Diagrams.Coordinates

Nice syntax for constructing and pattern-matching on literal points and vectors.

Documentation

data a :& b infixl 7

A pair of values, with a convenient infix (left-associative) data constructor.

Constructors

a :& b infixl 7

Instances

(Eq b, Eq a) => Eq ((:&) a b)

Methods

(==) :: (a :& b) -> (a :& b) -> Bool

(/=) :: (a :& b) -> (a :& b) -> Bool

(Ord b, Ord a) => Ord ((:&) a b)

Methods

compare :: (a :& b) -> (a :& b) -> Ordering

(<) :: (a :& b) -> (a :& b) -> Bool

(<=) :: (a :& b) -> (a :& b) -> Bool

(>) :: (a :& b) -> (a :& b) -> Bool

(>=) :: (a :& b) -> (a :& b) -> Bool

max :: (a :& b) -> (a :& b) -> a :& b

min :: (a :& b) -> (a :& b) -> a :& b

(Show b, Show a) => Show ((:&) a b)

Methods

showsPrec :: Int -> (a :& b) -> ShowS

show :: (a :& b) -> String

showList :: [a :& b] -> ShowS

Coordinates ((:&) a b)

Associated Types

type FinalCoord (a :& b) :: *

type PrevDim (a :& b) :: *

type Decomposition (a :& b) :: *

Methods

(^&) :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b

pr :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b

coords :: (a :& b) -> Decomposition (a :& b)

type FinalCoord ((:&) a b)

type FinalCoord ((:&) a b) = b

type PrevDim ((:&) a b)

type PrevDim ((:&) a b) = a

type Decomposition ((:&) a b)

type Decomposition ((:&) a b) = (:&) a b

class Coordinates c where

Types which are instances of the Coordinates class can be constructed using ^& (for example, a three-dimensional vector could be constructed by 1 ^& 6 ^& 3), and deconstructed using coords. A common pattern is to use coords in conjunction with the ViewPatterns extension, like so:

foo :: Vector3 -> ...
foo (coords -> x :& y :& z) = ...

Minimal complete definition

(^&), coords

Associated Types

type FinalCoord c :: *

The type of the final coordinate.

type PrevDim c :: *

The type of everything other than the final coordinate.

type Decomposition c :: *

Decomposition of c into applications of :&.

Methods

(^&) :: PrevDim c -> FinalCoord c -> c infixl 7

Construct a value of type c by providing something of one less dimension (which is perhaps itself recursively constructed using (^&)) and a final coordinate. For example,

2 ^& 3 :: P2
3 ^& 5 ^& 6 :: V3

Note that ^& is left-associative.

pr :: PrevDim c -> FinalCoord c -> c

Prefix synonym for ^&. pr stands for pair of PrevDim, FinalCoord

coords :: c -> Decomposition c

Decompose a value of type c into its constituent coordinates, stored in a nested (:&) structure.

Instances

Coordinates (V4 n)

Associated Types

type FinalCoord (V4 n) :: *

type PrevDim (V4 n) :: *

type Decomposition (V4 n) :: *

Methods

(^&) :: PrevDim (V4 n) -> FinalCoord (V4 n) -> V4 n

pr :: PrevDim (V4 n) -> FinalCoord (V4 n) -> V4 n

coords :: V4 n -> Decomposition (V4 n)

Coordinates (V3 n)

Associated Types

type FinalCoord (V3 n) :: *

type PrevDim (V3 n) :: *

type Decomposition (V3 n) :: *

Methods

(^&) :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n

pr :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n

coords :: V3 n -> Decomposition (V3 n)

Coordinates (V2 n)

Associated Types

type FinalCoord (V2 n) :: *

type PrevDim (V2 n) :: *

type Decomposition (V2 n) :: *

Methods

(^&) :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n

pr :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n

coords :: V2 n -> Decomposition (V2 n)

Coordinates (a, b)

Associated Types

type FinalCoord (a, b) :: *

type PrevDim (a, b) :: *

type Decomposition (a, b) :: *

Methods

(^&) :: PrevDim (a, b) -> FinalCoord (a, b) -> (a, b)

pr :: PrevDim (a, b) -> FinalCoord (a, b) -> (a, b)

coords :: (a, b) -> Decomposition (a, b)

Coordinates (v n) => Coordinates (Point v n)

Associated Types

type FinalCoord (Point v n) :: *

type PrevDim (Point v n) :: *

type Decomposition (Point v n) :: *

Methods

(^&) :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n

pr :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n

coords :: Point v n -> Decomposition (Point v n)

Coordinates ((:&) a b)

Associated Types

type FinalCoord (a :& b) :: *

type PrevDim (a :& b) :: *

type Decomposition (a :& b) :: *

Methods

(^&) :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b

pr :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b

coords :: (a :& b) -> Decomposition (a :& b)

Coordinates (a, b, c)

Associated Types

type FinalCoord (a, b, c) :: *

type PrevDim (a, b, c) :: *

type Decomposition (a, b, c) :: *

Methods

(^&) :: PrevDim (a, b, c) -> FinalCoord (a, b, c) -> (a, b, c)

pr :: PrevDim (a, b, c) -> FinalCoord (a, b, c) -> (a, b, c)

coords :: (a, b, c) -> Decomposition (a, b, c)

Coordinates (a, b, c, d)

Associated Types

type FinalCoord (a, b, c, d) :: *

type PrevDim (a, b, c, d) :: *

type Decomposition (a, b, c, d) :: *

Methods

(^&) :: PrevDim (a, b, c, d) -> FinalCoord (a, b, c, d) -> (a, b, c, d)

pr :: PrevDim (a, b, c, d) -> FinalCoord (a, b, c, d) -> (a, b, c, d)

coords :: (a, b, c, d) -> Decomposition (a, b, c, d)