), 
        # int($y - cos( ($second/30.0)*$pi) *$r ), 
            );
    $c -> delete('hourhand');
    $c -> create('line', ($hourx, $houry, $x, $y),
                 '-arrow' => 'first', 
                 '-tags'  => 'hourhand',
                 '-width' => 3,
                 );
    $c -> delete('minutehand');
    $c -> create('line', ($minutex, $minutey, $x, $y),
                 '-arrow' => 'first', 
                 '-tags'  => 'minutehand',
                 '-width' => 2,
                 );
#     $c -> delete('secondhand');
#     $c -> create('line', ($secondx, $secondy, $x, $y),
#                 '-tags'  => 'secondhand',
#                 );

    # DoOneEvent;                # <- use either this or
    $main -> update;           # <- this (both not necessary).

    sleep(1);                  # 1 sec compromise min cpu vs. lively-X

} # end timekeeping loop

__END__

=head1 NAME

pclock

=head1 SYNOPSIS

    pclock &

=head1 DESCRIPTION

B<pclock> is a clock implemented in Perl/Tk.

Here is the `date` on which this was written:

    Thu May  9 16:58:31 EDT 1996

It was then modified on:

    Fri May 10 16:31:10 EDT 1996

Thanks to Adrian Phillips and Simon Galton for helpful suggestions.

The choice between DoOneEvent; and $main->update; as well as sleep();
times may be system|X-server dependent.

As distributed by the author there is a second hand embedded within 
commented code in this program.

=head1 REQUIREMENTS
Perl with the Tk extension.
=head1 AUTHOR
Peter Prymmer pvhp@lns62.lns.cornell.edu  
=cut
[download]

#!/usr/bin/perl
use Tk;
my $mw = new MainWindow;
my $c  = $mw->Canvas->pack;

$c->createText(50, 50,
           -text => 'Hello',
               -width => 1,
                   );
               
               MainLoop;
[download]

Here is mine Tk::Zinc version, with a little help from Advantages of Tk::Zinc over plain Canvas, Tk::Clock, -tk Moving circle, it works, but rotate is busted :)

#!/usr/bin/perl --
use warnings;
use strict;
use Tk;
use Tk::Zinc ;
use Tk::Clock;

my $mw = tkinit;

my $canvas = $mw->Zinc(
    -width => 300,
    -height => 300,
    -backcolor => 'white',
)->pack(qw/
    -expand 1
    -fill both
    -padx 10
    -pady 10
/);

my $clock = $mw->Clock(  useAnalog   => 1, )->pack;

my $circle_radius = 100;
my $origin_x = $canvas->cget('-height') / 2 ;
my $origin_y = $canvas->cget('-width') / 2;
my $cgroup = $canvas->add('group',1,-visible=> 1);


#~ my $circle = $canvas->createOval(

my $innercircle = $canvas->add(
    'arc',
    $cgroup,
    [
        $origin_x - ( $circle_radius - 10 ),
        $origin_y - ( $circle_radius - 10 ),
        $origin_x + ( $circle_radius - 10 ),
        $origin_y + ( $circle_radius - 10 ),
    ],
);

my $circle = $canvas->add(
    'arc',
    $cgroup,
    [
        $origin_x - $circle_radius,
        $origin_y - $circle_radius,
        $origin_x + $circle_radius,
        $origin_y + $circle_radius,
    ],
);

my $ix=0;
my $PI=3.141592635;    
my $angle = -30;
for my $dtick ( 1 .. 12 ){
    my $d8 = 9;
    $angle += 30;
    my $cos = cos($angle*$PI/180);
    my $sin = sin($angle*$PI/180);
    
    my $x1 = $origin_x + ( ( $circle_radius - $d8  ) * $sin );
    my $y1 = $origin_y - ( ( $circle_radius - $d8  ) * $cos );
    my $x2 = $origin_x + ( ( $circle_radius + $d8  ) * $sin );
    my $y2 = $origin_y - ( ( $circle_radius + $d8  ) * $cos );

#~     my $line = $canvas->createLine (
    my $line = $canvas->add(
        'curve',
        $cgroup,
        [
            $x1, $y1,
            $x2, $y2,
        ],
        -tags  => "tick",
        -linecolor => 'red',
        -filled => 1,
        -linewidth => 1.0,
    );
    my $text = $canvas->add(
        'text', $cgroup,
        -position => [ $x1,$y1 ],
        -text => ixHour( $ix++) ,
        -color => 'blue',
    );

# no work, disappeared or crash
#~     $canvas->rotate( $text, $angle , 'degree' );
}


MainLoop;

sub ixHour {
    return [qw/
one two three four five six seven eight nine ten eleven twelve
    /]->[ -1 + shift ]
}

__END__
[download]

It may seem that way, but this is the only way to accomplish it.

You mark X points (12) on the circle, and use each point as the starting coordinates for drawing your box-labels.

You rotate the box-labels based on the angle, so it points in a direction (3 o'clock would point west)

You shift the box-label in the opposite direction ( 3 o'clock shifts east), based on the width of a letter.

See ASCII analog clock, it uses a grid of boxes a character wide.

I'm not sure I understand your question. It sounds like you know how to calculate the angle of where the text will be placed.

If that's the case, then divide the clock into four uneven parts: T = (−20deg, 20deg), R = (20deg, 160deg), B = (160deg, 200deg), L = (200deg, 340deg). If the text is in T or B, calculate the height of the text, and place the text above/below the circle by that height + margin. If the text is in L, then calculate the length of the text and start the text len($string)+$margin to the left of the angle you want to place it at. If the text is in R, then start the text $margin to the right of the circle.

You might also find a good answer in the R source code for plot.

I realize that this is not an answer to the question, but I still think it's worth saying, in case you have a say in what is finally done.

I hate rotated labels.

I have to rotate the image in order to read them. Keep the labels in their normal horizontal (or vertical if the language uses that) orientation and make it easier for people to read them. Personally, I'd prefer a circle of horizontal labels surrounding the clock. If necessary, you can add lines from them pointing to the actual reference point.

Rotating the labels also makes the hour hand point at a "9" when it is six o'clock.

Your description seems too vague to me. There are a number of different approaches.

Assuming you are not going to rotate the text then each "label" consumes a rectangle of space, and has a well defined point that it is trying to identify. A simple approach would be to position the centre of the rectangle on the location. Alternately you could define 8 cardinal points of the text rectangles (top left, top middle etc), select an appropriate one (for eleven the 'bottom centre' for example) and place that on the point you want.

The issue is that the size of the rectangles and the aesthetic effect you want will determine what works for you.

One approach I've used (in the distant past) is to place all the labels exactly where I want them (with the centre of the label in the desired location for example). Define a "goodness measure" that uses various rules (no two labels may overlap, the distance from the desired point can't be too great etc), try randomly moving one of the labels and if that increases the goodness keep it, if not try again. If you start with quite a big move size then gradually decrease it the various labels will end up in a configuration that best suits your defined measure.

This is essentially a "Simulated Annealing" approach

You could steal the code from Tk::Clock (look at the _where function in Clock.pm. This is - as zentara - using a Canvas.

I however think that most posted solutions here would be almost the same.

When it comes down to it the only real difficulty is deciding how you are going to justify the labels -- and you aren't necessarily going to key off the center of the labels. It depends if you are placing the number inside the circle, with the hands sweeping over them, outside the circle, or something in between. The look and "best" spacing will also be affected by what labels you use (arabic, roman, etc...)