Diagrams - Circular gray code

Circular gray code, like that used on some rotational sensors.

Author: Brent Yorgey

> import Diagrams.Backend.SVG.CmdLine

> {-# LANGUAGE NoMonomorphismRestriction #-}
> import Diagrams.Prelude     hiding (gray)
> import Data.List.Split      (chunksOf)
> import Data.Maybe           (catMaybes)
> import Control.Applicative
> import Data.Monoid          (mconcat)
> import Data.List            (transpose)

gray n recursively generates an n-bit Gray code, where each n-bit binary number differs from the next in exactly one position.

> gray 0 = [[]]
> gray n = map (False:) g ++ map (True:) (reverse g)
>   where g = gray (n-1)

Construct a circular diagram from the n-bit gray code: each bit position corresponds to a concentric ring, with black/white indicating 0/1. ringOffsets converts a list of booleans into a list of angular segments corresponding to consecutive runs of True.

> rings n = mkRingsDia . map ringOffsets . transpose . gray $ n
>   where ringOffsets :: [Bool] -> [(Direction V2 Double, Angle Double)]
>         ringOffsets = map l2t . chunksOf 2 . findEdges . zip [rotate α xDir | α <- [0 @@ turn, 1/(2^n) @@ turn .. fullTurn]]
>         l2t [x,y] =  (x, angleBetweenDirs x y)
>         l2t [x]   = (x, angleBetweenDirs x xDir) -- arc angle will never be > fullturn ^/ 2
> 
> findEdges :: Eq a => [(Direction V2 Double, a)] -> [Direction V2 Double]
> findEdges = catMaybes . (zipWith edge <*> tail)
>   where edge (_,c1) (a,c2) | c1 /= c2  = Just a
>                            | otherwise = Nothing

Generate concentric circular arcs from lists of angular segments.

> mkRingsDia = mconcat . zipWith mkRingDia [2,3..]
>   where mkRingDia r = lwL 1.05 . mconcat . map (strokeP . scale r . uncurry arc)
> 
> example = pad 1.1 (rings 10)

> main = mainWith (example :: Diagram B)