Here's a comment from some code that I posted to my blog. The idea was that this would explain in detail to someone reading the code what I was doing with the pieces of a wooden train set. This was critical to the operation of the program and I imagined that many of the readers of the code would need a careful explanation.
It turns out that I'd forgotten what this code does so the comment was helpful.
# The 15 possible pieces: a straight edge (which has $unit length) and
# is used as the measurement for everything else, a bridge (which is
# twice the length of the straight edge; it is actually supplied in
# two pieces but for the purposes of this program is considered to be
# a single piece) and a curve (using $radians_in_curve above the
# length of the straight line between the ends of the curve is
# calculated).
#
# Each entry consists of three parts:
#
# length: the length in a straight line between the ends of the piece
# at its centre.
#
# angle: the angle (in radians) between the straight line through the
# piece and a tangent to the curve at the piece's start. This only
# applies to curved pieces where the straight line is the line joining
# its two endpoints.
#
# count: how many of these pieces are supplied.
#
# Note that curves can be placed in either a clockwise or
# anticlockwise direction. The program detects this by looking at the
# angle. If it's non-zero then the piece has two orientations.
my %pieces = (
Bridge => { length => $unit * 2,
angle => 0,
count => 1 },
Straight => { length => $unit,
angle => 0,
count => 2 },
# Here's a curved piece, the angle a is $radians_in_curve, the
# length l of a side is $unit. So length is the distance between
# the points labelled s and f. Bisect the angle a you get a right
# angle triangle with hypotenuse of length $unit and angle at the
# vertex of $radians_in_curve/2. So the angle b is $PI/2 -
# $radians_in_curve/2. By simple trigonometry the length is twice
# $unit * cos($PI/2-$radians_in_curve/2).
#
# s
# C
# . . C
# . b C
# l . . C
# . C
# . . C
# . a C
# . . . . . . . C
# o f
#
# To calculate the angle to the tangent at point s (the angle c),
# note that the angle formed by os and the tangent is a right angle
# (since os comes from the centre of the circle). So b+c is $PI/2
# but b is $PI/2 - $radians_in_curve/2 and so c is
# $radians_in_curve/2
#
# s
# .
# . . .
# . b c .
# l . . .
# . .
# . . .
# . a .
# . . . . . . . . . . .
# o f
#
Curve => { length => 2 * $unit * cos($PI/2-$radians_in_curve/2),
angle => $radians_in_curve/2,
count => 16 }
);
http://blog.jgc.org/2010/01/more-fun-with-toys-ikea-lillabo-...Interestingly, the first line of this comment contains an error. There are 19 pieces not 15.