Data.Tiling.Class

Substitution tiling API.

Documentation

class Tiling t where

Substitution tilings. Instances must obey the following laws:

 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  ==>  t `overlaps` r
 t `encloses` r  ==>  t `overlaps` r
 t `overlaps` r  ==> not (t `outside` r)
 t `encloses` r && n >= 0  ==>  not $ any (`outside` r) (tile t r n)

Minimal complete definition: all except tile.

Methods

root :: t

The largest tile to start from.

children :: t -> [t]

The smaller children of a tile.

parent :: t -> Maybe t

The unique parent of a tile.

exterior :: t -> Rectangle

A rectangle that completely encloses the tile.

interior :: t -> Rectangle

A rectangle that is completely enclosed by the tile.

inside :: t -> Rectangle -> Bool

Test if a rectangle completely encloses the tile.

encloses :: t -> Rectangle -> Bool

Test if a rectangle is completely enclosed by the tile.

outside :: t -> Rectangle -> Bool

Test if a rectangle is completely disjoint from the tile.

overlaps :: t -> Rectangle -> Bool

Test if a rectangle has any overlap with the tile.

tile :: t -> Rectangle -> Int -> [t]

Generate a tiling that completely fills the given rectangle.

Preconditions:

 t `encloses` r
 n >= 0

Instances

Tiling Quad

Substitution tiling for square tiles.

tileDefault :: Tiling t => t -> Rectangle -> Int -> [t]

Default implementation for tile.

data Rectangle

An axis-aligned rectangle with Rational coordinates.

Invariant:

 westEdge r <= eastEdge r && southEdge r <= northEdge r

For substitution tilings that contain irrational lengths and/or scale factors, the intention is that the implementations of exterior and interior provide reasonably tight bounds, within a percent or two, say, while the data type maintains full precision internally (perhaps using algebraic field extensions over Rational).

Constructors

Rectangle

Fields

northEdge :: !Rational

southEdge :: !Rational

eastEdge :: !Rational

westEdge :: !Rational

Instances

Eq Rectangle

Data Rectangle

Ord Rectangle

Read Rectangle

Show Rectangle

Typeable Rectangle

rectangle

Arguments

:: Rational

x0

-> Rational

x1

-> Rational

y0

-> Rational

y1

-> Rectangle

rectangle

Create a valid rectangle, sorting the edges to meet the invariant.

insideR :: Rectangle -> Rectangle -> Bool

Check if a rectangle is inside another rectangle. The comparison is not strict, so that a rectangle is inside itself.

outsideR :: 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.

overlapsR :: 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.