Diagrams.Direction

Type for representing directions, polymorphic in vector space

Documentation

data Direction v n

A vector is described by a Direction and a magnitude. So we can think of a Direction as a vector that has forgotten its magnitude. Directions can be used with fromDirection and the lenses provided by its instances.

Instances

Functor v => Functor (Direction v)

Methods

fmap :: (a -> b) -> Direction v a -> Direction v b

(<$) :: a -> Direction v b -> Direction v a

HasPhi v => HasPhi (Direction v)

Methods

_phi :: RealFloat n => Lens' (Direction v n) (Angle n)

HasTheta v => HasTheta (Direction v)

Methods

_theta :: RealFloat n => Lens' (Direction v n) (Angle n)

Eq (v n) => Eq (Direction v n)

Methods

(==) :: Direction v n -> Direction v n -> Bool

(/=) :: Direction v n -> Direction v n -> Bool

Ord (v n) => Ord (Direction v n)

Methods

compare :: Direction v n -> Direction v n -> Ordering

(<) :: Direction v n -> Direction v n -> Bool

(<=) :: Direction v n -> Direction v n -> Bool

(>) :: Direction v n -> Direction v n -> Bool

(>=) :: Direction v n -> Direction v n -> Bool

max :: Direction v n -> Direction v n -> Direction v n

min :: Direction v n -> Direction v n -> Direction v n

Read (v n) => Read (Direction v n)

Methods

readsPrec :: Int -> ReadS (Direction v n)

readList :: ReadS [Direction v n]

readPrec :: ReadPrec (Direction v n)

readListPrec :: ReadPrec [Direction v n]

Show (v n) => Show (Direction v n)

Methods

showsPrec :: Int -> Direction v n -> ShowS

show :: Direction v n -> String

showList :: [Direction v n] -> ShowS

((~) (* -> *) (V (v n)) v, (~) * (N (v n)) n, Transformable (v n)) => Transformable (Direction v n)

Methods

transform :: Transformation (V (Direction v n)) (N (Direction v n)) -> Direction v n -> Direction v n

type V (Direction v n)

type V (Direction v n) = v

type N (Direction v n)

type N (Direction v n) = n

_Dir :: Iso' (Direction v n) (v n)

_Dir is provided to allow efficient implementations of functions in particular vector-spaces, but should be used with care as it exposes too much information.

direction :: v n -> Direction v n

direction v is the direction in which v points. Returns an unspecified value when given the zero vector as input.

dir :: v n -> Direction v n

Synonym for direction.

fromDirection :: (Metric v, Floating n) => Direction v n -> v n

fromDirection d is the unit vector in the direction d.

fromDir :: (Metric v, Floating n) => Direction v n -> v n

Synonym for fromDirection.

angleBetweenDirs :: (Metric v, Floating n, Ord n) => Direction v n -> Direction v n -> Angle n

compute the positive angle between the two directions in their common plane

dirBetween :: (Additive v, Num n) => Point v n -> Point v n -> Direction v n

dirBetween p q returns the direction from p to q.