Copyright	(c) 2011 diagrams-lib team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	None
Language	Haskell2010

Diagrams.ThreeD.Types

Contents

3D Euclidean space
Two-dimensional angles
Directions in 3D

Description

Basic types for three-dimensional Euclidean space.

Synopsis

3D Euclidean space

data R3 Source

The three-dimensional Euclidean vector space R^3.

Instances

Eq R3
Ord R3
Read R3
Show R3
Transformable R3
Wrapped R3	Lens wrapped isomorphisms for 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
Rewrapped R3 R3
type V R3 = R3
type Unwrapped R3 = (Double, Double, Double)
type Basis R3 = Either () (Either () ())
type Scalar R3 = Double
type FinalCoord R3 = Double
type PrevDim R3 = R2
type Decomposition R3 = (:&) ((:&) Double Double) Double

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

Construct a 3D vector from a triple of components.

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

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

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

Curried version of r3.

type P3 = Point R3 Source

Points in R^3.

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

Construct a 3D point from a triple of coordinates.

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

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

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

Curried version of r3.

type T3 = Transformation R3 Source

Transformations in R^3.

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

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

Two-dimensional angles

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

data Angle Source

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
type Scalar Angle = Double

rad :: Iso' Angle Double 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 :: Iso' Angle Double 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 :: Iso' Angle Double 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.

(@@) :: b -> Iso' a b -> a infixl 5 Source

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.

fullTurn :: Angle Source

An angle representing one full turn.

angleRatio :: Angle -> Angle -> Double Source

Calculate ratio between two angles.

Directions in 3D

class Direction d where Source

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

Methods

toSpherical :: d -> Spherical Source

Convert to spherical coördinates

fromSpherical :: Spherical -> d Source

Convert from spherical coördinates

Instances

Direction Spherical

data Spherical Source

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 Angle Angle

Instances

Eq Spherical
Read Spherical
Show Spherical
Direction Spherical

asSpherical :: Spherical -> Spherical Source

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.