Diagrams.Points

Points in space. For more tools for working with points and vectors, see Linear.Affine.

Points

newtype Point f a :: (* -> *) -> * -> *

A handy wrapper to help distinguish points from vectors at the type level

Constructors

P (f a)

Instances

Monad f => Monad (Point f)

Functor f => Functor (Point f)

Applicative f => Applicative (Point f)

Foldable f => Foldable (Point f)

Traversable f => Traversable (Point f)

Generic1 (Point f)

Apply f => Apply (Point f)

Distributive f => Distributive (Point f)

Representable f => Representable (Point f)

Serial1 f => Serial1 (Point f)

Additive f => Additive (Point f)

Additive f => Affine (Point f)

R4 f => R4 (Point f)

R3 f => R3 (Point f)

R2 f => R2 (Point f)

R1 f => R1 (Point f)

Metric f => Metric (Point f)

Bind f => Bind (Point f)

Eq1 f => Eq1 (Point f)

Ord1 f => Ord1 (Point f)

Read1 f => Read1 (Point f)

Show1 f => Show1 (Point f)

HasPhi v => HasPhi (Point v)

HasTheta v => HasTheta (Point v)

HasR v => HasR (Point v)

(Metric v, OrderedField n) => TrailLike [Point v n]

A list of points is trail-like; this instance simply computes the vertices of the trail, using trailPoints.

Eq (f a) => Eq (Point f a)

Fractional (f a) => Fractional (Point f a)

(Data (f a), Typeable (* -> *) f, Typeable * a) => Data (Point f a)

Num (f a) => Num (Point f a)

Ord (f a) => Ord (Point f a)

Read (f a) => Read (Point f a)

Show (f a) => Show (Point f a)

Ix (f a) => Ix (Point f a)

Generic (Point f a)

Storable (f a) => Storable (Point f a)

Binary (f a) => Binary (Point f a)

Serial (f a) => Serial (Point f a)

Serialize (f a) => Serialize (Point f a)

NFData (f a) => NFData (Point f a)

(OrderedField n, Metric v) => Enveloped (Point v n)

(Additive v, Ord n) => Traced (Point v n)

The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).

(Additive v, Num n) => Transformable (Point v n)

(Additive v, Num n) => HasOrigin (Point v n)

Hashable (f a) => Hashable (Point f a)

Ixed (f a) => Ixed (Point f a)

Wrapped (Point f a)

Epsilon (f a) => Epsilon (Point f a)

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

(~) * t (Point g b) => Rewrapped (Point f a) t

(~) * r (Point u n) => Deformable (Point v n) r

(Additive v, Foldable v, Num n, (~) * r (Point u n)) => AffineMappable (Point v n) r

LinearMappable (Point v n) (Point u m)

Traversable f => Each (Point f a) (Point f b) a b

Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n')

(Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n')

Only valid if the second point is not smaller than the first.

type Rep1 (Point f) = D1 D1Point (C1 C1_0Point (S1 NoSelector (Rec1 f)))

type Rep (Point f) = Rep f

type Diff (Point f) = f

type Rep (Point f a) = D1 D1Point (C1 C1_0Point (S1 NoSelector (Rec0 (f a))))

type V (Point v n) = v

type N (Point v n) = n

type Index (Point f a) = Index (f a)

type IxValue (Point f a) = IxValue (f a)

type Unwrapped (Point f a) = f a

type FinalCoord (Point v n) = FinalCoord (v n)

type PrevDim (Point v n) = PrevDim (v n)

type Decomposition (Point v n) = Decomposition (v n)

origin :: (Additive f, Num a) => Point f a

Vector spaces have origins.

(*.) :: (Functor v, Num n) => n -> Point v n -> Point v n

Scale a point by a scalar. Specialized version of '(*^)'.

Point-related utilities

centroid :: (Additive v, Fractional n) => [Point v n] -> Point v n

The centroid of a set of n points is their sum divided by n.

pointDiagram :: (Metric v, Fractional n) => Point v n -> QDiagram b v n m

Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.

_Point :: (Profunctor p, Functor f) => p (f a) (f (f a)) -> p (Point f a) (f (Point f a))

lensP :: Functor f => (g a -> f (g a)) -> Point g a -> f (Point g a)