63 lines
2.3 KiB
Haskell
63 lines
2.3 KiB
Haskell
import Data.List
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import Data.Ord
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import Text.Printf
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import System.Environment
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main = do
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argv <- getArgs
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listWordsUpToLength $ read $ argv !! 0
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listWordsUpToLength :: Int -> IO ()
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listWordsUpToLength n = do
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putStr $ unlines [printf "%s %d/%d %f"
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w
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(p `div` gcd p q)
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(q `div` gcd p q)
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(atan (sqrt 3 / (2*q_/p_ + 1))) |
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((p,q),w) <- wordlist (n `div` 2, n `div` 2),
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let p_ = fromIntegral p :: Double,
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let q_ = fromIntegral q :: Double,
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length w <= n,
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let x = 2*q + p,
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let y = 2*p + q]
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-- (sqrt 3 / 2 * fromIntegral p / (fromIntegral q + fromIntegral p / 2) :: Double) |
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-- (slopeWord "bca" (orthogonalSlope (p,q))) |
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wordlist :: (Int,Int) -> [((Int,Int),String)]
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wordlist (pmax,qmax) = nub $
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sortBy (comparing sl)
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[((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" (p,q)) |
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p <- [0..pmax],
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q <- [0..qmax],
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q /= 0] -- use p /= 0 || q /= 0 for more symmetric output
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where
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sl ((p,q),_) = fromIntegral p / fromIntegral q
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-- letters: reflection along e_1, reflection along e_2, other one; p,q >= 0
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-- the "slope" (p,q) means the Euclidean vector q*e_1 + p*e_2, where e_1,e_2 are at a 60 degree angle
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-- in Euclidean coordinates this is (q + p/2, sqrt(3)/2 * p)
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slopeWord :: [Char] -> (Int,Int) -> String
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slopeWord [x,y,z] (p,q)
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| p > q = slopeWord [y,x,z] (q,p)
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| otherwise = concat $ map word $ zipWith step list (tail list)
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where
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p_ = p `div` gcd p q
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q_ = q `div` gcd p q
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xmax = if (p_-q_) `mod` 3 == 0 then q_ else 3*q_ :: Int
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list = [(x,(x*p) `div` q) | x <- [0..xmax]]
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step (x1,y1) (x2,y2) = ((x1-y1) `mod` 3, y2-y1)
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word (0,0) = [z,x]
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word (1,0) = [y,z]
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word (2,0) = [x,y]
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word (0,1) = [z,y,x,y]
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word (1,1) = [y,x,z,x]
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word (2,1) = [x,z,y,z]
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-- assuming p, q >= 0
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orthogonalSlope :: (Int, Int) -> (Int, Int)
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orthogonalSlope (p,q)
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| p > q = (p-q, p+2*q)
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| p < q = (q+2*p, q-p)
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| otherwise = (1,0)
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