Penrose tiling in SATySFi

penrose-tiling.pdf

penrose-tiling.saty

@require: standalone
@require: gr
@require: list

let color-k = RGB(0.1, 0.2, 0.6)
let color-a = RGB(0.9, 1.0, 0.7)
let color-b = RGB(0.5, 0.7, 1.0)

% let color-k = RGB(0.0, 0.0, 0.0)
% let color-a = RGB(0.0, 0.0, 0.0)
% let color-b = RGB(0.3, 0.9, 0.6)

let linewidth = 0.05pt

let pi = acos (0. -. 1.)
let invphi = 2.0 /. (exp (log 5.0 /. 2.0) +. 1.0)

let div (x1, y1) (x2, y2) t =
  let cx = x1 *' (1. -. t) +' x2 *' t in
  let cy = y1 *' (1. -. t) +' y2 *' t in
    (cx, cy)

% ref. https://tartarus.org/~simon/20110412-penrose/penrose.xhtml

type tt = A | B
type triangle = tt * point * point * point

let subdivide (t, p, q, r) =
  let u = div p q invphi in
  let v = div p r invphi in
  match t with
  | A -> [(B, r, u, p); (A, r, u, q)]
  | B -> [(B, v, u, p); (A, v, u, q); (B, r, v, q)]

let-rec gen
  | 0 ps = ps
  | n ps = List.map subdivide ps |> List.concat |> gen (n - 1)


let draw-triangle transf (t, a, b, c) = 
  let p = Gr.polygon a [b; c] |> transf in
  let c =  match t with A -> color-a | B -> color-b in
    [fill c p; stroke linewidth color-k p]

let-inline ctx \penrose-tiling size n =
  let ox = size *' 0.5 in
  let t = ox *' (tan (pi /. 5.0)) in
  let p = (0pt, 0pt) in
  let r = (size, 0pt) in
  let t0 = [(B, p, (ox, t), r); (B, p, (ox, 0pt -' t), r)] in
  let transf = Gr.rotate-path (0pt, 0pt) 36.0 in
  let gs = gen n t0
           |> List.map (draw-triangle transf)
           |> List.concat in
    inline-graphics size size 0pt (fun o -> List.map (shift-graphics o) gs)

let-block ctx +test size n =
  let-rec f i acc =
    if i == n then acc
    else
      let ib = (read-inline ctx { \penrose-tiling(size)(i); }) ++ inline-fil in
      let bb = acc +++ (form-paragraph ctx ib) +++ clear-page in
        f (i + 1) bb
  in
    f 0 block-nil


in

standalone '< 
%  +p{ \penrose-tiling(400pt)(8); }
  +test(400pt)(8);
>