diagrams-lib-1.3.0.1: Embedded domain-specific language for declarative graphics

Copyright (c) 2011 diagrams-lib team (see LICENSE) BSD-style (see LICENSE) diagrams-discuss@googlegroups.com None Haskell2010

Diagrams.Points

Contents

Description

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

Synopsis

# 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) (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 Source

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)