Diagrams.Located

"Located" things, i.e. things with a concrete location: intuitively, Located a ~ (a, Point). Wrapping a translationally invariant thing (e.g. a Segment or Trail) in Located pins it down to a particular location and makes it no longer translationally invariant.

Documentation

data Located a

"Located" things, i.e. things with a concrete location: intuitively, Located a ~ (Point, a). Wrapping a translationally invariant thing (e.g. a Segment or Trail) in Located pins it down to a particular location and makes it no longer translationally invariant.

Located is intentionally abstract. To construct Located values, use at. To destruct, use viewLoc, unLoc, or loc. To map, use mapLoc.

Much of the utility of having a concrete type for the Located concept lies in the type class instances we can give it. The HasOrigin, Transformable, Enveloped, Traced, and TrailLike instances are particularly useful; see the documented instances below for more information.

Constructors

Loc

Fields

• loc :: Point (V a) (N a)

  Project out the location of a Located value.

• unLoc :: a

  Project the value of type a out of a Located a, discarding the location.

Instances

(Eq (V a (N a)), Eq a) => Eq (Located a)

Defined in Diagrams.Located

Methods

(==) :: Located a -> Located a -> Bool

(/=) :: Located a -> Located a -> Bool

(Ord (V a (N a)), Ord a) => Ord (Located a)

Defined in Diagrams.Located

Methods

compare :: Located a -> Located a -> Ordering

(<) :: Located a -> Located a -> Bool

(<=) :: Located a -> Located a -> Bool

(>) :: Located a -> Located a -> Bool

(>=) :: Located a -> Located a -> Bool

max :: Located a -> Located a -> Located a

min :: Located a -> Located a -> Located a

(Read (V a (N a)), Read a) => Read (Located a)

Defined in Diagrams.Located

Methods

readsPrec :: Int -> ReadS (Located a)

readList :: ReadS [Located a]

readPrec :: ReadPrec (Located a)

readListPrec :: ReadPrec [Located a]

(Show (V a (N a)), Show a) => Show (Located a)

Defined in Diagrams.Located

Methods

showsPrec :: Int -> Located a -> ShowS

show :: Located a -> String

showList :: [Located a] -> ShowS

Generic (Located a)

Defined in Diagrams.Located

Associated Types

type Rep (Located a) :: Type -> Type

Methods

from :: Located a -> Rep (Located a) x

to :: Rep (Located a) x -> Located a

(Serialize a, Serialize (V a (N a))) => Serialize (Located a)

Defined in Diagrams.Located

Methods

put :: Putter (Located a)

get :: Get (Located a)

Enveloped a => Juxtaposable (Located a)

Defined in Diagrams.Located

Methods

juxtapose :: Vn (Located a) -> Located a -> Located a -> Located a

Enveloped a => Enveloped (Located a)

The envelope of a Located a is the envelope of the a, translated to the location.

Defined in Diagrams.Located

Methods

getEnvelope :: Located a -> Envelope (V (Located a)) (N (Located a))

(Traced a, Num (N a)) => Traced (Located a)

The trace of a Located a is the trace of the a, translated to the location.

Defined in Diagrams.Located

Methods

getTrace :: Located a -> Trace (V (Located a)) (N (Located a))

Qualifiable a => Qualifiable (Located a)

Defined in Diagrams.Located

Methods

(.>>) :: IsName a0 => a0 -> Located a -> Located a

(Additive (V a), Num (N a), Transformable a) => Transformable (Located a)

Applying a transformation t to a Located a results in the transformation being applied to the location, and the linear portion of t being applied to the value of type a (i.e. it is not translated).

Defined in Diagrams.Located

Methods

transform :: Transformation (V (Located a)) (N (Located a)) -> Located a -> Located a

(Num (N a), Additive (V a)) => HasOrigin (Located a)

Located a is an instance of HasOrigin whether a is or not. In particular, translating a Located a simply translates the associated point (and does not affect the value of type a).

Defined in Diagrams.Located

Methods

moveOriginTo :: Point (V (Located a)) (N (Located a)) -> Located a -> Located a

(Metric v, OrderedField n) => Reversing (Located (Trail v n))

Same as reverseLocTrail.

Defined in Diagrams.Trail

Methods

reversing :: Located (Trail v n) -> Located (Trail v n)

(Metric v, OrderedField n) => Reversing (Located (Trail' l v n))

Same as reverseLocLine or reverseLocLoop.

Defined in Diagrams.Trail

Methods

reversing :: Located (Trail' l v n) -> Located (Trail' l v n)

(InSpace v n a, Fractional n, HasArcLength a, Codomain a ~ v) => HasArcLength (Located a)

Defined in Diagrams.Located

Methods

arcLengthBounded :: N (Located a) -> Located a -> Interval (N (Located a))

arcLength :: N (Located a) -> Located a -> N (Located a)

stdArcLength :: Located a -> N (Located a)

arcLengthToParam :: N (Located a) -> Located a -> N (Located a) -> N (Located a)

stdArcLengthToParam :: Located a -> N (Located a) -> N (Located a)

(InSpace v n a, Fractional n, Parametric a, Sectionable a, Codomain a ~ v) => Sectionable (Located a)

Defined in Diagrams.Located

Methods

splitAtParam :: Located a -> N (Located a) -> (Located a, Located a)

section :: Located a -> N (Located a) -> N (Located a) -> Located a

reverseDomain :: Located a -> Located a

(InSpace v n a, EndValues a, Codomain a ~ v) => EndValues (Located a)

Defined in Diagrams.Located

Methods

atStart :: Located a -> Codomain (Located a) (N (Located a))

atEnd :: Located a -> Codomain (Located a) (N (Located a))

(DomainBounds t, EndValues (Tangent t)) => EndValues (Tangent (Located t))

Defined in Diagrams.Tangent

Methods

atStart :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t)))

atEnd :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t)))

DomainBounds a => DomainBounds (Located a)

Defined in Diagrams.Located

Methods

domainLower :: Located a -> N (Located a)

domainUpper :: Located a -> N (Located a)

(InSpace v n a, Parametric a, Codomain a ~ v) => Parametric (Located a)

Defined in Diagrams.Located

Methods

atParam :: Located a -> N (Located a) -> Codomain (Located a) (N (Located a))

Parametric (Tangent t) => Parametric (Tangent (Located t))

Defined in Diagrams.Tangent

Methods

atParam :: Tangent (Located t) -> N (Tangent (Located t)) -> Codomain (Tangent (Located t)) (N (Tangent (Located t)))

Alignable a => Alignable (Located a)

Defined in Diagrams.Located

Methods

alignBy' :: (InSpace v n (Located a), Fractional n, HasOrigin (Located a)) => (v n -> Located a -> Point v n) -> v n -> n -> Located a -> Located a

defaultBoundary :: (V (Located a) ~ v, N (Located a) ~ n) => v n -> Located a -> Point v n

alignBy :: (InSpace v n (Located a), Fractional n, HasOrigin (Located a)) => v n -> n -> Located a -> Located a

TrailLike t => TrailLike (Located t)

Located things are trail-like as long as the underlying type is. The location is taken to be the location of the input located trail.

Defined in Diagrams.TrailLike

Methods

trailLike :: Located (Trail (V (Located t)) (N (Located t))) -> Located t

ToPath (Located [Segment Closed v n])

Defined in Diagrams.Path

Methods

toPath :: Located [Segment Closed v n] -> Path (V (Located [Segment Closed v n])) (N (Located [Segment Closed v n]))

ToPath (Located (Segment Closed v n))

Defined in Diagrams.Path

Methods

toPath :: Located (Segment Closed v n) -> Path (V (Located (Segment Closed v n))) (N (Located (Segment Closed v n)))

ToPath (Located (Trail v n))

Defined in Diagrams.Path

Methods

toPath :: Located (Trail v n) -> Path (V (Located (Trail v n))) (N (Located (Trail v n)))

ToPath (Located (Trail' l v n))

Defined in Diagrams.Path

Methods

toPath :: Located (Trail' l v n) -> Path (V (Located (Trail' l v n))) (N (Located (Trail' l v n)))

RealFloat n => HasQuery (Located (Trail V2 n)) Crossings

Defined in Diagrams.TwoD.Path

Methods

getQuery :: Located (Trail V2 n) -> Query (V (Located (Trail V2 n))) (N (Located (Trail V2 n))) Crossings

RealFloat n => HasQuery (Located (Trail' l V2 n)) Crossings

Defined in Diagrams.TwoD.Path

Methods

getQuery :: Located (Trail' l V2 n) -> Query (V (Located (Trail' l V2 n))) (N (Located (Trail' l V2 n))) Crossings

(LinearMappable a b, N a ~ N b, r ~ Located b) => AffineMappable (Located a) r

Defined in Diagrams.LinearMap

Methods

amap :: AffineMap (V (Located a)) (V r) (N r) -> Located a -> r

(LinearMappable a b, r ~ Located b) => LinearMappable (Located a) r

Defined in Diagrams.LinearMap

Methods

vmap :: (Vn (Located a) -> Vn r) -> Located a -> r

(Metric v, Metric u, OrderedField n, r ~ Located (Trail u n)) => Deformable (Located (Trail v n)) r

Defined in Diagrams.Deform

Methods

deform' :: N (Located (Trail v n)) -> Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r

deform :: Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r

Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Defined in Diagrams.Path

Methods

each :: Traversal (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Defined in Diagrams.Path

Methods

_Cons :: Prism (Path v n) (Path v' n') (Located (Trail v n), Path v n) (Located (Trail v' n'), Path v' n')

Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Defined in Diagrams.Path

Methods

_Snoc :: Prism (Path v n) (Path v' n') (Path v n, Located (Trail v n)) (Path v' n', Located (Trail v' n'))

type Rep (Located a)

Defined in Diagrams.Located

type Rep (Located a) = D1 (MetaData "Located" "Diagrams.Located" "diagrams-lib-1.4.3-8JTlbiKnHul1qsqRgNvXXl" False) (C1 (MetaCons "Loc" PrefixI True) (S1 (MetaSel (Just "loc") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Point (V a) (N a))) :*: S1 (MetaSel (Just "unLoc") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type V (Located a)

Defined in Diagrams.Located

type V (Located a) = V a

type N (Located a)

Defined in Diagrams.Located

type N (Located a) = N a

type Codomain (Located a)

Defined in Diagrams.Located

type Codomain (Located a) = Point (Codomain a)

at :: a -> Point (V a) (N a) -> Located a infix 5

Construct a Located a from a value of type a and a location. at is intended to be used infix, like x `at` origin.

viewLoc :: Located a -> (Point (V a) (N a), a)

Deconstruct a Located a into a location and a value of type a. viewLoc can be especially useful in conjunction with the ViewPatterns extension.

mapLoc :: SameSpace a b => (a -> b) -> Located a -> Located b

Located is not a Functor, since changing the type could change the type of the associated vector space, in which case the associated location would no longer have the right type. mapLoc has an extra constraint specifying that the vector space must stay the same.

(Technically, one can say that for every vector space v, Located is a little-f (endo)functor on the category of types with associated vector space v; but that is not covered by the standard Functor class.)

located :: SameSpace a b => Lens (Located a) (Located b) a b

A lens giving access to the object within a Located wrapper.

_loc :: Lens' (Located a) (Point (V a) (N a))

Lens onto the location of something Located.