diagrams-rubiks-cube (empty) → 0.1.0.0
raw patch · 14 files changed
+841/−0 lines, 14 filesdep +basedep +data-default-classdep +diagrams-libsetup-changed
Dependencies added: base, data-default-class, diagrams-lib, lens
Files
- LICENSE +20/−0
- README.md +21/−0
- Setup.hs +2/−0
- diagrams-rubiks-cube.cabal +32/−0
- diagrams/src_Diagrams_RubiksCube_Draw_drawCubeExample.svg +4/−0
- diagrams/src_Diagrams_RubiksCube_Draw_drawMoveExample.svg +4/−0
- diagrams/src_Diagrams_RubiksCube_Draw_drawMovesExample.svg +4/−0
- diagrams/src_Diagrams_RubiksCube_Draw_drawSideDia.svg +4/−0
- diagrams/src_Diagrams_RubiksCube_Draw_offsetsDia.svg +4/−0
- diagrams/src_Diagrams_RubiksCube_Draw_solvedCube.svg +4/−0
- src/Diagrams/RubiksCube.hs +9/−0
- src/Diagrams/RubiksCube/Draw.hs +278/−0
- src/Diagrams/RubiksCube/Model.hs +416/−0
- src/Diagrams/RubiksCube/Move.hs +39/−0
+ LICENSE view
@@ -0,0 +1,20 @@+Copyright (c) 2015 Tim Baumann++Permission is hereby granted, free of charge, to any person obtaining+a copy of this software and associated documentation files (the+"Software"), to deal in the Software without restriction, including+without limitation the rights to use, copy, modify, merge, publish,+distribute, sublicense, and/or sell copies of the Software, and to+permit persons to whom the Software is furnished to do so, subject to+the following conditions:++The above copyright notice and this permission notice shall be included+in all copies or substantial portions of the Software.++THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.+IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY+CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,+TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+ README.md view
@@ -0,0 +1,21 @@+# diagrams-rubiks-cube [![Hackage version][hackage-image]][hackage-url] [![Hackage dependencies][hackage-deps-image]][hackage-deps-url]++Haskell library for drawing the Rubik's Cube.++![Move sequence][moves-image]++## Installation++```bash+$ cabal install diagrams-rubiks-cube+```++## Documentation++See the docs on [Hackage][hackage-url].++[moves-image]: https://cdn.rawgit.com/timjb/diagrams-rubiks-cube/master/diagrams/src_Diagrams_RubiksCube_Draw_drawMovesExample.svg+[hackage-image]: https://img.shields.io/hackage/v/diagrams-rubiks-cube.svg?style=flat+[hackage-url]: http://hackage.haskell.org/package/diagrams-rubiks-cube+[hackage-deps-image]: https://img.shields.io/hackage-deps/v/diagrams-rubiks-cube.svg?style=flat+[hackage-deps-url]: http://packdeps.haskellers.com/feed?needle=diagrams-rubiks-cube.svg
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ diagrams-rubiks-cube.cabal view
@@ -0,0 +1,32 @@+name: diagrams-rubiks-cube+version: 0.1.0.0+synopsis: Library for drawing the Rubik's Cube.+description: Includes a facets model of the Rubik's Cube and a 'diagrams'-based renderer.+homepage: https://github.com/timjb/rubiks-cube+license: MIT+license-file: LICENSE+author: Tim Baumann+maintainer: tim@timbaumann.info+copyright: 2015 Tim Baumann+category: Graphics+build-type: Simple+extra-source-files: README.md, diagrams/*.svg+extra-doc-files: diagrams/*.svg+cabal-version: >= 1.10++source-repository head+ type: git+ location: https://github.com/timjb/diagrams-rubiks-cube.git++library+ ghc-options: -Wall+ exposed-modules: Diagrams.RubiksCube,+ Diagrams.RubiksCube.Move,+ Diagrams.RubiksCube.Model,+ Diagrams.RubiksCube.Draw+ build-depends: base >= 4.6 && < 5,+ diagrams-lib >= 1.2.0.7 && < 1.3,+ lens >= 4.6.0.1 && < 5,+ data-default-class >= 0.0.1 && < 0.1+ hs-source-dirs: src+ default-language: Haskell2010
+ diagrams/src_Diagrams_RubiksCube_Draw_drawCubeExample.svg view
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+ src/Diagrams/RubiksCube.hs view
@@ -0,0 +1,9 @@+module Diagrams.RubiksCube+ ( module Diagrams.RubiksCube.Move+ , module Diagrams.RubiksCube.Model+ , module Diagrams.RubiksCube.Draw+ ) where++import Diagrams.RubiksCube.Move+import Diagrams.RubiksCube.Model+import Diagrams.RubiksCube.Draw
+ src/Diagrams/RubiksCube/Draw.hs view
@@ -0,0 +1,278 @@+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE Rank2Types #-}++module Diagrams.RubiksCube.Draw+ ( solvedRubiksCube+ , drawSide+ , drawFoldingPattern+ , Offsets (..), offsetX, offsetY+ , drawRubiksCube+ , drawMove+ , MovesSettings (..), moveSep, showStart, showEnd, offsets+ , drawMoves, drawMovesBackward+ ) where++import Diagrams.RubiksCube.Move (Move (..))+import Diagrams.RubiksCube.Model++import Control.Lens hiding ((#))+import Diagrams.Prelude hiding (center)+import Data.List (sortBy, mapAccumL)+import Data.Function (on)+import qualified Diagrams.Prelude as P+import Data.Default.Class++-- > import Diagrams.RubiksCube.Draw+-- > solvedCube = drawFoldingPattern solvedRubiksCube++-- | The solved cube.+--+-- <<diagrams/src_Diagrams_RubiksCube_Draw_solvedCube.svg#diagram=solvedCube&height=150&width=200>>+solvedRubiksCube :: RubiksCube (Colour Double)+solvedRubiksCube = RubiksCube (Cube f b l r u d)+ where+ f = pure orange+ b = pure red+ l = pure white+ r = pure yellow+ u = pure green+ d = pure blue++-- > import Diagrams.RubiksCube+-- > drawSideDia =+-- > let side = drawSide (r2 (1,0)) (r2 (0,1)) (pure yellow & topLeft .~ green)+-- > dxArrow = arrowBetween (p2 (4,1)) (p2 (5,1))+-- > dxLabel = position [(p2 (4.5, 0.7), scale 0.4 (text "dx"))]+-- > dyArrow = arrowBetween (p2 (4,1)) (p2 (4,2))+-- > dyLabel = position [(p2 (3.65, 1.5), scale 0.4 (text "dy"))]+-- > in mconcat [side, dxArrow, dxLabel, dyArrow, dyLabel]++-- | Draws one 3x3 side of the cube.+--+-- <<diagrams/src_Diagrams_RubiksCube_Draw_drawSideDia.svg#diagram=drawSideDia&height=150&width=200>>+drawSide+ :: Renderable (Path R2) b+ => R2 -- ^ dx+ -> R2 -- ^ dy+ -> Side (Colour Double)+ -> Diagram b R2+drawSide dx dy side = mconcat $ do+ (y, row) <- count rows+ let Vec3 l c r = side ^. row+ [drawField 0 y l, drawField 1 y c, drawField 2 y r]+ where+ count = zip [(0 :: Int)..]+ rows = [bottomRow, middleRow, topRow]+ pos x y = p2 $ unr2 $ fromIntegral x *^ dx ^+^ fromIntegral y *^ dy+ drawField :: Renderable (Path R2) b => Int -> Int -> Colour Double -> Diagram b R2+ drawField x y color =+ fromVertices [pos x y, pos (x+1) y, pos (x+1) (y+1), pos x (y+1), pos x y]+ # mapLoc closeTrail # trailLike # fc color++-- | Draw the folding pattern of the cube. The front side is at the center of+-- the pattern.+drawFoldingPattern+ :: Renderable (Path R2) b+ => RubiksCube (Colour Double)+ -> Diagram b R2+drawFoldingPattern c' =+ let c = c' ^. cube+ drawSide' = drawSide (r2 (1,0)) (r2 (0,1))+ in hcat $ map P.center+ [ drawSide' (c ^. leftSide)+ , drawSide' (c ^. upSide) ===+ drawSide' (c ^. frontSide) ===+ drawSide' (c ^. downSide)+ , drawSide' (c ^. rightSide)+ , drawSide' (c ^. backSide)+ ]++-- > import Diagrams.RubiksCube+-- > offsetsDia =+-- > let off = Offsets 2 1+-- > c = drawRubiksCube off solvedRubiksCube+-- > oxArrow = arrowBetween (p2 (3,-1)) (p2 (5,-1))+-- > oxLabel = position [(p2 (4, -1.75), scale 0.8 (text "offX"))]+-- > oyArrow = arrowBetween (p2 (7,0)) (p2 (7,1))+-- > oyLabel = position [(p2 (8, 0.5), scale 0.8 (text "offY"))]+-- > line start end = fromVertices [p2 start, p2 end]+-- > lines = mconcat+-- > [ line (3,-1) (3,0)+-- > , line (5,-1) (5,2)+-- > , line (3,0) (7,0)+-- > , line (5,1) (7,1)+-- > ] # lc lightgray # dashingN [0.01,0.01] 0+-- > in mconcat [c, oxArrow, oxLabel, oyArrow, oyLabel, lines] # pad 1.1++-- | <<diagrams/src_Diagrams_RubiksCube_Draw_offsetsDia.svg#diagram=offsetsDia&height=200&width=200>>+data Offsets =+ Offsets { _offsetX :: Double+ , _offsetY :: Double+ } deriving (Show, Eq, Read)++makeLenses ''Offsets++instance Default Offsets where+ def = Offsets 0.3 0.35++-- | Draw the Rubik's cube in parallel perspective.+--+-- <<diagrams/src_Diagrams_RubiksCube_Draw_drawCubeExample.svg#diagram=drawCubeExample&height=150&width=150>>+--+-- > import Diagrams.RubiksCube+-- > import Control.Lens+-- > drawCubeExample =+-- > let c = solvedRubiksCube ^. undoMoves [R,U,R',U']+-- > in drawRubiksCube with c+drawRubiksCube+ :: Renderable (Path R2) b+ => Offsets+ -> RubiksCube (Colour Double)+ -> Diagram b R2+drawRubiksCube (Offsets dx dy) c' = position $+ [ f ] +++ sides +++ [ b ]+ where+ sides = map snd $ sortBy (compare `on` fst) $+ [ (-dx, r)+ , (dx, l)+ , (-dy, u)+ , (dy, d)+ ]+ dx' = r2 (1,0)+ dy' = r2 (0,1)+ dz' = r2 (dx,dy)+ drawSide' dx1 dx2 side = drawSide dx1 dx2 (c' ^. cube . side)+ f = (p2 (0, 0), drawSide' dx' dy' frontSide)+ b = (p2 (3*dx, 3+3*dy), drawSide' dx' (-dy') backSide)+ r = (p2 (3,0), drawSide' dz' dy' rightSide)+ l = (p2 (3*dx, 3*dy), drawSide' (-dz') dy' leftSide)+ u = (p2 (0,3), drawSide' dx' dz' upSide)+ d = (p2 (3*dx, 3*dy), drawSide' dx' (-dz') downSide)++moveArrow+ :: Renderable (Path R2) b+ => Bool -> P2 -> P2 -> Diagram b R2+moveArrow rev s e =+ (if rev then arrowBetween' opts e s else arrowBetween' opts s e) # lc red+ where opts = with & shaftStyle %~ lw ultraThick & headLength .~ veryLarge++drawMoveU, drawMoveD, drawMoveL, drawMoveR, drawMoveF+ :: Renderable (Path R2) b+ => Bool -- ^ invert+ -> Offsets+ -> RubiksCube (Colour Double)+ -> Diagram b R2+drawMoveU rev off c =+ atop (moveArrow rev (p2 (2.8, 2.5)) (p2 (0.2, 2.5)))+ (drawRubiksCube off c)+drawMoveD rev (Offsets dx dy) c =+ atop (moveArrow rev (p2 (0.2, 0.5)) (p2 (2.8, 0.5)))+ (drawRubiksCube (Offsets dx (-dy)) c)+drawMoveL rev (Offsets dx dy) c =+ atop (moveArrow rev (p2 (0.5, 2.8)) (p2 (0.5, 0.2)))+ (drawRubiksCube (Offsets dx dy) c)+drawMoveR rev off c =+ atop (moveArrow rev (p2 (2.5, 0.2)) (p2 (2.5, 2.8)))+ (drawRubiksCube off c)+drawMoveF rev off c =+ arr (opts & arrowShaft .~ quarterTurn) (p2 (1.5, 2.6)) (p2 (2.5, 1.3))+ `atop`+ arr (opts & arrowShaft .~ quarterTurn) (p2 (1.5, 0.4)) (p2 (0.5, 1.7))+ `atop`+ drawRubiksCube off c+ where+ quarterTurn = arc (0 @@ turn) (1/4 @@ turn) # (if rev then id else reverseTrail)+ opts = with & shaftStyle %~ lw ultraThick & headLength .~ veryLarge+ arr opts' s e = (if rev then arrowBetween' opts' e s else arrowBetween' opts' s e)+ # lc red++-- | Draw the Rubik's cube in parallel perspective with an arrow indicating the+-- next move. If the the bottom layer is moved, the cube will be shown from below.+--+-- <<diagrams/src_Diagrams_RubiksCube_Draw_drawMoveExample.svg#diagram=drawMoveExample&height=150&width=150>>+--+-- > import Diagrams.RubiksCube+-- > import Control.Lens+-- > drawMoveExample =+-- > let c = solvedRubiksCube ^. undoMoves [L,U,L',U']+-- > in drawMove L with c+drawMove+ :: Renderable (Path R2) b+ => Move+ -> Offsets+ -> RubiksCube (Colour Double)+ -> Diagram b R2+drawMove U = drawMoveU False+drawMove U' = drawMoveU True+drawMove D = drawMoveD False+drawMove D' = drawMoveD True+drawMove L = drawMoveL False+drawMove L' = drawMoveL True+drawMove R = drawMoveR False+drawMove R' = drawMoveR True+drawMove F = drawMoveF False+drawMove F' = drawMoveF True+drawMove _ = error "can't draw back moves!"++data MovesSettings =+ MovesSettings { _moveSep :: Double -- ^ space between cubes+ , _showStart :: Bool -- ^ show the start configuration?+ , _showEnd :: Bool -- ^ show the end configuration?+ , _offsets :: Offsets+ } deriving (Eq, Show, Read)++makeLenses ''MovesSettings++instance Default MovesSettings where+ def = MovesSettings 1.75 False True def++-- | Draws a sequence of moves.+--+-- <<diagrams/src_Diagrams_RubiksCube_Draw_drawMovesExample.svg#diagram=drawMovesExample&height=100&width=600>>+--+-- > import Diagrams.RubiksCube+-- > import Control.Lens+-- > drawMovesExample =+-- > let moves = [R, F', R', D', F, F]+-- > startPos = solvedRubiksCube ^. undoMoves moves+-- > settings = with & showStart .~ True+-- > in drawMoves settings startPos moves+drawMoves+ :: Renderable (Path R2) b+ => MovesSettings+ -> RubiksCube (Colour Double) -- ^ the start configuration+ -> [Move]+ -> Diagram b R2+drawMoves settings c moves =+ let ((j, c'), ps) = mapAccumL iter (0 :: Int, c) moves+ allCubes = (if settings ^. showStart then ((pos ((-1) :: Int), drawRubiksCube off c) :) else id) $+ (if settings ^. showEnd then ((pos j, drawRubiksCube off c') :) else id) ps+ in position allCubes+ where+ off = settings ^. offsets+ pos i = p2 (fromIntegral i * (3 + settings ^. moveSep), 0)+ iter (i, c') m =+ let c'' = c' ^. move m+ in ((i+1, c''), (pos i, drawMove m off c'))++-- | Like 'drawMoves', but takes the end configuration instead of the start+-- configuration. The previous example can be simplified with this:+--+-- > import Diagrams.RubiksCube+-- > import Control.Lens+-- > drawMovesExample' =+-- > let moves = [R, F', R', D', F, F]+-- > endPos = solvedRubiksCube+-- > settings = with & showStart .~ True+-- > in drawMovesBackward settings endPos moves+drawMovesBackward+ :: Renderable (Path R2) b+ => MovesSettings+ -> RubiksCube (Colour Double) -- ^ the end configuration+ -> [Move]+ -> Diagram b R2+drawMovesBackward settings c moves =+ drawMoves settings (c ^. undoMoves moves) moves
+ src/Diagrams/RubiksCube/Model.hs view
@@ -0,0 +1,416 @@+{-# LANGUAGE DeriveFunctor #-}+{-# LANGUAGE DeriveFoldable #-}+{-# LANGUAGE DeriveTraversable #-}+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE Rank2Types #-}++module Diagrams.RubiksCube.Model (+ -- * Constructing cubes+ Side (..)+ , topLeft, topCenter, topRight+ , middleLeft, middleCenter, middleRight+ , bottomLeft, bottomCenter, bottomRight+ , rotateSideCW, rotateSideCCW+ , Cube (..), frontSide, backSide, leftSide, rightSide, upSide, downSide+ , RubiksCube (..), cube+ -- * Selecting rows and columns+ , Vec3 (..)+ , topRow, middleRow, bottomRow+ , leftCol, centerCol, rightCol+ -- * Traversing facets+ -- ** By layer+ , topLayerFacets, middleLayerFacets, bottomLayerFacets+ -- ** By position+ , centerFacets, cornerFacets, edgeFacets+ -- * Rotating the whole cube+ , Aut+ , rotateLeft, rotateRight+ , rotateDown, rotateUp+ , rotateCW, rotateCCW+ -- * Moving layers of the cube+ , move, doMoves, undoMoves+ ) where++import Control.Lens+import Diagrams.RubiksCube.Move (Move (..))+import Data.Foldable (Foldable)+import Control.Applicative (Applicative (..), (<$>))++-- | The type of automorphisms+type Aut a = Iso' a a++-- | A list of fixed length 3.+data Vec3 a = Vec3 a a a deriving (Show, Eq, Functor, Foldable, Traversable)++instance Applicative Vec3 where+ pure v = Vec3 v v v+ Vec3 f1 f2 f3 <*> Vec3 v1 v2 v3 =+ Vec3 (f1 v1) (f2 v2) (f3 v3)++instance Reversing (Vec3 a) where+ reversing (Vec3 a b c) = Vec3 c b a++-- | A list of fixed length 4.+data Vec4 a = Vec4 a a a a deriving (Show, Eq, Functor, Foldable, Traversable)++instance Applicative Vec4 where+ pure v = Vec4 v v v v+ Vec4 f1 f2 f3 f4 <*> Vec4 v1 v2 v3 v4 =+ Vec4 (f1 v1) (f2 v2) (f3 v3) (f4 v4)++cycRight :: Vec4 a -> Vec4 a+cycRight (Vec4 a b c d) = Vec4 d a b c++cycLeft :: Vec4 a -> Vec4 a+cycLeft (Vec4 a b c d) = Vec4 b c d a++cycleLeft :: Aut (Vec4 a)+cycleLeft = iso cycLeft cycRight++cycleRight :: Aut (Vec4 a)+cycleRight = iso cycRight cycLeft++-- | One side of the Rubik's Cube with 3*3 facets.+data Side a =+ Side { _topLeft :: a+ , _topCenter :: a+ , _topRight :: a+ , _middleLeft :: a+ , _middleCenter :: a+ , _middleRight :: a+ , _bottomLeft :: a+ , _bottomCenter :: a+ , _bottomRight :: a+ } deriving (Show, Eq, Functor, Foldable, Traversable)++instance Applicative Side where+ pure v = Side v v v v v v v v v+ Side f1 f2 f3 f4 f5 f6 f7 f8 f9 <*> Side v1 v2 v3 v4 v5 v6 v7 v8 v9 =+ Side (f1 v1) (f2 v2) (f3 v3) (f4 v4) (f5 v5) (f6 v6) (f7 v7) (f8 v8) (f9 v9)++makeLenses ''Side++instance Reversing (Side a) where+ reversing (Side tl tc tr ml mc mr bl bc br) =+ Side br bc bl mr mc ml tr tc tl++rotCW :: Side a -> Side a+rotCW (Side tl tc tr ml mc mr bl bc br) =+ Side bl ml tl bc mc tc br mr tr++rotCCW :: Side a -> Side a+rotCCW (Side tl tc tr ml mc mr bl bc br) =+ Side tr mr br tc mc bc tl ml bl++-- | Rotate the side clockwise.+rotateSideCW :: Aut (Side a)+rotateSideCW = iso rotCW rotCCW++-- | Rotate the side counter-clockwise.+rotateSideCCW :: Aut (Side a)+rotateSideCCW = iso rotCCW rotCW++-- | The top three facets (from left to right).+topRow :: Lens' (Side a) (Vec3 a)+topRow = lens getter setter+ where+ getter (Side tl tc tr _ _ _ _ _ _) = Vec3 tl tc tr+ setter (Side _ _ _ ml mc mr bl bc br) (Vec3 tl tc tr) =+ Side tl tc tr ml mc mr bl bc br++-- | The middle three facets (from left to right).+middleRow :: Lens' (Side a) (Vec3 a)+middleRow = lens getter setter+ where+ getter (Side _ _ _ ml mc mr _ _ _) = Vec3 ml mc mr+ setter (Side tl tc tr _ _ _ bl bc br) (Vec3 ml mc mr) =+ Side tl tc tr ml mc mr bl bc br++-- | The bottom three facets (from left to right).+bottomRow :: Lens' (Side a) (Vec3 a)+bottomRow = lens getter setter+ where+ getter (Side _ _ _ _ _ _ bl bc br) = Vec3 bl bc br+ setter (Side tl tc tr ml mc mr _ _ _) (Vec3 bl bc br) =+ Side tl tc tr ml mc mr bl bc br++-- | The left column (from top to down).+leftCol :: Lens' (Side a) (Vec3 a)+leftCol = lens getter setter+ where+ getter (Side tl _ _ ml _ _ bl _ _) = Vec3 tl ml bl+ setter (Side _ tc tr _ mc mr _ bc br) (Vec3 tl ml bl) =+ Side tl tc tr ml mc mr bl bc br++-- | The center column (from top to down).+centerCol :: Lens' (Side a) (Vec3 a)+centerCol = lens getter setter+ where+ getter (Side _ tc _ _ mc _ _ bc _) = Vec3 tc mc bc+ setter (Side tl _ tr ml _ mr bl _ br) (Vec3 tc mc bc) =+ Side tl tc tr ml mc mr bl bc br++-- | The right column (from top to down).+rightCol :: Lens' (Side a) (Vec3 a)+rightCol = lens getter setter+ where+ getter (Side _ _ tr _ _ mr _ _ br) = Vec3 tr mr br+ setter (Side tl tc _ ml mc _ bl bc _) (Vec3 tr mr br) =+ Side tl tc tr ml mc mr bl bc br++-- | The four corners.+sideCorners :: Traversal' (Side a) a+sideCorners f (Side tl tc tr ml mc mr bl bc br) =+ (\tl' tr' bl' br' -> Side tl' tc tr' ml mc mr bl' bc br')+ <$> f tl <*> f tr <*> f bl <*> f br++-- | The four edges.+sideEdges :: Traversal' (Side a) a+sideEdges f (Side tl tc tr ml mc mr bl bc br) =+ (\tc' ml' mr' bc' -> Side tl tc' tr ml' mc mr' bl bc' br)+ <$> f tc <*> f ml <*> f mr <*> f bc++-- | A cube with six sides.+--+-- @+-- +---++-- | u |+-- +---+---+---+---++-- | l | f | r | b |+-- +---+---+---+---++-- | d |+-- +---++-- @+data Cube a =+ Cube { _frontSide :: a+ , _backSide :: a+ , _leftSide :: a+ , _rightSide :: a+ , _upSide :: a+ , _downSide :: a+ } deriving (Show, Eq, Functor, Foldable, Traversable)++instance Applicative Cube where+ pure v = Cube v v v v v v+ Cube ff fb fl fr fu fd <*> Cube vf vb vl vr vu vd =+ Cube (ff vf) (fb vb) (fl vl) (fr vr) (fu vu) (fd vd)++rotRight' :: Cube a -> Cube a+rotRight' (Cube f b l r u d) = Cube l r b f u d++rotLeft' :: Cube a -> Cube a+rotLeft' (Cube f b l r u d) = Cube r l f b u d++rotateRight' :: Aut (Cube a)+rotateRight' = iso rotRight' rotLeft'++_rotateLeft' :: Aut (Cube a)+_rotateLeft' = from rotateRight'++rotDown' :: Reversing a => Cube a -> Cube a+rotDown' (Cube f b l r u d) = Cube u (reversing d) l r (reversing b) f++rotUp' :: Reversing a => Cube a -> Cube a+rotUp' (Cube f b l r u d) = Cube d (reversing u) l r f (reversing b)++rotateDown' :: Reversing a => Aut (Cube a)+rotateDown' = iso rotDown' rotUp'++_rotateUp' :: Reversing a => Aut (Cube a)+_rotateUp' = from rotateDown'++makeLenses ''Cube++-- | A normal Rubik's cube with 6 sides with 9 facets each.+newtype RubiksCube a =+ RubiksCube { _cube :: Cube (Side a)+ } deriving (Show, Eq, Functor)++instance Applicative RubiksCube where+ pure = RubiksCube . pure . pure+ RubiksCube f <*> RubiksCube v = RubiksCube ((<*>) <$> f <*> v)++makeLenses ''RubiksCube++cong :: Traversal' s a -> Aut a -> Aut s+cong t i = withIso i $ \f g -> iso (over t f) (over t g)++-- | Rotate the whole Rubik's Cube such that the front side becomes the new+-- right side and the top and bottom sides stay fixed.+rotateRight :: Aut (RubiksCube a)+rotateRight =+ cong cube $ rotateRight'+ . cong upSide rotateSideCCW+ . cong downSide rotateSideCW++-- | Rotate the whole Rubik's Cube such that the front side becomes the new+-- left side and the top and bottom sides stay fixed.+rotateLeft :: Aut (RubiksCube a)+rotateLeft = from rotateRight++-- | Rotate the whole Rubik's Cube such that the front side becomes the new+-- bottom side and the left and right sides stay fixed.+rotateDown :: Aut (RubiksCube a)+rotateDown =+ cong cube $ rotateDown'+ . cong leftSide rotateSideCW+ . cong rightSide rotateSideCCW++-- | Rotate the whole Rubik's Cube such that the front side becomes the new+-- top side and the left and right sides stay fixed.+rotateUp :: Aut (RubiksCube a)+rotateUp = from rotateDown++-- | Rotate the whole Rubik's Cube such that the top side becomes the new+-- right side and the front and back sides stay fixed.+rotateCW :: Aut (RubiksCube a)+rotateCW = rotateUp . rotateLeft . rotateDown++-- | Rotate the whole Rubik's Cube such that the top side becomes the new+-- left side and the front and back sides stay fixed.+rotateCCW :: Aut (RubiksCube a)+rotateCCW = from rotateCW++type RowsLens a = Lens' (Cube (Side a)) (Vec4 (Vec3 a))+type ColsLens a = Lens' (Cube (Side a)) (Vec4 (Vec3 a))++horizontalRows :: Lens' (Side a) (Vec3 a) -> RowsLens a+horizontalRows rowLens = lens getter setter+ where+ getter (Cube f b l r _u _d) =+ fmap (view rowLens) (Vec4 f r b l)+ setter (Cube f b l r u d) (Vec4 f' r' b' l') =+ Cube (set rowLens f' f) (set rowLens b' b)+ (set rowLens l' l) (set rowLens r' r) u d++upRows :: RowsLens a+upRows = horizontalRows topRow++middleRows :: RowsLens a+middleRows = horizontalRows middleRow++downRows :: RowsLens a+downRows = horizontalRows bottomRow++moveU :: Aut (RubiksCube a)+moveU =+ cong cube $ cong upRows cycleLeft+ . cong upSide rotateSideCW++moveD :: Aut (RubiksCube a)+moveD =+ cong cube $ cong downRows cycleRight+ . cong downSide rotateSideCW++verticalCols :: Lens' (Side a) (Vec3 a) -> ColsLens a+verticalCols colLens = lens getter setter+ where+ getter (Cube f b _l _r u d) =+ Vec4 (f ^. colLens) (u ^. colLens) (b ^. reversed . colLens) (d ^. colLens)+ setter (Cube f b l r u d) (Vec4 f' u' b' d') =+ Cube (set colLens f' f) (set (reversed . colLens) b' b) l r+ (set colLens u' u) (set colLens d' d)++leftCols :: ColsLens a+leftCols = verticalCols leftCol++_centerCols :: ColsLens a+_centerCols = verticalCols centerCol++rightCols :: ColsLens a+rightCols = verticalCols rightCol++moveL :: Aut (RubiksCube a)+moveL =+ cong cube $ cong leftCols cycleLeft+ . cong leftSide rotateSideCW++moveR :: Aut (RubiksCube a)+moveR =+ cong cube $ cong rightCols cycleRight+ . cong rightSide rotateSideCW++ringCols :: Lens' (Side a) (Vec3 a) -> ColsLens a+ringCols colLens = lens getter setter+ where+ getter (Cube _f _b l r u d) =+ Vec4 (r ^. colLens) (u ^. rotateSideCW . colLens)+ (l ^. reversed . colLens) (d ^. rotateSideCCW . colLens)+ setter (Cube f b l r u d) (Vec4 r' u' l' d') =+ Cube f b (set (reversed . colLens) l' l) (set colLens r' r)+ (set (rotateSideCW . colLens) u' u) (set (rotateSideCCW . colLens) d' d)++frontCols :: ColsLens a+frontCols = ringCols leftCol++_betweenCols :: ColsLens a+_betweenCols = ringCols centerCol++backCols :: ColsLens a+backCols = ringCols rightCol++moveF :: Aut (RubiksCube a)+moveF =+ cong cube $ cong frontCols cycleLeft+ . cong frontSide rotateSideCW++moveB :: Aut (RubiksCube a)+moveB =+ cong cube $ cong backCols cycleRight+ . cong backSide rotateSideCW++-- | Perform a move.+move :: Move -> Aut (RubiksCube a)+move D = moveD+move D' = from moveD+move U = moveU+move U' = from moveU+move L = moveL+move L' = from moveL+move R = moveR+move R' = from moveR+move F = moveF+move F' = from moveF+move B = moveB+move B' = from moveB++-- | Perform a list of moves.+doMoves :: [Move] -> Aut (RubiksCube a)+doMoves [] = iso id id+doMoves (m:ms) = move m . doMoves ms++-- | Undo the actions of a list of moves.+undoMoves :: [Move] -> Aut (RubiksCube a)+undoMoves = from . doMoves++-- | The 21=4*3+9 facets in the top layer.+topLayerFacets :: Traversal' (RubiksCube a) a+topLayerFacets f =+ cube $ \c ->+ (\upSide' upRows' -> c & upSide .~ upSide' & upRows .~ upRows')+ <$> (traverse f (c ^. upSide))+ <*> (traverse (traverse f) (c ^. upRows))++-- | The 12=4*3 facets in the middle layer.+middleLayerFacets :: Traversal' (RubiksCube a) a+middleLayerFacets = cube.middleRows.traverse.traverse++-- | The 21=4*3+9 facets in the bottom layer.+bottomLayerFacets :: Traversal' (RubiksCube a) a+bottomLayerFacets f =+ cube $ \c ->+ (\downSide' downRows' -> c & downSide .~ downSide' & downRows .~ downRows')+ <$> (traverse f (c ^. downSide))+ <*> (traverse (traverse f) (c ^. downRows))++-- | The six facets that are the center of their side.+centerFacets :: Traversal' (RubiksCube a) a+centerFacets = cube.traverse.middleCenter++-- | The 24=6*4=8*3 corner facets.+cornerFacets :: Traversal' (RubiksCube a) a+cornerFacets = cube.traverse.sideCorners++-- | The 24=6*4=12*2 edge facets.+edgeFacets :: Traversal' (RubiksCube a) a+edgeFacets = cube.traverse.sideEdges
+ src/Diagrams/RubiksCube/Move.hs view
@@ -0,0 +1,39 @@+module Diagrams.RubiksCube.Move+ ( Move (..)+ , mirror+ , invert+ ) where++-- | A move in <http://ruwix.com/the-rubiks-cube/notation/ standard notation>.+data Move = D | D' | U | U' | L | L' | R | R' | F | F' | B | B'+ deriving (Eq, Show, Read)++-- | The opposite move.+invert :: Move -> Move+invert D = D'+invert D' = D+invert U = U'+invert U' = U+invert L = L'+invert L' = L+invert R = R'+invert R' = R+invert F = F'+invert F' = F+invert B = B'+invert B' = B++-- | Swaps left and right.+mirror :: Move -> Move+mirror D = D'+mirror D' = D+mirror U = U'+mirror U' = U+mirror L = R'+mirror L' = R+mirror R = L'+mirror R' = L+mirror F = F'+mirror F' = F+mirror B = B'+mirror B' = B