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

HasBasis R2

VectorSpace R2

InnerSpace R2

AdditiveGroup R2

HasY P2

HasY R2

HasX P2

HasX R2

Coordinates R2

Traced (FixedSegment R2)

Traced (Trail R2)

Traced (Path R2)

Wrapped [Path R2] [Path R2] Clip Clip

Traced (Segment Closed R2)

Wrapped (Double, Double) (Double, Double) R2 R2

Lens wrapped isomorphisms for 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

class Num a => Angle a where

Type class for types that measure angles.

Methods

toTurn :: a -> Turn

Convert to a turn, i.e. a fraction of a circle.

fromTurn :: Turn -> a

Convert from a turn, i.e. a fraction of a circle.

Instances

Angle Turn

Angle Rad

tau radians = 1 full turn.

Angle Deg

360 degrees = 1 full turn.

newtype Turn

Newtype wrapper used to represent angles as fractions of a circle. For example, 1/3 turn = tau/3 radians = 120 degrees.

Constructors

Turn Double

Instances

Enum Turn

Eq Turn

Fractional Turn

Num Turn

Ord Turn

Read Turn

Real Turn

RealFrac Turn

Show Turn

VectorSpace Turn

AdditiveGroup Turn

Angle Turn

Wrapped Double Double Turn Turn

asTurn :: Turn -> Turn

The identity function with a restricted type, for conveniently declaring that some value should have type Turn. For example, rotation . asTurn . fromRational constructs a rotation from a rational value considered as a Turn. Without asTurn, the angle type would be ambiguous.

type CircleFrac = Turn

Deprecated synonym for Turn, retained for backwards compatibility.

newtype Rad

Newtype wrapper for representing angles in radians.

Constructors

Rad Double

Instances

Enum Rad

Eq Rad

Floating Rad

Fractional Rad

Num Rad

Ord Rad

Read Rad

Real Rad

RealFloat Rad

RealFrac Rad

Show Rad

VectorSpace Rad

AdditiveGroup Rad

Angle Rad

tau radians = 1 full turn.

Wrapped Double Double Rad Rad

asRad :: Rad -> Rad

The identity function with a restricted type, for conveniently declaring that some value should have type Rad. For example, rotation . asRad . fromRational constructs a rotation from a rational value considered as a value in radians. Without asRad, the angle type would be ambiguous.

newtype Deg

Newtype wrapper for representing angles in degrees.

Constructors

Deg Double

Instances

Enum Deg

Eq Deg

Fractional Deg

Num Deg

Ord Deg

Read Deg

Real Deg

RealFrac Deg

Show Deg

VectorSpace Deg

AdditiveGroup Deg

Angle Deg

360 degrees = 1 full turn.

Wrapped Double Double Deg Deg

asDeg :: Deg -> Deg

The identity function with a restricted type, for conveniently declaring that some value should have type Deg. For example, rotation . asDeg . fromIntegral constructs a rotation from an integral value considered as a value in degrees. Without asDeg, the angle type would be ambiguous.

fullTurn :: Angle a => a

An angle representing one full turn.

fullCircle :: Angle a => a

Deprecated synonym for fullTurn, retained for backwards compatibility.

convertAngle :: (Angle a, Angle b) => a -> b

Convert between two angle representations.

angleRatio :: Angle a => a -> a -> Double

Calculate ratio between two angles