{- Copyright 2011 Google Inc. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. -} {-# LANGUAGE TypeFamilies, TypeSynonymInstances #-} -- | Describes a dodecahedron in terms of faces, edges, and vertices. module Twisty.Dodeca where import Twisty.Cycles import Twisty.Group import Twisty.Lists import qualified Twisty.Memo as Memo import Twisty.Polyhedron import Twisty.Twists import Twisty.Wreath import Data.Array.IArray (Ix, (!), Array, listArray) import Data.List (transpose) import GHC.Enum (boundedEnumFrom, boundedEnumFromThen) -- | The faces of the dodecahedron. The north polar face is An, and -- the remaining northern hemisphere faces are Xn, X in (B..F). The -- opposite face to Xn is Xs. The order is such that the opposite -- face for face X is the same distance from the back of the list as X -- is from the front. data Face = An | Bn | Cn | Dn | En | Fn | Fs | Es | Ds | Cs | Bs | As deriving (Eq, Ord, Enum, Bounded, Ix) oppositeFaceNumber :: Int -> Int oppositeFaceNumber = (11 -) oppositeFace :: Face -> Face oppositeFace = toEnum . oppositeFaceNumber . fromEnum isOpposite f1 f2 = f1 == oppositeFace f2 instance PolyFace Face where newtype PolyEdge Face = Edge Int deriving (Eq, Ord, Ix) newtype PolyVertex Face = Vertex Int deriving (Eq, Ord, Ix) faceNames = [(An, 'A'), (Bn, 'B'), (Cn, 'C'), (Dn, 'D'), (En, 'E'), (Fn, 'F'), (As, 'a'), (Bs, 'b'), (Cs, 'c'), (Ds, 'd'), (Es, 'e'), (Fs, 'f')] neighboringFaces = Memo.array nf where nf :: Face -> [Face] nf f | f == An = [Bn, Cn, Dn, En, Fn] | f <= Fn = let same n = toEnum (1 + (fromEnum f - 1 + n) `mod` 5) opp = oppositeFace . same in [An, same(-1), opp 2, opp(-2), same 1] | otherwise = map oppositeFace \$ reverse . nf . oppositeFace \$ f -- | The distinguished faces for dodecahedron edges are: the north or south -- polar face, for the ten polar edges; and the faces which would move the -- edge to a polar face if the face were rotated clockwise (north) or -- counterclockwise (south) once or twice, for the ten vertical and ten -- equatorial edges. allEdgesAsFaces = polarEdges ++ verticalEdges ++ equatorialEdges where polarEdges = faceEdgesAsFaces An ++ faceEdgesAsFaces As verticalEdges = northVerticalEdges ++ invert northVerticalEdges equatorialEdges = northEquatorialEdges ++ invert northEquatorialEdges northVerticalEdges = transpose [northNeighbors, rotate 1 northNeighbors] northEquatorialEdges = transpose [northNeighbors, map oppositeFace \$ rotate 3 northNeighbors] northNeighbors = neighboringFaces An invert = map (map oppositeFace) -- | The distinguished faces for dodecahedron vertices are: the north or south -- polar face, for the ten polar vertices; and the face which would move the -- vertex to a polar face if the face were rotated clockwise (north) or -- counterclockwise (south), for the ten equatorial vertices. allVerticesAsFaces = polarVertices ++ equatorialVertices where polarVertices = faceNeighborTriples An ++ faceNeighborTriples As equatorialVertices = northEquatorialVertices ++ invert northEquatorialVertices northEquatorialVertices = transpose [fs1, fs2, fs3] where fs1 = neighboringFaces An fs2 = map oppositeFace \$ rotate 3 fs1 fs3 = rotate 1 fs1 invert = map invertFaces invertFaces = swapFaces . map oppositeFace swapFaces [f1, f2, f3] = [f1, f3, f2] type Edge = PolyEdge Face type Vertex = PolyVertex Face instance WreathPermutable Edge where type WreathTwist Edge = Flip instance WreathPermutable Vertex where type WreathTwist Vertex = Twist3 instance Show Face where showsPrec _ = showChar . faceToName instance Read Face where readsPrec _ = readSFace instance Enum Edge where toEnum = toBoundedEnum Edge fromEnum (Edge e) = e enumFrom = boundedEnumFrom enumFromThen = boundedEnumFromThen instance Bounded Edge where minBound = Edge 0 maxBound = Edge \$ length (allEdgesAsFaces::[[Face]]) - 1 instance Show Edge where showsPrec _ = showString . edgeName instance Read Edge where readsPrec _ = readSEdge instance Enum Vertex where toEnum = toBoundedEnum Vertex fromEnum (Vertex v) = v enumFrom = boundedEnumFrom enumFromThen = boundedEnumFromThen instance Bounded Vertex where minBound = Vertex 0 maxBound = Vertex \$ length (allVerticesAsFaces::[[Face]]) - 1 instance Show Vertex where showsPrec _ = showString . vertexName instance Read Vertex where readsPrec _ = readSVertex