diagrams-lib-1.3: Embedded domain-specific language for declarative graphics

Copyright(c) 2013 diagrams-lib team (see LICENSE)
LicenseBSD-style (see LICENSE)
Maintainerdiagrams-discuss@googlegroups.com
Safe HaskellNone
LanguageHaskell2010

Diagrams.Angle

Contents

Description

Type for representing angles.

Synopsis

Angle type

data Angle n Source

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

Instances

Functor Angle 
Applicative Angle 
Additive Angle 
Enum n => Enum (Angle n) 
Eq n => Eq (Angle n) 
Ord n => Ord (Angle n) 
Read n => Read (Angle n) 
Show n => Show (Angle n) 
Num n => Semigroup (Angle n) 
Num n => Monoid (Angle n) 
type N (Angle n) = n 

Using angles

(@@) :: b -> AReview a b -> a infixl 5 Source

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

>>> pi @@ rad
3.141592653589793 @@ rad

>>> 1 @@ turn
6.283185307179586 @@ rad

>>> 30 @@ deg
0.5235987755982988 @@ rad

For Iso's, (@@) 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.

This is the same as a flipped review.

(@@) :: a -> Iso'      s a -> s
(@@) :: a -> Prism'    s a -> s
(@@) :: a -> Review    s a -> s
(@@) :: a -> Equality' s a -> s

rad :: Iso' (Angle n) n Source

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 :: Floating n => Iso' (Angle n) n Source

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 :: Floating n => Iso' (Angle n) n Source

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

Common angles

fullTurn :: Floating v => Angle v Source

An angle representing one full turn.

halfTurn :: Floating v => Angle v Source

An angle representing a half turn.

quarterTurn :: Floating v => Angle v Source

An angle representing a quarter turn.

Trigonometric functions

sinA :: Floating n => Angle n -> n Source

The sine of the given Angle.

cosA :: Floating n => Angle n -> n Source

The cosine of the given Angle.

tanA :: Floating n => Angle n -> n Source

The tangent function of the given Angle.

asinA :: Floating n => n -> Angle n Source

The Angle with the given sine.

acosA :: Floating n => n -> Angle n Source

The Angle with the given cosine.

atanA :: Floating n => n -> Angle n Source

The Angle with the given tangent.

atan2A :: RealFloat n => n -> n -> Angle n Source

atan2A y x is the angle between the positive x-axis and the vector given by the coordinates (x, y). The Angle returned is in the [-pi,pi] range.

atan2A' :: OrderedField n => n -> n -> Angle n Source

Similar to atan2A but without the RealFloat constraint. This means it doesn't handle negative zero cases. However, for most geometric purposes, the outcome will be the same.

Angle utilities

angleBetween :: (Metric v, Floating n) => v n -> v n -> Angle n Source

Compute the positive angle between the two vectors in their common plane. Returns NaN if either of the vectors are zero.

angleRatio :: Floating n => Angle n -> Angle n -> n Source

Calculate ratio between two angles.

normalizeAngle :: (Floating n, Real n) => Angle n -> Angle n Source

Normalize an angle so that it lies in the [0,tau) range.

Classes

class HasTheta t where Source

The class of types with at least one angle coordinate, called _theta.

Minimal complete definition

Nothing

Methods

_theta :: RealFloat n => Lens' (t n) (Angle n) Source

Instances

class HasTheta t => HasPhi t where Source

The class of types with at least two angle coordinates, the second called _phi. _phi is the positive angle measured from the z axis.

Minimal complete definition

Nothing

Methods

_phi :: RealFloat n => Lens' (t n) (Angle n) Source

Instances