-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | substitution tilings
--   
--   Substitution tilings. The term substitution, in connection with
--   tilings, describes a simple but powerful method to produce tilings
--   with many interesting properties.
--   
--   The main idea is to use a finite set of building blocks called
--   prototiles, an expanding linear map (the inflation factor), and a rule
--   how to dissect each scaled tile into copies of the original
--   prototiles.
--   
--   For some examples of substitution tilings, and a glossary of
--   terminology, see the <i>tilings encyclopedia</i> at
--   <a>http://tilings.math.uni-bielefeld.de/</a>
@package tilings
@version 0.1


-- | Substitution tiling API.
module Data.Tiling.Class

-- | Substitution tilings. Instances must obey the following laws:
--   
--   <pre>
--   parent root == Nothing
--   all (== Just t) . map parent . children $ t
--   t `inside`   exterior t
--   t `encloses` interior t
--   interior t `insideR` exterior t
--   t `inside` r  ==&gt;  t `overlaps` r
--   t `encloses` r  ==&gt;  t `overlaps` r
--   t `overlaps` r  ==&gt; not (t `outside` r)
--   t `encloses` r &amp;&amp; n &gt;= 0  ==&gt;  not $ any (`outside` r) (tile t r n)
--   </pre>
--   
--   Minimal complete definition: all except <a>tile</a>.
class Tiling t
root :: Tiling t => t
children :: Tiling t => t -> [t]
parent :: Tiling t => t -> Maybe t
exterior :: Tiling t => t -> Rectangle
interior :: Tiling t => t -> Rectangle
inside :: Tiling t => t -> Rectangle -> Bool
encloses :: Tiling t => t -> Rectangle -> Bool
outside :: Tiling t => t -> Rectangle -> Bool
overlaps :: Tiling t => t -> Rectangle -> Bool
tile :: Tiling t => t -> Rectangle -> Int -> [t]

-- | Default implementation for <a>tile</a>.
tileDefault :: Tiling t => t -> Rectangle -> Int -> [t]

-- | An axis-aligned rectangle with <a>Rational</a> coordinates.
--   
--   Invariant:
--   
--   <pre>
--   westEdge r &lt;= eastEdge r &amp;&amp; southEdge r &lt;= northEdge r
--   </pre>
--   
--   For substitution tilings that contain irrational lengths and/or scale
--   factors, the intention is that the implementations of <a>exterior</a>
--   and <a>interior</a> provide reasonably tight bounds, within a percent
--   or two, say, while the data type maintains full precision internally
--   (perhaps using algebraic field extensions over <a>Rational</a>).
data Rectangle
Rectangle :: !Rational -> !Rational -> !Rational -> !Rational -> Rectangle
northEdge :: Rectangle -> !Rational
southEdge :: Rectangle -> !Rational
eastEdge :: Rectangle -> !Rational
westEdge :: Rectangle -> !Rational

-- | Create a valid rectangle, sorting the edges to meet the invariant.
rectangle :: Rational -> Rational -> Rational -> Rational -> Rectangle

-- | Check if a rectangle is inside another rectangle. The comparison is
--   not strict, so that a rectangle is inside itself.
insideR :: Rectangle -> Rectangle -> Bool

-- | Check if a rectangle is disjoint from another rectangle. The
--   comparison is strict, so that neighbouring rectangles that share an
--   edge will not be outside each other.
outsideR :: Rectangle -> Rectangle -> Bool

-- | Check if a rectangle overlaps with another rectangle. The comparison
--   is not strict, so that neighbouring rectangles that share an edge will
--   overlap each other.
overlapsR :: Rectangle -> Rectangle -> Bool
instance Typeable Rectangle
instance Eq Rectangle
instance Ord Rectangle
instance Read Rectangle
instance Show Rectangle
instance Data Rectangle


-- | Simple substitution tiling with each square divided into four
--   quadrants (with no rotation).
module Data.Tiling.Quad

-- | Which quadrant.
data Quadrant
NorthWest :: Quadrant
NorthEast :: Quadrant
SouthWest :: Quadrant
SouthEast :: Quadrant
isNorth :: Quadrant -> Bool
isSouth :: Quadrant -> Bool
isWest :: Quadrant -> Bool
isEast :: Quadrant -> Bool

-- | All quadrants.
quadrants :: [Quadrant]

-- | A square tile.
data Quad
Quad :: !Int -> !Integer -> !Integer -> Quad
quadLevel :: Quad -> !Int
quadWest :: Quad -> !Integer
quadNorth :: Quad -> !Integer

-- | The child tile at a given quadrant.
quadChild :: Quadrant -> Quad -> Quad

-- | The parent with quadrant information for the tile. Satisfies:
--   
--   <pre>
--   quadParent (quadChild c q) == Just (c, q)
--   </pre>
quadParent :: Quad -> Maybe (Quadrant, Quad)

-- | The path from this tile to the root. Satisfies:
--   
--   <pre>
--   foldr quadChild root (quadPath q) == q
--   </pre>
quadPath :: Quad -> [Quadrant]

-- | Suggested file system location for data pertaining to a <a>Quad</a>.
quadFile :: Quad -> Maybe ([FilePath], FilePath)
instance Typeable Quad
instance Typeable Quadrant
instance Read Quad
instance Show Quad
instance Eq Quad
instance Ord Quad
instance Data Quad
instance Read Quadrant
instance Show Quadrant
instance Eq Quadrant
instance Ord Quadrant
instance Enum Quadrant
instance Bounded Quadrant
instance Data Quadrant
instance Tiling Quad


-- | Substitution tilings. The term substitution, in connection with
--   tilings, describes a simple but powerful method to produce tilings
--   with many interesting properties.
--   
--   The main idea is to use a finite set of building blocks called
--   prototiles, an expanding linear map (the inflation factor), and a rule
--   how to dissect each scaled tile into copies of the original
--   prototiles.
--   
--   For some examples of substitution tilings, and a glossary of
--   terminology, see the <i>tilings encyclopedia</i> at
--   <a>http://tilings.math.uni-bielefeld.de/</a>
module Data.Tiling