Diagrams.ThreeD.Types

Basic types for three-dimensional Euclidean space.

3D Euclidean space

data R3

The three-dimensional Euclidean vector space R^3.

Instances

Eq R3

Ord R3

Read R3

Show R3

Transformable R3

HasCross3 R3

HasBasis R3

VectorSpace R3

InnerSpace R3

AdditiveGroup R3

HasZ P3

HasZ R3

HasY P3

HasY R3

HasX P3

HasX R3

Coordinates R3

Wrapped (Double, Double, Double) (Double, Double, Double) R3 R3

Lens wrapped isomorphisms for R3.

r3 :: (Double, Double, Double) -> R3

Construct a 3D vector from a triple of components.

unr3 :: R3 -> (Double, Double, Double)

Convert a 3D vector back into a triple of components.

mkR3 :: Double -> Double -> Double -> R3

Curried version of r3.

type P3 = Point R3

Points in R^3.

p3 :: (Double, Double, Double) -> P3

Construct a 3D point from a triple of coordinates.

unp3 :: P3 -> (Double, Double, Double)

Convert a 3D point back into a triple of coordinates.

mkP3 :: Double -> Double -> Double -> P3

Curried version of r3.

type T3 = Transformation R3

Transformations in R^3.

r3Iso :: Iso' R3 (Double, Double, Double)

p3Iso :: Iso' P3 (Double, Double, Double)

Two-dimensional angles

These are defined in Diagrams.TwoD.Types but reëxported here for convenience.

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.

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

Convert between two angle representations.

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

Calculate ratio between two angles

Directions in 3D

class Direction d where

Direction is a type class representing directions in R3. The interface is based on that of the Angle class in 2D.

Methods

toSpherical :: Angle a => d -> Spherical a

Convert to polar angles

fromSpherical :: Angle a => Spherical a -> d

Convert from polar angles

Instances

Angle a => Direction (Spherical a)

data Spherical a

A direction expressed as a pair of spherical coordinates. `Spherical 0 0` is the direction of unitX. The first coordinate represents rotation about the Z axis, the second rotation towards the Z axis.

Constructors

Spherical a a

Instances

Functor Spherical

Applicative Spherical

Eq a => Eq (Spherical a)

Read a => Read (Spherical a)

Show a => Show (Spherical a)

Angle a => Direction (Spherical a)

asSpherical :: Spherical Turn -> Spherical Turn

The identity function with a restricted type, for conveniently restricting unwanted polymorphism. For example, fromDirection . asSpherical . camForward gives a unit vector pointing in the direction of the camera view. Without asSpherical, the intermediate type would be ambiguous.