diff --git a/grid.cabal b/grid.cabal --- a/grid.cabal +++ b/grid.cabal @@ -1,5 +1,5 @@ name: grid -version: 4.1 +version: 5.0 synopsis: Tools for working with regular grids (graphs, lattices). description: Provides tools for working with regular arrangements of tiles, such as might be used in a board game or some @@ -42,7 +42,7 @@ build-depends: base ==4.*, exact-combinatorics ==0.2.*, test-framework-quickcheck2 ==0.3.*, - QuickCheck ==2.4.* || ==2.5.*, + QuickCheck ==2.4.* || ==2.5.* || ==2.6.*, test-framework ==0.8.*, grid, base-unicode-symbols ==0.2.* diff --git a/src/Math/Geometry/Grid.hs b/src/Math/Geometry/Grid.hs --- a/src/Math/Geometry/Grid.hs +++ b/src/Math/Geometry/Grid.hs @@ -12,9 +12,34 @@ -- The userguide is available at -- . -- +-- In this package, tiles are called \"triangular\", \"square\", etc., +-- based on the number of /neighbours/ they have. +-- For example, a square tile has four neighbours, and a hexagonal +-- tile has six. +-- There are only three regular polygons that can tile a plane: +-- triangles, squares, and hexagons. +-- Of course, other plane tilings are possible if you use irregular +-- polygons, or curved shapes, or if you combine tiles of different +-- shapes. +-- +-- When you tile other surfaces, things get very interesting. +-- Octagons will tile a /hyperbolic/ plane. +-- (Alternatively, you can think of these as squares on a board game +-- where diagonal moves are allowed.) +-- +-- For a board game, you probably want to choose the grid type based +-- on the number of /directions/ a player can move, rather than the +-- number of sides the tile will have when you display it. +-- For example, for a game that uses square tiles and allows the user +-- to move diagonally as well as horizontally and vertically, +-- consider using one of the grids with /octagonal/ tiles to model the +-- board. +-- You can still /display/ the tiles as squares, but for internal +-- calculations they are octagons. +-- -- NOTE: Version 4.0 uses associated (type) synonyms instead of -- multi-parameter type classes. - +-- -- NOTE: Version 3.0 changed the order of parameters for many functions. -- This makes it easier for the user to write mapping and folding -- operations. @@ -25,6 +50,8 @@ module Math.Geometry.Grid ( + -- * Example + -- $Example -- * The Grid class Grid(..), FiniteGrid(..), @@ -61,9 +88,16 @@ hexHexGrid, -- ** Parallelogram-shaped grid with hexagonal tiles ParaHexGrid, - paraHexGrid - -- * Example - -- $Example + paraHexGrid, + -- * Grids with octagonal tiles + -- ** Unbounded grid with octagonal tiles + UnboundedOctGrid, + -- ** Rectangular grid with octagonal tiles + RectOctGrid, + rectOctGrid, + -- ** Toroidal grid with octagonal tiles + TorOctGrid, + torOctGrid ) where import Math.Geometry.GridInternal (Grid(..), FiniteGrid(..), @@ -71,7 +105,9 @@ ParaTriGrid, paraTriGrid, RectTriGrid, rectTriGrid, TorTriGrid, torTriGrid, UnboundedSquareGrid, RectSquareGrid, rectSquareGrid, TorSquareGrid, torSquareGrid, - UnboundedHexGrid, HexHexGrid, hexHexGrid, ParaHexGrid, paraHexGrid) + UnboundedHexGrid, HexHexGrid, hexHexGrid, ParaHexGrid, paraHexGrid, + UnboundedOctGrid, RectOctGrid, rectOctGrid, TorOctGrid, torOctGrid) + {- $Example Create a grid. diff --git a/src/Math/Geometry/GridInternal.hs b/src/Math/Geometry/GridInternal.hs --- a/src/Math/Geometry/GridInternal.hs +++ b/src/Math/Geometry/GridInternal.hs @@ -37,7 +37,12 @@ HexHexGrid, hexHexGrid, ParaHexGrid, - paraHexGrid + paraHexGrid, + UnboundedOctGrid, + RectOctGrid, + rectOctGrid, + TorOctGrid, + torOctGrid, ) where import Prelude hiding (null) @@ -49,7 +54,7 @@ import Data.Ord.Unicode ((≤), (≥)) -- | A regular arrangement of tiles. --- Minimal complete definition: @indices@ and @distance@. +-- Minimal complete definition: @Index@, @indices@ and @distance@. class Grid g where type Index g @@ -225,6 +230,9 @@ -- Triangular tiles -- +-- | An unbounded grid with triangular tiles. +-- The grid and its indexing scheme are illustrated in the user guide, +-- available at . data UnboundedTriGrid = UnboundedTriGrid deriving Show instance Grid UnboundedTriGrid where @@ -453,6 +461,9 @@ -- Square tiles -- +-- | An unbounde grid with square tiles. +-- The grid and its indexing scheme are illustrated in the user guide, +-- available at . data UnboundedSquareGrid = UnboundedSquareGrid deriving Show instance Grid UnboundedSquareGrid where @@ -540,7 +551,7 @@ -- [((x-1) `mod` c,y), (x,(y+1) `mod` r), ((x+1) `mod` c,y), -- (x,(y-1) `mod` r)] neighbours g = nub . map (normalise g) . neighbours UnboundedSquareGrid - distance g@(TorSquareGrid (r,c) _) (x1, y1) (x2, y2) = + distance g@(TorSquareGrid (r,c) _) (x1, y1) (x2, y2) = -- TODO redo if g `contains` (x1, y1) && g `contains` (x2, y2) then min adx (abs (c-adx)) + min ady (abs (r-ady)) else undefined @@ -555,6 +566,18 @@ normalise g (x,y) = (x `mod` c, y `mod` r) where (r, c) = size g +denormaliseTor + :: (FiniteGrid g, Index g ~ (Int, Int), (Int, Int) ~ Size g) => + g -> Index g -> [Index g] +denormaliseTor g (x,y) = nub [(x2,y1), (x,y1), (x1,y1), + (x2,y), (x,y), (x1,y), + (x2,y2), (x,y2), (x1,y2)] + where (r, c) = size g + x1 = x + c + y1 = y + r + x2 = x - c + y2 = y - r + -- | @'torSquareGrid' r c@ returns a toroidal grid with @r@ -- rows and @c@ columns, using square tiles. If @r@ and @c@ are -- both nonnegative, the resulting grid will have @r*c@ tiles. Otherwise, @@ -566,6 +589,9 @@ -- Hexagonal tiles -- +-- | An unbounded grid with hexagonal tiles +-- The grid and its indexing scheme are illustrated in the user guide, +-- available at . data UnboundedHexGrid = UnboundedHexGrid deriving Show instance Grid UnboundedHexGrid where @@ -656,4 +682,93 @@ paraHexGrid ∷ Int → Int → ParaHexGrid paraHexGrid r c = ParaHexGrid (r,c) [(x, y) | x ← [0..c-1], y ← [0..r-1]] + + +-- +-- Octagonal tiles +-- + +-- | An unbounded grid with octagonal tiles. +-- The grid and its indexing scheme are illustrated in the user guide, +-- available at . +data UnboundedOctGrid = UnboundedOctGrid deriving Show + +instance Grid UnboundedOctGrid where + type Index UnboundedOctGrid = (Int, Int) + indices _ = undefined + neighbours _ (x,y) = [(x-1,y+1), (x,y+1), (x+1,y+1), (x+1,y), + (x+1,y-1), (x,y-1), (x-1,y-1), (x-1,y)] + distance _ (x1, y1) (x2, y2) = max (abs (x2-x1)) (abs (y2-y1)) + contains _ _ = True + +-- +-- Rectangular grids with octagonal tiles +-- + +-- | A rectangular grid with octagonal tiles. +-- The grid and its indexing scheme are illustrated in the user guide, +-- available at . +data RectOctGrid = RectOctGrid (Int, Int) [(Int, Int)] deriving Eq + +instance Show RectOctGrid where + show (RectOctGrid (r,c) _) = + "rectOctGrid " ++ show r ++ " " ++ show c + +instance Grid RectOctGrid where + type Index RectOctGrid = (Int, Int) + indices (RectOctGrid _ xs) = xs + neighbours = neighboursBasedOn UnboundedOctGrid + distance = distanceBasedOn UnboundedOctGrid + +instance FiniteGrid RectOctGrid where + type Size RectOctGrid = (Int, Int) + size (RectOctGrid s _) = s + +instance BoundedGrid RectOctGrid where + tileSideCount _ = 4 + boundary g = cartesianIndices . size $ g + centre g = cartesianCentre . size $ g + +-- | @'rectOctGrid' r c@ produces a rectangular grid with @r@ rows +-- and @c@ columns, using octagonal tiles. If @r@ and @c@ are both +-- nonnegative, the resulting grid will have @r*c@ tiles. Otherwise, +-- the resulting grid will be null and the list of indices will be +-- null. +rectOctGrid ∷ Int → Int → RectOctGrid +rectOctGrid r c = + RectOctGrid (r,c) [(x,y) | x ← [0..c-1], y ← [0..r-1]] + +-- +-- Toroidal grids with octagonal tiles. +-- + +-- | A toroidal grid with octagonal tiles. +-- The grid and its indexing scheme are illustrated in the user guide, +-- available at . +data TorOctGrid = TorOctGrid (Int, Int) [(Int, Int)] deriving Eq + +instance Show TorOctGrid where + show (TorOctGrid (r,c) _) = "torOctGrid " ++ show r ++ " " ++ show c + +instance Grid TorOctGrid where + type Index TorOctGrid = (Int, Int) + indices (TorOctGrid _ xs) = xs + neighbours g = nub . map (normalise g) . neighbours UnboundedOctGrid + distance g a b = minimum . map (distance UnboundedOctGrid a) $ bs + where bs = denormaliseTor g b + +instance FiniteGrid TorOctGrid where + type Size TorOctGrid = (Int, Int) + size (TorOctGrid s _) = s + +instance WrappedGrid TorOctGrid where + normalise g (x,y) = (x `mod` c, y `mod` r) + where (r, c) = size g + +-- | @'torOctGrid' r c@ returns a toroidal grid with @r@ +-- rows and @c@ columns, using octagonal tiles. If @r@ and @c@ are +-- both nonnegative, the resulting grid will have @r*c@ tiles. Otherwise, +-- the resulting grid will be null and the list of indices will be null. +torOctGrid ∷ Int → Int → TorOctGrid +torOctGrid r c = TorOctGrid (r,c) [(x, y) | x ← [0..c-1], y ← [0..r-1]] diff --git a/src/Math/Geometry/GridMap.hs b/src/Math/Geometry/GridMap.hs --- a/src/Math/Geometry/GridMap.hs +++ b/src/Math/Geometry/GridMap.hs @@ -42,7 +42,7 @@ -- | A regular arrangement of tiles, having a value associated with -- each tile. -- Minimal complete definition: @toMap@, @toGrid@, @adjustWithKey@, --- @mapWithKey. +-- @mapWithKey@. -- -- Note: Some of the methods have an @Ord@ constraint on the grid -- index. This is purely to make it easier to write implementations. @@ -101,12 +101,16 @@ elems = M.elems . toMap -- | Map a function over all values in the map. - map ∷ GridMap gm b ⇒ (v → b) → gm v → gm b + map + ∷ (GridMap gm v2, + G.Index (BaseGrid gm v) ~ G.Index (BaseGrid gm v2)) ⇒ + (v → v2) → gm v → gm v2 map f = mapWithKey (\_ v → f v) -- | Map a function over all values in the map. mapWithKey - ∷ (k ~ G.Index (BaseGrid gm v), GridMap gm v2) ⇒ + ∷ (k ~ G.Index (BaseGrid gm v), k ~ G.Index (BaseGrid gm v2), + GridMap gm v2) ⇒ (k → v → v2) → gm v → gm v2 {- $Compare diff --git a/test/Math/Geometry/GridQC.hs b/test/Math/Geometry/GridQC.hs --- a/test/Math/Geometry/GridQC.hs +++ b/test/Math/Geometry/GridQC.hs @@ -31,6 +31,17 @@ pointAt g i = indices g !! (i `mod` n) where n = (length . indices) g +minPathCount + ∷ (Eq (Index g), Grid g) ⇒ g → Index g → Index g → Int +minPathCount g a b = length . minimalPaths g a $ b + +minPathCount2 + ∷ (Eq (Index g), Grid g) ⇒ g → [Index g] → Index g → Int +minPathCount2 g as b = sum . map (\x → minPathCount g x b) $ as + +neighbourCount ∷ ∀ g. Grid g ⇒ g → Index g → Int +neighbourCount g x = length . neighbours g $ x + -- -- Tests that should apply to and are identical for all grids -- @@ -61,10 +72,10 @@ sort (delete a (neighbours g a)) ≡ sort expected where a = g `pointAt` i expected = map fst $ filter (\p → 1 ≡ snd p) $ viewpoint g a --- Note: In a small grid, a tile can be its own neighbour. However, when --- we calculate the distance between a tile and itself, we get 0, not 1. --- That's why we have to delete the tile from its list before comparing --- to the result from the neighbours function. +-- Note: In a small but unbounded grid, a tile can be its own neighbour. +-- However, when we calculate the distance between a tile and itself, we +-- get 0, not 1. That's why we have to delete the tile from its list +-- before comparing to the result from the neighbours function. prop_edges_cw_neighbours ∷ (Grid g, Ord (Index g)) ⇒ g → Int → Property prop_edges_cw_neighbours g i = nonNull g ==> @@ -182,9 +193,7 @@ prop_TriTriGrid_neighbour_count_in_bounds ∷ TriTriGrid → Int → Property prop_TriTriGrid_neighbour_count_in_bounds g i = nonNull g ==> - if tileCount g ≡ 1 - then length (neighbours g x) ≡ 0 - else length (neighbours g x) `elem` [1,2,3] + neighbourCount g x ≤ 3 where x = g `pointAt` i prop_TriTriGrid_boundary_count_correct ∷ TriTriGrid → Property @@ -237,9 +246,7 @@ prop_ParaTriGrid_neighbour_count_in_bounds ∷ ParaTriGrid → Int → Property prop_ParaTriGrid_neighbour_count_in_bounds g i = nonNull g ==> - if tileCount g ≡ 1 - then length (neighbours g x) ≡ 0 - else length (neighbours g x) `elem` [1,2,3] + neighbourCount g x ≤ 3 where x = g `pointAt` i prop_ParaTriGrid_boundary_count_correct ∷ ParaTriGrid → Property @@ -283,9 +290,7 @@ prop_RectTriGrid_neighbour_count_in_bounds ∷ RectTriGrid → Int → Property prop_RectTriGrid_neighbour_count_in_bounds g i = nonNull g ==> - if tileCount g ≡ 1 - then length (neighbours g x) ≡ 0 - else length (neighbours g x) `elem` [1,2,3] + neighbourCount g x ≤ 3 where x = g `pointAt` i prop_RectTriGrid_boundary_count_correct ∷ RectTriGrid → Property @@ -330,9 +335,7 @@ prop_TorTriGrid_neighbour_count_in_bounds ∷ TorTriGrid → Int → Property prop_TorTriGrid_neighbour_count_in_bounds g i = nonNull g ==> - if tileCount g ≡ 1 - then length (neighbours g x) ≡ 0 - else length (neighbours g x) `elem` [1,2,3] + neighbourCount g x ≤ 3 where x = g `pointAt` i -- @@ -374,18 +377,14 @@ prop_RectSquareGrid_neighbour_count_in_bounds ∷ RectSquareGrid → Int → Property -prop_RectSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> f +prop_RectSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> + neighbourCount g x ≤ 4 where x = g `pointAt` i - neighbourCount = length (neighbours g x) - (r, c) = size g - f | tileCount g ≡ 1 = neighbourCount ≡ 0 - | r ≡ 1 || c ≡ 1 = neighbourCount `elem` [1,2] - | otherwise = neighbourCount `elem` [2,3,4] prop_RectSquareGrid_num_min_paths_correct ∷ RectSquareGrid → Int → Int → Property prop_RectSquareGrid_num_min_paths_correct g i j = nonNull g ==> - length (minimalPaths g a b) ≡ M.choose (deltaX+deltaY) deltaX + minPathCount g a b ≡ M.choose (deltaX+deltaY) deltaX where a = g `pointAt` i b = g `pointAt` j deltaX = abs $ fst b - fst a @@ -408,7 +407,7 @@ -- --- Toroidal grids with square-ish tiles +-- Toroidal grids with square tiles -- -- We want the number of tiles in a test grid to be O(n) @@ -442,21 +441,14 @@ ps = indices g a = head ps b = last ps - f | r ≡ 1 && c ≡ 1 = 0 -- zero-size torus + f | r ≡ 1 && c ≡ 1 = 0 -- single-tile torus | r ≡ 1 || c ≡ 1 = 1 -- a and b are the same | otherwise = 2 prop_TorSquareGrid_neighbour_count_in_bounds ∷ TorSquareGrid → Int → Property -prop_TorSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> f +prop_TorSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> + neighbourCount g x ≤ 4 where x = g `pointAt` i - neighbourCount = length . neighbours g $ x - (r, c) = size g - f | tileCount g ≡ 1 = neighbourCount ≡ 1 - | (r,c) ≡ (1,2) || (r,c) ≡ (2,1) = neighbourCount ≡ 2 - | (r,c) ≡ (2,2) = neighbourCount ≡ 2 - | r ≡ 1 || c ≡ 1 = neighbourCount ≡ 3 - | r ≡ 2 || c ≡ 2 = neighbourCount ≡ 3 - | otherwise = neighbourCount ≡ 4 -- -- Circular hexagonal grids @@ -494,9 +486,7 @@ prop_HexHexGrid_neighbour_count_in_bounds ∷ HexHexGrid → Int → Property prop_HexHexGrid_neighbour_count_in_bounds g i = nonNull g ==> - if tileCount g ≡ 1 - then length (neighbours g x) ≡ 0 - else length (neighbours g x) `elem` [2,3,4,5,6] + neighbourCount g x ≤ 6 where x = g `pointAt` i prop_HexHexGrid_boundary_count_correct ∷ HexHexGrid → Property @@ -549,13 +539,9 @@ (r, c) = size g prop_ParaHexGrid_neighbour_count_in_bounds ∷ ParaHexGrid → Int → Property -prop_ParaHexGrid_neighbour_count_in_bounds g i = nonNull g ==> f +prop_ParaHexGrid_neighbour_count_in_bounds g i = nonNull g ==> + neighbourCount g x ≤ 6 where x = g `pointAt` i - neighbourCount = length (neighbours g x) - (r, c) = size g - f | tileCount g ≡ 1 = neighbourCount ≡ 0 - | r ≡ 1 || c ≡ 1 = neighbourCount `elem` [1,2] - | otherwise = neighbourCount `elem` [2,3,4,5,6] prop_ParaHexGrid_boundary_count_correct ∷ ParaHexGrid → Property prop_ParaHexGrid_boundary_count_correct g = property $ @@ -565,7 +551,110 @@ prop_ParaHexGrid_boundary_tiles_have_fewer_neighbours g = property $ all (5>) . map (numNeighbours g) . boundary $ g +-- +-- Rectangular grids with octagonal tiles +-- +-- We want the number of tiles in a test grid to be O(n) +sizedRectOctGrid ∷ Int → Gen RectOctGrid +sizedRectOctGrid n = do + let n' = min n 12 -- calculation time for these grids grows quickly! + r ← choose (0,n') + let c = n' `div` (r+1) + return $ rectOctGrid r c + +instance Arbitrary RectOctGrid where + arbitrary = sized sizedRectOctGrid + +prop_RectOctGrid_tile_count_correct ∷ RectOctGrid → Property +prop_RectOctGrid_tile_count_correct g = property $ + tileCount g ≡ if r ≤ 0 || c ≤ 0 then 0 else r*c + where (r, c) = size g + +prop_RectOctGrid_distance_in_bounds ∷ RectOctGrid → Int → Int → Property +prop_RectOctGrid_distance_in_bounds g i j = nonNull g ==> + distance g a b ≤ max r c + where (r, c) = size g + a = g `pointAt` i + b = g `pointAt` j + +-- If the ordering produced by rectOctGrid is ever changed, this +-- property may need to be changed too. It relies on the first and last +-- elements being at opposite corners. +prop_RectOctGrid_distance_corner_to_corner ∷ RectOctGrid → Property +prop_RectOctGrid_distance_corner_to_corner g = r > 0 && c > 0 ==> + a ≡ b || distance g a b ≡ (max r c) - 1 + where (r, c) = size g + ps = indices g + a = head ps + b = last ps + +prop_RectOctGrid_neighbour_count_in_bounds ∷ + RectOctGrid → Int → Property +prop_RectOctGrid_neighbour_count_in_bounds g i = nonNull g ==> + neighbourCount g x ≤ 8 + where x = g `pointAt` i + +prop_RectOctGrid_num_min_paths_correct ∷ + RectOctGrid → Int → Int → Property +prop_RectOctGrid_num_min_paths_correct g i j = nonNull g ==> + minPathCount g a b ≡ + if a ≡ b then 1 else minPathCount2 g att b + where a = g `pointAt` i + b = g `pointAt` j + att = adjacentTilesToward g a b + +prop_RectOctGrid_boundary_count_correct ∷ RectOctGrid → Property +prop_RectOctGrid_boundary_count_correct g = property $ + (length . boundary) g ≡ (cartesianBoundaryCount . size) g + +prop_RectOctGrid_boundary_tiles_have_fewer_neighbours ∷ RectOctGrid → Property +prop_RectOctGrid_boundary_tiles_have_fewer_neighbours g = property $ + all (6>) . map (numNeighbours g) . boundary $ g + + +-- +-- Toroidal grids with octagonal tiles +-- + +-- We want the number of tiles in a test grid to be O(n) +sizedTorOctGrid ∷ Int → Gen TorOctGrid +sizedTorOctGrid n = do + r ← choose (0,n) + let c = n `div` (r+1) + return $ torOctGrid r c + +instance Arbitrary TorOctGrid where + arbitrary = sized sizedTorOctGrid + +prop_TorOctGrid_tile_count_correct ∷ TorOctGrid → Property +prop_TorOctGrid_tile_count_correct g = property $ + tileCount g ≡ if r ≤ 0 || c ≤ 0 then 0 else r*c + where (r, c) = size g + +prop_TorOctGrid_distance_in_bounds ∷ TorOctGrid → Int → Int → Property +prop_TorOctGrid_distance_in_bounds g i j = nonNull g ==> + distance g a b ≤ min r c + abs (r-c) + where (r, c) = size g + a = g `pointAt` i + b = g `pointAt` j + +-- If the ordering produced by torOctGrid is ever changed, this property +-- may need to be changed too. +prop_TorOctGrid_distance_corner_to_corner ∷ TorOctGrid → Property +prop_TorOctGrid_distance_corner_to_corner g = r > 0 && c > 0 ==> + distance g a b ≡ if tileCount g ≡ 1 then 0 else 1 + where (r, c) = size g + ps = indices g + a = head ps + b = last ps + +prop_TorOctGrid_neighbour_count_in_bounds ∷ TorOctGrid → Int → Property +prop_TorOctGrid_neighbour_count_in_bounds g i = nonNull g ==> + neighbourCount g x ≤ 8 + where x = g `pointAt` i + + test ∷ Test test = testGroup "Math.Geometry.GridQC" [ @@ -601,17 +690,17 @@ testProperty "prop_neighbours_cw_viewpoint - TriTriGrid" (prop_neighbours_cw_viewpoint ∷ TriTriGrid → Int → Property), testProperty "prop_edges_cw_neighbours - TriTriGrid" - ( prop_edges_cw_neighbours ∷ TriTriGrid → Int → Property), + (prop_edges_cw_neighbours ∷ TriTriGrid → Int → Property), testProperty "prop_edges_are_adjacent - TriTriGrid" - ( prop_edges_are_adjacent ∷ TriTriGrid → Property), + (prop_edges_are_adjacent ∷ TriTriGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - TriTriGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ TriTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - TriTriGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ TriTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - TriTriGrid" - ( prop_minimal_paths_are_valid ∷ TriTriGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ TriTriGrid → Int → Int → Property), -- ParaTriGrid tests testProperty "prop_ParaTriGrid_tile_count_correct" @@ -645,17 +734,17 @@ testProperty "prop_neighbours_cw_viewpoint - ParaTriGrid" (prop_neighbours_cw_viewpoint ∷ ParaTriGrid → Int → Property), testProperty "prop_edges_cw_neighbours - ParaTriGrid" - ( prop_edges_cw_neighbours ∷ ParaTriGrid → Int → Property), + (prop_edges_cw_neighbours ∷ ParaTriGrid → Int → Property), testProperty "prop_edges_are_adjacent - ParaTriGrid" - ( prop_edges_are_adjacent ∷ ParaTriGrid → Property), + (prop_edges_are_adjacent ∷ ParaTriGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - ParaTriGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ ParaTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - ParaTriGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ ParaTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - ParaTriGrid" - ( prop_minimal_paths_are_valid ∷ ParaTriGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ ParaTriGrid → Int → Int → Property), -- RectTriGrid tests testProperty "prop_RectTriGrid_tile_count_correct" @@ -687,17 +776,17 @@ testProperty "prop_neighbours_cw_viewpoint - RectTriGrid" (prop_neighbours_cw_viewpoint ∷ RectTriGrid → Int → Property), testProperty "prop_edges_cw_neighbours - RectTriGrid" - ( prop_edges_cw_neighbours ∷ RectTriGrid → Int → Property), + (prop_edges_cw_neighbours ∷ RectTriGrid → Int → Property), testProperty "prop_edges_are_adjacent - RectTriGrid" - ( prop_edges_are_adjacent ∷ RectTriGrid → Property), + (prop_edges_are_adjacent ∷ RectTriGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - RectTriGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ RectTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - RectTriGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ RectTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - RectTriGrid" - ( prop_minimal_paths_are_valid ∷ RectTriGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ RectTriGrid → Int → Int → Property), -- TorTriGrid tests testProperty "prop_TorTriGrid_tile_count_correct" @@ -715,17 +804,17 @@ testProperty "prop_neighbours_cw_viewpoint - TorTriGrid" (prop_neighbours_cw_viewpoint ∷ TorTriGrid → Int → Property), testProperty "prop_edges_cw_neighbours - TorTriGrid" - ( prop_edges_cw_neighbours ∷ TorTriGrid → Int → Property), + (prop_edges_cw_neighbours ∷ TorTriGrid → Int → Property), testProperty "prop_edges_are_adjacent - TorTriGrid" - ( prop_edges_are_adjacent ∷ TorTriGrid → Property), + (prop_edges_are_adjacent ∷ TorTriGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - TorTriGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ TorTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - TorTriGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ TorTriGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - TorTriGrid" - ( prop_minimal_paths_are_valid ∷ TorTriGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ TorTriGrid → Int → Int → Property), -- RectSquareGrid tests testProperty "prop_RectSquareGrid_tile_count_correct" @@ -759,17 +848,17 @@ testProperty "prop_neighbours_cw_viewpoint - RectSquareGrid" (prop_neighbours_cw_viewpoint ∷ RectSquareGrid → Int → Property), testProperty "prop_edges_cw_neighbours - RectSquareGrid" - ( prop_edges_cw_neighbours ∷ RectSquareGrid → Int → Property), + (prop_edges_cw_neighbours ∷ RectSquareGrid → Int → Property), testProperty "prop_edges_are_adjacent - RectSquareGrid" - ( prop_edges_are_adjacent ∷ RectSquareGrid → Property), + (prop_edges_are_adjacent ∷ RectSquareGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - RectSquareGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ RectSquareGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - RectSquareGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ RectSquareGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - RectSquareGrid" - ( prop_minimal_paths_are_valid ∷ RectSquareGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ RectSquareGrid → Int → Int → Property), testProperty "prop_RectSquareGrid_num_min_paths_correct" prop_RectSquareGrid_num_min_paths_correct, @@ -791,17 +880,17 @@ testProperty "prop_neighbours_cw_viewpoint - TorSquareGrid" (prop_neighbours_cw_viewpoint ∷ TorSquareGrid → Int → Property), testProperty "prop_edges_cw_neighbours - TorSquareGrid" - ( prop_edges_cw_neighbours ∷ TorSquareGrid → Int → Property), + (prop_edges_cw_neighbours ∷ TorSquareGrid → Int → Property), testProperty "prop_edges_are_adjacent - TorSquareGrid" - ( prop_edges_are_adjacent ∷ TorSquareGrid → Property), + (prop_edges_are_adjacent ∷ TorSquareGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - TorSquareGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ TorSquareGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - TorSquareGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ TorSquareGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - TorSquareGrid" - ( prop_minimal_paths_are_valid ∷ TorSquareGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ TorSquareGrid → Int → Int → Property), -- HexHexGrid tests testProperty "prop_HexHexGrid_tile_count_correct" @@ -835,17 +924,17 @@ testProperty "prop_neighbours_cw_viewpoint - HexHexGrid" (prop_neighbours_cw_viewpoint ∷ HexHexGrid → Int → Property), testProperty "prop_edges_cw_neighbours - HexHexGrid" - ( prop_edges_cw_neighbours ∷ HexHexGrid → Int → Property), + (prop_edges_cw_neighbours ∷ HexHexGrid → Int → Property), testProperty "prop_edges_are_adjacent - HexHexGrid" - ( prop_edges_are_adjacent ∷ HexHexGrid → Property), + (prop_edges_are_adjacent ∷ HexHexGrid → Property), testProperty "prop_adjacentTilesToward_moves_closer - HexHexGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ HexHexGrid → Int → Int → Property), testProperty "prop_minimal_paths_have_min_length - HexHexGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ HexHexGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - HexHexGrid" - ( prop_minimal_paths_are_valid ∷ HexHexGrid → Int → Int → Property), + (prop_minimal_paths_are_valid ∷ HexHexGrid → Int → Int → Property), -- ParaHexGrid tests testProperty "prop_ParaHexGrid_tile_count_correct" @@ -879,16 +968,92 @@ testProperty "prop_neighbours_cw_viewpoint - ParaHexGrid" (prop_neighbours_cw_viewpoint ∷ ParaHexGrid → Int → Property), testProperty "prop_edges_cw_neighbours - ParaHexGrid" - ( prop_edges_cw_neighbours ∷ ParaHexGrid → Int → Property), + (prop_edges_cw_neighbours ∷ ParaHexGrid → Int → Property), testProperty "prop_adjacentTilesToward_moves_closer - ParaHexGrid" - ( prop_adjacentTilesToward_moves_closer ∷ + (prop_adjacentTilesToward_moves_closer ∷ ParaHexGrid → Int → Int → Property), testProperty "prop_edges_are_adjacent - ParaHexGrid" - ( prop_edges_are_adjacent ∷ ParaHexGrid → Property), + (prop_edges_are_adjacent ∷ ParaHexGrid → Property), testProperty "prop_minimal_paths_have_min_length - ParaHexGrid" - ( prop_minimal_paths_have_min_length ∷ + (prop_minimal_paths_have_min_length ∷ ParaHexGrid → Int → Int → Property), testProperty "prop_minimal_paths_are_valid - ParaHexGrid" - ( prop_minimal_paths_are_valid ∷ ParaHexGrid → Int → Int → Property) + (prop_minimal_paths_are_valid ∷ ParaHexGrid → Int → Int → Property), + + -- RectOctGrid tests + testProperty "prop_RectOctGrid_tile_count_correct" + prop_RectOctGrid_tile_count_correct, + testProperty "prop_distance_reflexive - RectOctGrid" + (prop_distance_reflexive ∷ RectOctGrid → Int → Property), + testProperty "prop_distance_symmetric - RectOctGrid" + (prop_distance_symmetric ∷ RectOctGrid → Int → Int → Property), + testProperty "prop_minDistance_cw_distance - RectOctGrid" + (prop_minDistance_cw_distance ∷ RectOctGrid → Int → [Int] → Property), + testProperty "prop_grid_and_boundary_are_both_null_or_not - RectOctGrid" + (prop_grid_and_boundary_are_both_null_or_not ∷ RectOctGrid → Property), + testProperty "prop_boundary_in_grid - RectOctGrid" + (prop_boundary_in_grid ∷ RectOctGrid → Property), + testProperty "prop_boundary_tiles_have_fewer_neighbours - RectOctGrid" + (prop_boundary_tiles_have_fewer_neighbours ∷ RectOctGrid → Int → Property), + testProperty "prop_RectOctGrid_boundary_count_correct" + prop_RectOctGrid_boundary_count_correct, + testProperty "prop_RectOctGrid_boundary_tiles_have_fewer_neighbours" + prop_RectOctGrid_boundary_tiles_have_fewer_neighbours, + testProperty "prop_centres_equidistant_from_boundary - RectOctGrid" + (prop_centres_equidistant_from_boundary ∷ RectOctGrid → Property), + testProperty "prop_centres_farthest_from_boundary - RectOctGrid" + (prop_centres_farthest_from_boundary ∷ RectOctGrid → Int → Property), + testProperty "prop_RectOctGrid_distance_in_bounds" + prop_RectOctGrid_distance_in_bounds, + testProperty "prop_RectOctGrid_distance_corner_to_corner" + prop_RectOctGrid_distance_corner_to_corner, + testProperty "prop_RectOctGrid_neighbour_count_in_bounds" + prop_RectOctGrid_neighbour_count_in_bounds, + testProperty "prop_neighbours_cw_viewpoint - RectOctGrid" + (prop_neighbours_cw_viewpoint ∷ RectOctGrid → Int → Property), + testProperty "prop_edges_cw_neighbours - RectOctGrid" + (prop_edges_cw_neighbours ∷ RectOctGrid → Int → Property), + testProperty "prop_edges_are_adjacent - RectOctGrid" + (prop_edges_are_adjacent ∷ RectOctGrid → Property), + testProperty "prop_adjacentTilesToward_moves_closer - RectOctGrid" + (prop_adjacentTilesToward_moves_closer ∷ + RectOctGrid → Int → Int → Property), + testProperty "prop_minimal_paths_have_min_length - RectOctGrid" + (prop_minimal_paths_have_min_length ∷ + RectOctGrid → Int → Int → Property), + testProperty "prop_minimal_paths_are_valid - RectOctGrid" + (prop_minimal_paths_are_valid ∷ RectOctGrid → Int → Int → Property), + testProperty "prop_RectOctGrid_num_min_paths_correct" + prop_RectOctGrid_num_min_paths_correct, + + -- TorOctGrid tests + testProperty "prop_TorOctGrid_tile_count_correct" + prop_TorOctGrid_tile_count_correct, + testProperty "prop_distance_reflexive - TorOctGrid" + (prop_distance_reflexive ∷ TorOctGrid → Int → Property), + testProperty "prop_distance_symmetric - TorOctGrid" + (prop_distance_symmetric ∷ TorOctGrid → Int → Int → Property), + testProperty "prop_minDistance_cw_distance - TorOctGrid" + (prop_minDistance_cw_distance ∷ TorOctGrid → Int → [Int] → Property), + testProperty "prop_TorOctGrid_distance_in_bounds" + prop_TorOctGrid_distance_in_bounds, + testProperty "prop_TorOctGrid_distance_corner_to_corner" + prop_TorOctGrid_distance_corner_to_corner, + testProperty "prop_TorOctGrid_neighbour_count_in_bounds" + prop_TorOctGrid_neighbour_count_in_bounds, + testProperty "prop_neighbours_cw_viewpoint - TorOctGrid" + (prop_neighbours_cw_viewpoint ∷ TorOctGrid → Int → Property), + testProperty "prop_edges_cw_neighbours - TorOctGrid" + (prop_edges_cw_neighbours ∷ TorOctGrid → Int → Property), + testProperty "prop_edges_are_adjacent - TorOctGrid" + (prop_edges_are_adjacent ∷ TorOctGrid → Property), + testProperty "prop_adjacentTilesToward_moves_closer - TorOctGrid" + (prop_adjacentTilesToward_moves_closer ∷ + TorOctGrid → Int → Int → Property), + testProperty "prop_minimal_paths_have_min_length - TorOctGrid" + (prop_minimal_paths_have_min_length ∷ + TorOctGrid → Int → Int → Property), + testProperty "prop_minimal_paths_are_valid - TorOctGrid" + (prop_minimal_paths_are_valid ∷ TorOctGrid → Int → Int → Property) ]