Diagrams.ThreeD.Types

Basic types for three-dimensional Euclidean space.

3D Euclidean space

r3 :: (n, n, n) -> V3 n

Construct a 3D vector from a triple of components.

unr3 :: V3 n -> (n, n, n)

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

mkR3 :: n -> n -> n -> V3 n

Curried version of r3.

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

Construct a 3D point from a triple of coordinates.

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

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

mkP3 :: n -> n -> n -> P3 n

Curried version of r3.

r3Iso :: Iso' (V3 n) (n, n, n)

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

project :: (Metric v, Fractional a) => v a -> v a -> v a

project u v computes the projection of v onto u.

r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n)

r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n)

data V3 a :: * -> *

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Monad V3

Functor V3

MonadFix V3

Applicative V3

Foldable V3

Traversable V3

Generic1 V3

Apply V3

Distributive V3

Representable V3

MonadZip V3

Serial1 V3

Additive V3

Traversable1 V3

Affine V3

R3 V3

R2 V3

R1 V3

Metric V3

Bind V3

Foldable1 V3

Eq1 V3

Ord1 V3

Read1 V3

Show1 V3

Unbox a => Vector Vector (V3 a)

Unbox a => MVector MVector (V3 a)

Bounded a => Bounded (V3 a)

Eq a => Eq (V3 a)

Floating a => Floating (V3 a)

Fractional a => Fractional (V3 a)

Data a => Data (V3 a)

Num a => Num (V3 a)

Ord a => Ord (V3 a)

Read a => Read (V3 a)

Show a => Show (V3 a)

Ix a => Ix (V3 a)

Generic (V3 a)

Storable a => Storable (V3 a)

Binary a => Binary (V3 a)

Serial a => Serial (V3 a)

Serialize a => Serialize (V3 a)

NFData a => NFData (V3 a)

Hashable a => Hashable (V3 a)

Unbox a => Unbox (V3 a)

Ixed (V3 a)

Epsilon a => Epsilon (V3 a)

Coordinates (V3 n)

FunctorWithIndex (E V3) V3

FoldableWithIndex (E V3) V3

TraversableWithIndex (E V3) V3

Each (V3 a) (V3 b) a b

TypeableFloat n => Traced (BoundingBox V3 n)

type Rep1 V3 = D1 D1V3 (C1 C1_0V3 ((:*:) (S1 NoSelector Par1) ((:*:) (S1 NoSelector Par1) (S1 NoSelector Par1))))

type Rep V3 = E V3

type Diff V3 = V3

data MVector s (V3 a) = MV_V3 !Int !(MVector s a)

type Rep (V3 a) = D1 D1V3 (C1 C1_0V3 ((:*:) (S1 NoSelector (Rec0 a)) ((:*:) (S1 NoSelector (Rec0 a)) (S1 NoSelector (Rec0 a)))))

type V (V3 n) = V3

type N (V3 n) = n

data Vector (V3 a) = V_V3 !Int !(Vector a)

type Index (V3 a) = E V3

type IxValue (V3 a) = a

type FinalCoord (V3 n) = n

type PrevDim (V3 n) = V2 n

type Decomposition (V3 n) = (:&) ((:&) n n) n

type P3 = Point V3

type T3 = Transformation V3

class R1 t where

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Methods

_x :: Functor f => (a -> f a) -> t a -> f (t a)

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

R1 Identity

R1 V4

R1 V3

R1 V2

R1 V1

R1 f => R1 (Point f)

class R1 t => R2 t where

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

Nothing

Methods

_y :: Functor f => (a -> f a) -> t a -> f (t a)

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a)

Instances

R2 V4

R2 V3

R2 V2

R2 f => R2 (Point f)

class R2 t => R3 t where

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Minimal complete definition

Nothing

Methods

_z :: Functor f => (a -> f a) -> t a -> f (t a)

>>> V3 1 2 3 ^. _z
3

_xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)

Instances

R3 V4

R3 V3

R3 f => R3 (Point f)