Penrose Tiling in Elm

PenroseTilling.elm

module Penrose where
import List(foldr, map)
import Graphics.Collage(..)
import Graphics.Element(..)
import Color(..)
goldenRatio = (1 + sqrt 5) / 2

type alias Point = (Float, Float)
type Triangle
  =  Kite (Point, Point, Point)
  |  Dart (Point, Point, Point)

interpolate : Float -> Float -> Float
interpolate v0 v1 = v0 + (v1-v0) / goldenRatio

split :  Point-> Point -> Point
split (x1,y1) (x2,y2) = (interpolate x1 x2, interpolate y1 y2)

subDivide : Triangle -> List Triangle
subDivide tr =
  case tr of
    Kite  (p1,p2,p3) ->
      let p4 = split p1 p2
      in [
        Kite (p3, p4, p2),
        Dart (p4, p3, p1)
      ]
    Dart (p1,p2,p3) ->
      let p4 = split p2 p1
          p5 = split p2 p3
      in [
        Dart (p5, p3, p1),
        Dart (p4, p5, p2),
        Kite (p5, p4, p1)
      ]

subDivideTriangles : List Triangle -> number-> List Triangle
subDivideTriangles tr i =
  if | i == 0 -> tr
     | otherwise -> subDivideTriangles (foldr (\t l -> subDivide t ++ l) [] tr) (i-1)

toForm : Triangle -> Form
toForm tr =
  case tr of
    Kite (p1,p2,p3) -> (filled red [p1,p2,p3])
    Dart (p1,p2,p3) -> (filled blue [p1,p2,p3])

pointOnCircle : Point ->Float ->  Float -> Point
pointOnCircle (x,y) r a = (x + cos a * r, y + sin a * r)

createTriangle : Float -> Triangle
createTriangle i =
  let
    o = if (round i) % 2 == 0 then 1 else -1
    a1 = (2*i - 1 * o) * pi / 10
    a2 = (2*i + 1 * o) * pi / 10
    c =  (-100.0, 40.0)
    pointAt =  pointOnCircle c 400
  in
    Kite (c, pointAt a1, pointAt a2)

trs = map createTriangle [1..10]
path = subDivideTriangles trs 4

main : Element
main =  collage 800 800 (map toForm  path)