diagrams-contrib-1.3.0.4: Collection of user contributions to diagrams EDSL

Diagrams.TwoD.Tilings

Description

Tools for generating and drawing plane tilings made of regular polygons.

Synopsis

# The ring Q[sqrt 2, sqrt 3]

data Q236 Source

`Q236 a b c d` represents ```a + b sqrt(2) + c sqrt(3) + d sqrt(6)```. Note that the `Ord` instance is suitable for use in `Map` and `Set`, but does not correspond to numeric ordering (`Q236` is not an ordered field under this ordering).

Instances

 Source Source Source Source Source Source

toFloating :: Floating n => Q236 -> n Source

Convert a `Q236` value to a `Double`.

type Q2 = V2 Q236 Source

toV2 :: Floating n => Q2 -> V2 n Source

toP2 :: Floating n => Q2 -> P2 n Source

# Regular polygons

data TilingPoly Source

Regular polygons which may appear in a tiling of the plane.

Constructors

 Triangle Square Hexagon Octagon Dodecagon

polyFromSides :: (Num a, Eq a, Show a) => a -> TilingPoly Source

Cosine of a polygon's internal angle.

Sine of a polygon's internal angle.

Rotate by polygon internal angle.

Rotate by polygon external angle.

# Tilings

## Types

data Tiling Source

A tiling, represented as a sort of zipper. `curConfig` indicates the polygons around the current vertex, in couterclockwise order starting from the edge along which we entered the vertex. `follow` allows one to move along an edge to an adjacent vertex, where the edges are numbered counterclockwise from zero, beginning with the edge along which we entered the current vertex.

Constructors

 Tiling FieldscurConfig :: [TilingPoly] follow :: Int -> Tiling

data Edge Source

An edge is represented by a pair of vertices. Do not use the `Edge` constructor directly; use `mkEdge` instead.

Instances

 Source Source Source

mkEdge :: Q2 -> Q2 -> Edge Source

Smart constructor for `Edge`, which puts the vertices in a canonical order.

newtype Polygon Source

A polygon is represented by a list of its vertices, in counterclockwise order. However, the `Eq` and `Ord` instances for polygons ignore the order.

Constructors

 Polygon FieldspolygonVertices :: [Q2]

Instances

 Source Source Source

## Generation

The state maintained while generating a tiling, recording which vertices have been visited and which edges and polygons have been drawn.

Constructors

 TP FieldsvisitedVertices :: Set Q2 visitedEdges :: Set Edge visitedPolygons :: Set Polygon

type TilingM w a = WriterT w (State TilingState) a Source

The `TilingM` monad tracks a `TilingState`, and can output elements of some monoid `w` along the way.

Arguments

 :: Monoid w => Tiling The tiling to generate -> Q2 The location of the starting vertex. -> Q2 The starting direction, i.e. the direction along which we came into the starting vertex. -> (Q2 -> Bool) Predicate on vertices specifying which should be visited. The vertices for which the predicate evaluates to True must form a single connected component. -> (Edge -> w) what to do with edges -> (Polygon -> w) what to do with polygons -> w

## Pre-defined tilings

mk3Tiling :: [Int] -> Tiling Source

Create a tiling with the same 3 polygons surrounding each vertex. The argument is the number of sides of the polygons surrounding a vertex.

Arguments

 :: [Int] The number of sides of the polygons surrounding a typical vertex, counterclockwise starting from edge 0. -> [Int] The transition list: if the ith entry of this list is j, it indicates that the edge labeled i is labeled j with respect to the vertex on its other end. -> Tiling

Create a tiling where every vertex is the same up to rotation and translation (but not reflection). Arbitrarily pick one of the edges emanating from a vertex and number the edges counterclockwise starting with 0 for the chosen edge.

rot :: (Num a, Eq a) => a -> [t] -> [t] Source

# Diagrams

drawEdge :: (Renderable (Path V2 n) b, TypeableFloat n) => Style V2 n -> Edge -> QDiagram b V2 n Any Source

Draw an edge with the given style.

drawPoly :: (Renderable (Path V2 n) b, TypeableFloat n) => (Polygon -> Style V2 n) -> Polygon -> QDiagram b V2 n Any Source

Draw a polygon with the given style.

drawTiling :: (Renderable (Path V2 n) b, TypeableFloat n) => Tiling -> n -> n -> QDiagram b V2 n Any Source

Draw a tiling, with a given width and height and default colors for the polygons.

drawTilingStyled :: forall b n. (Renderable (Path V2 n) b, TypeableFloat n) => Style V2 n -> (Polygon -> Style V2 n) -> Tiling -> n -> n -> QDiagram b V2 n Any Source

Draw a tiling with customizable styles for the polygons. This is just an example, which you can use as the basis of your own tiling-drawing routine.