// A jigsaw puzzle. Every edge between two pieces gets a knob that points
// one way or the other, picked by the seed.

/* [Puzzle] */
// Pieces across
cols = 5; // [2:1:12]
// Pieces down
rows = 4; // [2:1:12]
// Size of one piece
piece = 30; // [15:1:60]
// Knob size, as a share of the edge
knob = 0.22; // [0.15:0.01:0.3]
// Different seeds give different knob directions
seed = 3; // [1:1:99]

/* [Hidden] */
w = cols * piece;
h = rows * piece;
flips = rands(0, 1, 2 * cols * rows, seed);

// One edge from [0, 0] to [len, 0] with a knob on side s (1 or -1).
function edge(len, s) = let (
  rr = knob * len / 2,
  c = [len / 2, s * (rr * 1.65)],
  n = 24
) concat(
  [[0, 0], [len / 2 - rr * 1.1, 0], [len / 2 - rr * 0.75, s * rr * 0.55]],
  [for (i = [0:n]) let (a = 235 - i * 290 / n) [c[0] + rr * cos(a), c[1] + s * rr * sin(a)]],
  [[len / 2 + rr * 0.75, s * rr * 0.55], [len / 2 + rr * 1.1, 0], [len, 0]]
);

function side(i) = flips[i] < 0.5 ? -1 : 1;

rect([w, h], r = 3);

// Edges between columns.
for (c = [1:cols - 1], r = [0:rows - 1])
  translate([c * piece, r * piece]) rotate(90) polyline(edge(piece, side(c * rows + r)));

// Edges between rows.
for (r = [1:rows - 1], c = [0:cols - 1])
  translate([c * piece, r * piece]) polyline(edge(piece, side(cols * rows + r * cols + c)));