Copyright | (c) 2013 diagrams-lib team (see LICENSE) |
---|---|

License | BSD-style (see LICENSE) |

Maintainer | diagrams-discuss@googlegroups.com |

Safe Haskell | None |

Language | Haskell2010 |

Type for representing angles.

## Synopsis

- data Angle n
- (@@) :: b -> AReview a b -> a
- rad :: Iso' (Angle n) n
- turn :: Floating n => Iso' (Angle n) n
- deg :: Floating n => Iso' (Angle n) n
- fullTurn :: Floating v => Angle v
- halfTurn :: Floating v => Angle v
- quarterTurn :: Floating v => Angle v
- sinA :: Floating n => Angle n -> n
- cosA :: Floating n => Angle n -> n
- tanA :: Floating n => Angle n -> n
- asinA :: Floating n => n -> Angle n
- acosA :: Floating n => n -> Angle n
- atanA :: Floating n => n -> Angle n
- atan2A :: RealFloat n => n -> n -> Angle n
- atan2A' :: OrderedField n => n -> n -> Angle n
- angleBetween :: (Metric v, Floating n, Ord n) => v n -> v n -> Angle n
- angleRatio :: Floating n => Angle n -> Angle n -> n
- normalizeAngle :: (Floating n, Real n) => Angle n -> Angle n
- class HasTheta t where
- class HasTheta t => HasPhi t where
- rotation :: Floating n => Angle n -> Transformation V2 n
- rotate :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t

# Angle type

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

## Instances

Functor Angle # | |

Applicative Angle # | |

Additive Angle # | |

Defined in Diagrams.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) # | |

(V t ~ V2, N t ~ n, Transformable t, Floating n) => Action (Angle n) t # | Angles act on other things by rotation. |

Defined in Diagrams.Angle | |

type N (Angle n) # | |

Defined in Diagrams.Angle |

## Using angles

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

`30 @@ deg`

is an `Angle`

of the given measure and units.

`>>>`

3.141592653589793 @@ rad`pi @@ rad`

`>>>`

6.283185307179586 @@ rad`1 @@ turn`

`>>>`

0.5235987755982988 @@ rad`30 @@ deg`

For `Iso'`

s, (`@@`

) reverses the `Iso'`

on its right, and applies
the `Iso'`

to the value on the left. `Angle`

s 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

## Common angles

quarterTurn :: Floating v => Angle v #

An angle representing a quarter turn.

## Trigonometric functions

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

`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 #

## Angle utilities

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

Compute the positive angle between the two vectors in their common
plane in the [0,pi] range. For a signed angle see
`signedAngleBetween`

.

Returns NaN if either of the vectors are zero.

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

Calculate ratio between two angles.

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

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

## Classes

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

.

class HasTheta t => HasPhi t where #

The class of types with at least two angle coordinates, the second called
`_phi`

. `_phi`

is the positive angle measured from the z axis.

# Rotation

rotation :: Floating n => Angle n -> Transformation V2 n #

Create a transformation which performs a rotation about the local
origin by the given angle. See also `rotate`

.

rotate :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t #

Rotate about the local origin by the given angle. Positive angles
correspond to counterclockwise rotation, negative to
clockwise. The angle can be expressed using any of the `Iso`

s on
`Angle`

. For example, `rotate (1/4 @@ `

, `turn`

)```
rotate
(tau/4 @@ rad)
```

, and `rotate (90 @@ deg)`

all
represent the same transformation, namely, a counterclockwise
rotation by a right angle. To rotate about some point other than
the local origin, see `rotateAbout`

.

Note that writing `rotate (1/4)`

, with no `Angle`

constructor,
will yield an error since GHC cannot figure out which sort of
angle you want to use. In this common situation you can use
`rotateBy`

, which interprets its argument as a number of turns.