Swarm.Util.Location

Locations and headings.

Documentation

type Location = Point V2 Int32

A Location is a pair of (x,y) coordinates, both up to 32 bits. The positive x-axis points east and the positive y-axis points north. These are the coordinates that are shown to players.

See also the Coords type defined in Swarm.Game.World, which use a (row, column) format instead, which is more convenient for internal use. The Swarm.Game.World module also defines conversions between Location and Coords.

pattern Location :: Int32 -> Int32 -> Location

A convenient way to pattern-match on Location values.

type Heading = V2 Int32

A Heading is a 2D vector, with 32-bit coordinates.

Location and Heading are both represented using types from the linear package, so they can be manipulated using a large number of operators from that package. For example:

• Two headings can be added with ^+^.
• The difference between two Locations is a Heading (via .-.).
• A Location plus a Heading is another Location (via .^+).

origin :: forall (f :: Type -> Type) a. (Additive f, Num a) => Point f a

Vector spaces have origins.

class Additive (Diff p) => Affine (p :: Type -> Type) where

An affine space is roughly a vector space in which we have forgotten or at least pretend to have forgotten the origin.

a .+^ (b .-. a)  =  b@
(a .+^ u) .+^ v  =  a .+^ (u ^+^ v)@
(a .-. b) ^+^ v  =  (a .+^ v) .-. q@

Minimal complete definition

(.-.), (.+^)

Associated Types

type Diff (p :: Type -> Type) :: Type -> Type

Methods

(.-.) :: Num a => p a -> p a -> Diff p a infixl 6

Get the difference between two points as a vector offset.

(.+^) :: Num a => p a -> Diff p a -> p a infixl 6

Add a vector offset to a point.

(.-^) :: Num a => p a -> Diff p a -> p a infixl 6

Subtract a vector offset from a point.

Instances

Affine ZipList

Defined in Linear.Affine

Associated Types

type Diff ZipList :: Type -> Type

Methods

(.-.) :: Num a => ZipList a -> ZipList a -> Diff ZipList a

(.+^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a

(.-^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a

Affine Complex

Defined in Linear.Affine

Associated Types

type Diff Complex :: Type -> Type

Methods

(.-.) :: Num a => Complex a -> Complex a -> Diff Complex a

(.+^) :: Num a => Complex a -> Diff Complex a -> Complex a

(.-^) :: Num a => Complex a -> Diff Complex a -> Complex a

Affine Identity

Defined in Linear.Affine

Associated Types

type Diff Identity :: Type -> Type

Methods

(.-.) :: Num a => Identity a -> Identity a -> Diff Identity a

(.+^) :: Num a => Identity a -> Diff Identity a -> Identity a

(.-^) :: Num a => Identity a -> Diff Identity a -> Identity a

Affine IntMap

Defined in Linear.Affine

Associated Types

type Diff IntMap :: Type -> Type

Methods

(.-.) :: Num a => IntMap a -> IntMap a -> Diff IntMap a

(.+^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a

(.-^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a

Affine Plucker

Defined in Linear.Affine

Associated Types

type Diff Plucker :: Type -> Type

Methods

(.-.) :: Num a => Plucker a -> Plucker a -> Diff Plucker a

(.+^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a

(.-^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a

Affine Quaternion

Defined in Linear.Affine

Associated Types

type Diff Quaternion :: Type -> Type

Methods

(.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a

(.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a

(.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a

Affine V0

Defined in Linear.Affine

Associated Types

type Diff V0 :: Type -> Type

Methods

(.-.) :: Num a => V0 a -> V0 a -> Diff V0 a

(.+^) :: Num a => V0 a -> Diff V0 a -> V0 a

(.-^) :: Num a => V0 a -> Diff V0 a -> V0 a

Affine V1

Defined in Linear.Affine

Associated Types

type Diff V1 :: Type -> Type

Methods

(.-.) :: Num a => V1 a -> V1 a -> Diff V1 a

(.+^) :: Num a => V1 a -> Diff V1 a -> V1 a

(.-^) :: Num a => V1 a -> Diff V1 a -> V1 a

Affine V2

Defined in Linear.Affine

Associated Types

type Diff V2 :: Type -> Type

Methods

(.-.) :: Num a => V2 a -> V2 a -> Diff V2 a

(.+^) :: Num a => V2 a -> Diff V2 a -> V2 a

(.-^) :: Num a => V2 a -> Diff V2 a -> V2 a

Affine V3

Defined in Linear.Affine

Associated Types

type Diff V3 :: Type -> Type

Methods

(.-.) :: Num a => V3 a -> V3 a -> Diff V3 a

(.+^) :: Num a => V3 a -> Diff V3 a -> V3 a

(.-^) :: Num a => V3 a -> Diff V3 a -> V3 a

Affine V4

Defined in Linear.Affine

Associated Types

type Diff V4 :: Type -> Type

Methods

(.-.) :: Num a => V4 a -> V4 a -> Diff V4 a

(.+^) :: Num a => V4 a -> Diff V4 a -> V4 a

(.-^) :: Num a => V4 a -> Diff V4 a -> V4 a

Affine Vector

Defined in Linear.Affine

Associated Types

type Diff Vector :: Type -> Type

Methods

(.-.) :: Num a => Vector a -> Vector a -> Diff Vector a

(.+^) :: Num a => Vector a -> Diff Vector a -> Vector a

(.-^) :: Num a => Vector a -> Diff Vector a -> Vector a

Affine Maybe

Defined in Linear.Affine

Associated Types

type Diff Maybe :: Type -> Type

Methods

(.-.) :: Num a => Maybe a -> Maybe a -> Diff Maybe a

(.+^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a

(.-^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a

Affine []

Defined in Linear.Affine

Associated Types

type Diff [] :: Type -> Type

Methods

(.-.) :: Num a => [a] -> [a] -> Diff [] a

(.+^) :: Num a => [a] -> Diff [] a -> [a]

(.-^) :: Num a => [a] -> Diff [] a -> [a]

Ord k => Affine (Map k)

Defined in Linear.Affine

Associated Types

type Diff (Map k) :: Type -> Type

Methods

(.-.) :: Num a => Map k a -> Map k a -> Diff (Map k) a

(.+^) :: Num a => Map k a -> Diff (Map k) a -> Map k a

(.-^) :: Num a => Map k a -> Diff (Map k) a -> Map k a

Additive f => Affine (Point f)

Defined in Linear.Affine

Associated Types

type Diff (Point f) :: Type -> Type

Methods

(.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a

(.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a

(.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a

(Eq k, Hashable k) => Affine (HashMap k)

Defined in Linear.Affine

Associated Types

type Diff (HashMap k) :: Type -> Type

Methods

(.-.) :: Num a => HashMap k a -> HashMap k a -> Diff (HashMap k) a

(.+^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a

(.-^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a

Dim n => Affine (V n)

Defined in Linear.Affine

Associated Types

type Diff (V n) :: Type -> Type

Methods

(.-.) :: Num a => V n a -> V n a -> Diff (V n) a

(.+^) :: Num a => V n a -> Diff (V n) a -> V n a

(.-^) :: Num a => V n a -> Diff (V n) a -> V n a

(Affine f, Affine g) => Affine (Product f g)

Defined in Linear.Affine

Associated Types

type Diff (Product f g) :: Type -> Type

Methods

(.-.) :: Num a => Product f g a -> Product f g a -> Diff (Product f g) a

(.+^) :: Num a => Product f g a -> Diff (Product f g) a -> Product f g a

(.-^) :: Num a => Product f g a -> Diff (Product f g) a -> Product f g a

Affine ((->) b)

Defined in Linear.Affine

Associated Types

type Diff ((->) b) :: Type -> Type

Methods

(.-.) :: Num a => (b -> a) -> (b -> a) -> Diff ((->) b) a

(.+^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a

(.-^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a

Orphan instances

FromJSON Location

Methods

parseJSON :: Value -> Parser Location

parseJSONList :: Value -> Parser [Location]

ToJSON Location

Methods

toJSON :: Location -> Value

toEncoding :: Location -> Encoding

toJSONList :: [Location] -> Value

toEncodingList :: [Location] -> Encoding

FromJSON (V2 Int32)

Methods

parseJSON :: Value -> Parser (V2 Int32)

parseJSONList :: Value -> Parser [V2 Int32]

FromJSONKey (V2 Int32)

Methods

fromJSONKey :: FromJSONKeyFunction (V2 Int32)

fromJSONKeyList :: FromJSONKeyFunction [V2 Int32]

ToJSON (V2 Int32)

Methods

toJSON :: V2 Int32 -> Value

toEncoding :: V2 Int32 -> Encoding

toJSONList :: [V2 Int32] -> Value

toEncodingList :: [V2 Int32] -> Encoding

ToJSONKey (V2 Int32)

Methods

toJSONKey :: ToJSONKeyFunction (V2 Int32)

toJSONKeyList :: ToJSONKeyFunction [V2 Int32]