Diagrams.TwoD.Types

Basic types for two-dimensional Euclidean space.

2D Euclidean space

data R2

The two-dimensional Euclidean vector space R^2. This type is intentionally abstract.

• To construct a vector, use r2, or ^& (from Diagrams.Coordinates):

 r2 (3,4) :: R2
 3 ^& 4    :: R2

Note that Diagrams.Coordinates is not re-exported by Diagrams.Prelude and must be explicitly imported.

• To construct the vector from the origin to a point p, use p .-. origin.
• To convert a vector v into the point obtained by following v from the origin, use origin .+^ v.
• To convert a vector back into a pair of components, use unv2 or coords (from Diagrams.Coordinates). These are typically used in conjunction with the ViewPatterns extension:

 foo (unr2 -> (x,y)) = ...
 foo (coords -> x :& y) = ...

Constructors

R2 !Double !Double

Instances

Eq R2

Fractional R2

Num R2

Ord R2

Read R2

Show R2

Typeable R2

Transformable R2

Wrapped R2

Lens wrapped isomorphisms for R2.

HasBasis R2

VectorSpace R2

InnerSpace R2

AdditiveGroup R2

HasY P2

HasY R2

HasX P2

HasX R2

Coordinates R2

Rewrapped R2 R2

Traced (FixedSegment R2)

Traced (Trail R2)

Traced (Path R2)

Traced (Segment Closed R2)

Renderable (Path R2) b => TrailLike (QDiagram b R2 Any)

r2 :: (Double, Double) -> R2

Construct a 2D vector from a pair of components. See also &.

unr2 :: R2 -> (Double, Double)

Convert a 2D vector back into a pair of components. See also coords.

mkR2 :: Double -> Double -> R2

Curried form of r2.

r2Iso :: Iso' R2 (Double, Double)

type P2 = Point R2

Points in R^2. This type is intentionally abstract.

• To construct a point, use p2, or ^& (see Diagrams.Coordinates):

 p2 (3,4)  :: P2
 3 ^& 4    :: P2

• To construct a point from a vector v, use origin .+^ v.
• To convert a point p into the vector from the origin to p, use p .-. origin.
• To convert a point back into a pair of coordinates, use unp2, or coords (from Diagrams.Coordinates). It's common to use these in conjunction with the ViewPatterns extension:

 foo (unp2 -> (x,y)) = ...
 foo (coords -> x :& y) = ...

p2 :: (Double, Double) -> P2

Construct a 2D point from a pair of coordinates. See also ^&.

mkP2 :: Double -> Double -> P2

Curried form of p2.

unp2 :: P2 -> (Double, Double)

Convert a 2D point back into a pair of coordinates. See also coords.

p2Iso :: Iso' P2 (Double, Double)

type T2 = Transformation R2

Transformations in R^2.

Angles

data Angle

Angles can be expressed in a variety of units. Internally, they are represented in radians.

Instances

Enum Angle

Eq Angle

Ord Angle

Read Angle

Show Angle

VectorSpace Angle

AdditiveGroup Angle

rad :: Iso' Angle Double

The radian measure of an Angle a can be accessed as a ^. rad. A new Angle can be defined in radians as pi @@ rad.

turn :: Iso' Angle Double

The measure of an Angle a in full circles can be accessed as a ^. turn. A new Angle of one-half circle can be defined in as 1/2 @@ turn.

deg :: Iso' Angle Double

The degree measure of an Angle a can be accessed as a ^. deg. A new Angle can be defined in degrees as 180 @@ deg.

fullTurn :: Angle

An angle representing one full turn.

fullCircle :: Angle

Deprecated synonym for fullTurn, retained for backwards compatibility.

angleRatio :: Angle -> Angle -> Double

Calculate ratio between two angles.

(@@) :: b -> Iso' a b -> a

30 @@ deg is an Angle of the given measure and units.

More generally, @@ reverses the Iso' on its right, and applies the Iso' to the value on the left. Angles are the motivating example where this order improves readability.