94 lines
3.5 KiB
Haskell
94 lines
3.5 KiB
Haskell
module Main where
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import Control.Monad (forM_)
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import Data.List (intercalate)
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import Debug.Trace (trace)
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import Math.NumberTheory.Roots (integerSquareRoot, integerCubeRoot)
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type Cell = Int -- ^ The index of a cell in the cube
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type Layer = Int -- ^ A layer of our cube
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type Ring = Int -- ^ A ring of a 2D spiral
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type Length = Int -- ^ The length of an line segment
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type X = Int
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type Y = Int
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type Z = Int
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type Point = (X, Y, Z)
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area :: Int -> Int
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area a = a * a
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cube :: Int -> Int
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cube a = a * a * a
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layer :: Cell -> Layer
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layer c = integerCubeRoot c `div` 2
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ring :: Cell -> Ring
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ring o = integerSquareRoot o `div` 2
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edge :: Layer -> Length
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edge l = 2 * l + 2
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-- | Offset of a cell within its layer
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lOffset :: Cell -> Cell
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lOffset c = c - cube (edge $ layer c - 1)
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-- | Offset of a cell in a layer within its spiral ring
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rOffset :: Cell -> Cell
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rOffset o = o - area (edge $ ring o - 1)
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location :: Cell -> Point
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location c | o < a = locationOnTop (e `div` 2 - 1) o
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| o < a + (e - 2) * (e - 1) * 4 = locationAround c
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| otherwise = locationOnBottom ((-e) `div` 2) c (o - a - (e - 2) * (e - 1) * 4)
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where o = lOffset c -- ^ offset within the current layer
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l = layer c -- ^ the current layer
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e = edge l -- ^ the length of the edge of the current layer
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a = area e -- ^ the area of a side of the current layer
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locationOnTop :: Z -> Cell -> Point
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locationOnTop z o | o == 0 = (0, 0, z)
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| ro < e - 1 = (r, ro - r, z) -- 64
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| ro < 2 * e - 2 = (3 * r - ro, r, z)
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| ro < 3 * e - 3 = (0 - r - 1, 5 * r - ro + 1, z)
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| otherwise = (ro - 7 * r - 3, 0 - r - 1, z)
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where r = ring o -- ^ the current spiral ring
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ro = rOffset o -- ^ offset within this ring
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e = edge r -- ^ edge of the this ring
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locationAround :: Cell -> Point
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locationAround c | o <= r = (l - r + o, 0 - l - 1, l - r - 1)
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| o <= r + e - 1 = (l, 0 - l - 1 + o - r, l - r - 1)
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| o <= r + 2 * e - 2 = (l - o + r + e - 1, l, l - r - 1)
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| o <= r + 3 * e - 3 = (0 - l - 1, l - o + r + 2 * e - 2, l - r - 1)
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| otherwise = (0 - l - 1 + o - r - 3 * e + 3, 0 - l - 1, l - r - 1)
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where l = layer c
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e = edge l
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s = lOffset c - area e -- ^ offset since starting the sides of the cude
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r = s `div` (4 * e - 4) -- ^ revolutions since starting on the side
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o = s - (4 * e - 4) * r -- ^ offset within this revolution
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locationOnBottom :: Z -> Cell -> Cell -> Point
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locationOnBottom z c b | False = (r, r, z)
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| otherwise = (3, -3, z)
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where l = layer c
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r = integerSquareRoot (area (edge l) - b - 1) `div` 2 -- ^ the current spiral ring
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asMatrix :: Length -> [[[Cell]]]
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asMatrix e = foldl (\c (i, x, y, z) -> replace c z $ replace (c!!z) y $ replace (c!!z!!y) x i)
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(replicate e $ replicate e $ replicate e (-1))
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[ (i, x + div e 2, y + div e 2, z + div e 2)
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| i <- [0..cube e - 1]
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, let (x, y, z) = location i
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-- , x + div e 2 >= 0, y + div e 2 >= 0, z + div e 2 >= 0
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-- , x < div e 2, y < div e 2, z < div e 2
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]
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where replace :: [a] -> Int -> a -> [a]
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replace l i e = take i l ++ [e] ++ drop (i+1) l
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main :: IO ()
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main = forM_ (reverse $ asMatrix 6) $ \plane -> do
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forM_ (reverse plane) $ \row -> do
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putStrLn $ intercalate ",\t" $ map show row
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putStrLn ""
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