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

Methods

(>>=) :: V3 a -> (a -> V3 b) -> V3 b

(>>) :: V3 a -> V3 b -> V3 b

return :: a -> V3 a

fail :: String -> V3 a

Functor V3

Methods

fmap :: (a -> b) -> V3 a -> V3 b

(<$) :: a -> V3 b -> V3 a

MonadFix V3

Methods

mfix :: (a -> V3 a) -> V3 a

Applicative V3

Methods

pure :: a -> V3 a

(<*>) :: V3 (a -> b) -> V3 a -> V3 b

liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c

(*>) :: V3 a -> V3 b -> V3 b

(<*) :: V3 a -> V3 b -> V3 a

Foldable V3

Methods

fold :: Monoid m => V3 m -> m

foldMap :: Monoid m => (a -> m) -> V3 a -> m

foldr :: (a -> b -> b) -> b -> V3 a -> b

foldr' :: (a -> b -> b) -> b -> V3 a -> b

foldl :: (b -> a -> b) -> b -> V3 a -> b

foldl' :: (b -> a -> b) -> b -> V3 a -> b

foldr1 :: (a -> a -> a) -> V3 a -> a

foldl1 :: (a -> a -> a) -> V3 a -> a

toList :: V3 a -> [a]

null :: V3 a -> Bool

length :: V3 a -> Int

elem :: Eq a => a -> V3 a -> Bool

maximum :: Ord a => V3 a -> a

minimum :: Ord a => V3 a -> a

sum :: Num a => V3 a -> a

product :: Num a => V3 a -> a

Traversable V3

Methods

traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b)

sequenceA :: Applicative f => V3 (f a) -> f (V3 a)

mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b)

sequence :: Monad m => V3 (m a) -> m (V3 a)

Apply V3

Methods

(<.>) :: V3 (a -> b) -> V3 a -> V3 b

(.>) :: V3 a -> V3 b -> V3 b

(<.) :: V3 a -> V3 b -> V3 a

Distributive V3

Methods

distribute :: Functor f => f (V3 a) -> V3 (f a)

collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b)

distributeM :: Monad m => m (V3 a) -> V3 (m a)

collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b)

Representable V3

Associated Types

type Rep (V3 :: * -> *) :: *

Methods

tabulate :: (Rep V3 -> a) -> V3 a

index :: V3 a -> Rep V3 -> a

Eq1 V3

Methods

liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool

Ord1 V3

Methods

liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering

Read1 V3

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a]

Show1 V3

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS

MonadZip V3

Methods

mzip :: V3 a -> V3 b -> V3 (a, b)

mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c

munzip :: V3 (a, b) -> (V3 a, V3 b)

Serial1 V3

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m ()

deserializeWith :: MonadGet m => m a -> m (V3 a)

Additive V3

Methods

zero :: Num a => V3 a

(^+^) :: Num a => V3 a -> V3 a -> V3 a

(^-^) :: Num a => V3 a -> V3 a -> V3 a

lerp :: Num a => a -> V3 a -> V3 a -> V3 a

liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a

liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c

Traversable1 V3

Methods

traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b)

sequence1 :: Apply f => V3 (f b) -> f (V3 b)

Affine V3

Associated Types

type Diff (V3 :: * -> *) :: * -> *

Methods

(.-.) :: Num a => V3 a -> V3 a -> Diff V3 a

(.+^) :: Num a => V3 a -> Diff V3 a -> V3 a

(.-^) :: Num a => V3 a -> Diff V3 a -> V3 a

R3 V3

Methods

_z :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

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

R2 V3

Methods

_y :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

_xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a)

R1 V3

Methods

_x :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

Finite V3

Associated Types

type Size (V3 :: * -> *) :: Nat

Methods

toV :: V3 a -> V Nat (Size V3) a

fromV :: V Nat (Size V3) a -> V3 a

Metric V3

Methods

dot :: Num a => V3 a -> V3 a -> a

quadrance :: Num a => V3 a -> a

qd :: Num a => V3 a -> V3 a -> a

distance :: Floating a => V3 a -> V3 a -> a

norm :: Floating a => V3 a -> a

signorm :: Floating a => V3 a -> V3 a

Foldable1 V3

Methods

fold1 :: Semigroup m => V3 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m

toNonEmpty :: V3 a -> NonEmpty a

Bind V3

Methods

(>>-) :: V3 a -> (a -> V3 b) -> V3 b

join :: V3 (V3 a) -> V3 a

Unbox a => Vector Vector (V3 a)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a))

basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a))

basicLength :: Vector (V3 a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a)

basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m ()

elemseq :: Vector (V3 a) -> V3 a -> b -> b

Unbox a => MVector MVector (V3 a)

Methods

basicLength :: MVector s (V3 a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a)

basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a))

Bounded a => Bounded (V3 a)

Methods

minBound :: V3 a

maxBound :: V3 a

Eq a => Eq (V3 a)

Methods

(==) :: V3 a -> V3 a -> Bool

(/=) :: V3 a -> V3 a -> Bool

Floating a => Floating (V3 a)

Methods

pi :: V3 a

exp :: V3 a -> V3 a

log :: V3 a -> V3 a

sqrt :: V3 a -> V3 a

(**) :: V3 a -> V3 a -> V3 a

logBase :: V3 a -> V3 a -> V3 a

sin :: V3 a -> V3 a

cos :: V3 a -> V3 a

tan :: V3 a -> V3 a

asin :: V3 a -> V3 a

acos :: V3 a -> V3 a

atan :: V3 a -> V3 a

sinh :: V3 a -> V3 a

cosh :: V3 a -> V3 a

tanh :: V3 a -> V3 a

asinh :: V3 a -> V3 a

acosh :: V3 a -> V3 a

atanh :: V3 a -> V3 a

log1p :: V3 a -> V3 a

expm1 :: V3 a -> V3 a

log1pexp :: V3 a -> V3 a

log1mexp :: V3 a -> V3 a

Fractional a => Fractional (V3 a)

Methods

(/) :: V3 a -> V3 a -> V3 a

recip :: V3 a -> V3 a

fromRational :: Rational -> V3 a

Data a => Data (V3 a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a)

toConstr :: V3 a -> Constr

dataTypeOf :: V3 a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a))

gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r

gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a)

Num a => Num (V3 a)

Methods

(+) :: V3 a -> V3 a -> V3 a

(-) :: V3 a -> V3 a -> V3 a

(*) :: V3 a -> V3 a -> V3 a

negate :: V3 a -> V3 a

abs :: V3 a -> V3 a

signum :: V3 a -> V3 a

fromInteger :: Integer -> V3 a

Ord a => Ord (V3 a)

Methods

compare :: V3 a -> V3 a -> Ordering

(<) :: V3 a -> V3 a -> Bool

(<=) :: V3 a -> V3 a -> Bool

(>) :: V3 a -> V3 a -> Bool

(>=) :: V3 a -> V3 a -> Bool

max :: V3 a -> V3 a -> V3 a

min :: V3 a -> V3 a -> V3 a

Read a => Read (V3 a)

Methods

readsPrec :: Int -> ReadS (V3 a)

readList :: ReadS [V3 a]

readPrec :: ReadPrec (V3 a)

readListPrec :: ReadPrec [V3 a]

Show a => Show (V3 a)

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

Ix a => Ix (V3 a)

Methods

range :: (V3 a, V3 a) -> [V3 a]

index :: (V3 a, V3 a) -> V3 a -> Int

unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int

inRange :: (V3 a, V3 a) -> V3 a -> Bool

rangeSize :: (V3 a, V3 a) -> Int

unsafeRangeSize :: (V3 a, V3 a) -> Int

Generic (V3 a)

Associated Types

type Rep (V3 a) :: * -> *

Methods

from :: V3 a -> Rep (V3 a) x

to :: Rep (V3 a) x -> V3 a

Storable a => Storable (V3 a)

Methods

sizeOf :: V3 a -> Int

alignment :: V3 a -> Int

peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a)

pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (V3 a)

pokeByteOff :: Ptr b -> Int -> V3 a -> IO ()

peek :: Ptr (V3 a) -> IO (V3 a)

poke :: Ptr (V3 a) -> V3 a -> IO ()

Binary a => Binary (V3 a)

Methods

put :: V3 a -> Put

get :: Get (V3 a)

putList :: [V3 a] -> Put

Serial a => Serial (V3 a)

Methods

serialize :: MonadPut m => V3 a -> m ()

deserialize :: MonadGet m => m (V3 a)

Serialize a => Serialize (V3 a)

Methods

put :: Putter (V3 a)

get :: Get (V3 a)

NFData a => NFData (V3 a)

Methods

rnf :: V3 a -> ()

Hashable a => Hashable (V3 a)

Methods

hashWithSalt :: Int -> V3 a -> Int

hash :: V3 a -> Int

Unbox a => Unbox (V3 a)

Ixed (V3 a)

Methods

ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a))

Epsilon a => Epsilon (V3 a)

Methods

nearZero :: V3 a -> Bool

Coordinates (V3 n)

Associated Types

type FinalCoord (V3 n) :: *

type PrevDim (V3 n) :: *

type Decomposition (V3 n) :: *

Methods

(^&) :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n

pr :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n

coords :: V3 n -> Decomposition (V3 n)

Generic1 * V3

Associated Types

type Rep1 V3 (f :: V3 -> *) :: k -> *

Methods

from1 :: f a -> Rep1 V3 f a

to1 :: Rep1 V3 f a -> f a

FunctorWithIndex (E V3) V3

Methods

imap :: (E V3 -> a -> b) -> V3 a -> V3 b

imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b)

FoldableWithIndex (E V3) V3

Methods

ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m

ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a)

ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b

ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b

ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b

ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b

TraversableWithIndex (E V3) V3

Methods

itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b)

itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b)

Each (V3 a) (V3 b) a b

Methods

each :: Traversal (V3 a) (V3 b) a b

TypeableFloat n => Traced (BoundingBox V3 n)

Methods

getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n))

type Rep V3

type Rep V3 = E V3

type Diff V3

type Diff V3 = V3

type Size V3

type Size V3 = 3

data MVector s (V3 a)

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

type Rep (V3 a)

type Rep (V3 a) = D1 * (MetaData "V3" "Linear.V3" "linear-1.20.7-BqPvIjWzrIe27Hr7QGo0u0" False) (C1 * (MetaCons "V3" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * a)))))

type V (V3 n)

type V (V3 n) = V3

type N (V3 n)

type N (V3 n) = n

data Vector (V3 a)

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

type Index (V3 a)

type Index (V3 a) = E V3

type IxValue (V3 a)

type IxValue (V3 a) = a

type FinalCoord (V3 n)

type FinalCoord (V3 n) = n

type PrevDim (V3 n)

type PrevDim (V3 n) = V2 n

type Decomposition (V3 n)

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

type Rep1 * V3

type Rep1 * V3 = D1 * (MetaData "V3" "Linear.V3" "linear-1.20.7-BqPvIjWzrIe27Hr7QGo0u0" False) (C1 * (MetaCons "V3" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))))

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

_x

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

Methods

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

R1 V4

Methods

_x :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

R1 V3

Methods

_x :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

R1 V2

Methods

_x :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

R1 V1

Methods

_x :: Functor f => (a -> f a) -> V1 a -> f (V1 a)

R1 f => R1 (Point f)

Methods

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

class R1 t => R2 (t :: * -> *) where

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

Minimal complete definition

_xy

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

Methods

_y :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

_xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 a)

R2 V3

Methods

_y :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

_xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a)

R2 V2

Methods

_y :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

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

R2 f => R2 (Point f)

Methods

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

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

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

_z, _xyz

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

Methods

_z :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

_xyz :: Functor f => (V3 a -> f (V3 a)) -> V4 a -> f (V4 a)

R3 V3

Methods

_z :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

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

R3 f => R3 (Point f)

Methods

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

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

Orphan instances

HasPhi V3

Methods

_phi :: RealFloat n => Lens' (V3 n) (Angle n)

HasTheta V3

Methods

_theta :: RealFloat n => Lens' (V3 n) (Angle n)

HasR V3

Methods

_r :: RealFloat n => Lens' (V3 n) n

Transformable (V3 n)

Methods

transform :: Transformation (V (V3 n)) (N (V3 n)) -> V3 n -> V3 n