By popular demand... here's the code, written in Processing that actually draws the train sets. I hadn't released it because I didn't think it was very interesting, but you are welcome to it.

// --------------------------------------------------------------------------

//

// Small program to draw pictures of Ikea Lillabo track layouts using

// instructions derived from my Perl program.

//

// Written by John Graham-Cumming (http://www.jgc.org/)

//

// Released under the General Public License, version 2

//

// --------------------------------------------------------------------------

// This is the cursor position (x, y) coordinates and angle to the

// horizontal

float x, y, a;

// The length in pixels of a single straight piece

float len = 40;

// See the Perl program for a full explanation, but there are 8 curves

// in a circle and from that the radians of curve arc, the length of the

// straight line between the curve ends and the curve angle to the

// horizontal can be calculated.

float curves_in_circle = 8;

float radians_in_curve = 2 * PI / curves_in_circle;

float curve_angle = radians_in_curve / 2;

float curve_length = len * 2 * cos(PI/2 - radians_in_curve/2);

// The Processing equivalent of main()

void setup() {

// Set up the basic parameters for the drawing: a 1000x1000 canvas,

// with a white background. None of the elements drawn will be filled

// and the lines will be four pixels wide.

size(1000,1000);

background(255,255,255);

strokeWeight(4);

noFill();

// These are the nine possible layouts discovered by the Perl program

// and were copy/pasted here. Clearly this would be better done

// dynamically with this program reading the Perl program's output.

int layouts = 9;

String s[] = new String[layouts];

s[0] = "AAAACCAAAASSAAB";

s[1] = "CCCCCCSSAAAAAAB";

s[2] = "CAAAAACASSAAAAB";

s[3] = "CAAAAASCASAAAAB";

s[4] = "CAAAAASSCAAAAAB";

s[5] = "AAACAACAAASSAAB";

s[6] = "ACAAAASACSAAAAB";

s[7] = "ACAAAASSACAAAAB";

s[8] = "AACAAASSAACAAAB";

// (row, col) is the row and column position of the next layout to draw

// starting from the top left of the canvas. Since we know there are

// 9 the loop below lays them out 3x3. h is the height of space

// reserved for a layout.

int row = 0;

int col = 0;

int h = 250;

int w = h + 50;

for ( int j = 0; j < layouts; j++ ) {

// Start 200 pixels from the top left corner and with an initial

// angle of 0

a = 0;

x = 200 + w * col;

y = 200 + h * row;

col++;

if ( col == 3 ) {

col = 0;

row++;

}

for ( int i = 0; i < s[j].length(); i++ ) {

switch(s[j].charAt(i)) {

case 'B':

bridge();

break;

case 'C':

clockwise();

break;

case 'A':

anticlockwise();

break;

case 'S':

straight();

break;

}

}

}

}

// Function to draw a piece and update (x, y) and a

void draw_piece( float l, // Length of piece to be drawn

float ang ) // The angular change due to the piece

{

// If the ang is zero then this is a straight piece so use line(), if

// non-zero then it's a curve and so use arc()

if ( ang == 0 ) {

// (dx, dy) is the end of the piece truncated (the 0.8 multiplier)

// to leave a little gap between pieces.

float dx = x + l * 0.8 * cos(a + ang);

float dy = y + l * 0.8 * sin(a + ang);

line( x, y, dx, dy );

} else {

int h = (ang<0)?-1:1;

// (ox, oy) is the location of the centre of the circle on which the

// arc we are drawing lies. s and e are the starting and ending angles

// of arc to draw. Note that s must be less than e. Note the 1.5 here

// is used to shorten the arc to leave a small gap between pieces.

float ox = x - h * len * cos(PI/2-a);

float oy = y + h * len * sin(PI/2-a);

float s = a;

float e = a + ang * 1.5;

if ( s > e ) {

float t = e;

e = s;

s = t;

}

// The PI/2 adjustment here is needed because the angles in s and e are

// derived from a which is to the horizontal and the arc() function needs

// angles to the vertical

ellipseMode(CENTER);

arc( ox, oy, len*2, len*2, s - h * PI/2, e - h * PI/2 );

}

// Update (x,y) and a to be at the end of the new piece that's been

// added and with the correct orientation.

x += l * cos(a + ang);

y += l * sin(a + ang);

a += 2 * ang;

}

// Four functions to draw the four pieces giving them different colours.

void bridge()

{

stroke(255,0,0);

draw_piece(2*len,0);

}

void straight()

{

stroke(0,255,0);

draw_piece(len,0);

}

void clockwise()

{

stroke(255,0,255);

draw_piece(curve_length,curve_angle);

}

void anticlockwise()

{

stroke(0,0,255);

draw_piece(curve_length,-curve_angle);

}

## Comments

I was interested in the designs for two sets. I have it running with the second bridge as two straight sections. It's got about 1250 layouts generated so far. Some of them are not buildable due to stacked tracks. I'm thinking on how to check for this condition.