Safe Haskell	None
Language	Haskell2010

Physics.Linear

Description

Arithmetic utility functions for vectors and matrices.

Synopsis

Documentation

data V2 Source #

Constructors

V2 Double# Double#

Instances

Show V2 Source #
Methods showsPrec :: Int -> V2 -> ShowS # show :: V2 -> String # showList :: [V2] -> ShowS #
Arbitrary V2 Source #
Methods arbitrary :: Gen V2 # shrink :: V2 -> [V2] #
NFData V2 Source #
Methods rnf :: V2 -> () #
Unbox V2 Source #

WorldTransformable V2 Source #
Methods transform :: WorldTransform -> V2 -> V2 Source # untransform :: WorldTransform -> V2 -> V2 Source # wExtract :: LocalT V2 -> WorldT V2 Source # wExtract_ :: LocalT V2 -> V2 Source # wInject :: WorldTransform -> WorldT V2 -> LocalT V2 Source # wInject_ :: WorldTransform -> V2 -> V2 Source #
Vector Vector V2 Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) V2 -> m (Vector V2) # basicUnsafeThaw :: PrimMonad m => Vector V2 -> m (Mutable Vector (PrimState m) V2) # basicLength :: Vector V2 -> Int # basicUnsafeSlice :: Int -> Int -> Vector V2 -> Vector V2 # basicUnsafeIndexM :: Monad m => Vector V2 -> Int -> m V2 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) V2 -> Vector V2 -> m () # elemseq :: Vector V2 -> V2 -> b -> b #
MVector MVector V2 Source #
Methods basicLength :: MVector s V2 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s V2 -> MVector s V2 # basicOverlaps :: MVector s V2 -> MVector s V2 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) V2) # basicInitialize :: PrimMonad m => MVector (PrimState m) V2 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V2 -> m (MVector (PrimState m) V2) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) V2 -> Int -> m V2 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) V2 -> Int -> V2 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) V2 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) V2 -> V2 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) V2 -> MVector (PrimState m) V2 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) V2 -> MVector (PrimState m) V2 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) V2 -> Int -> m (MVector (PrimState m) V2) #
data Vector V2 Source #
data Vector V2 = V_V2 (Vector (Double, Double))
data MVector s V2 Source #
data MVector s V2 = MV_V2 (MVector s (Double, Double))

toListV2 :: V2 -> [Double] Source #

fromListV2 :: [Double] -> V2 Source #

dotV2 :: V2 -> V2 -> Double# Source #

lift2V2 :: (Double# -> Double# -> Double#) -> V2 -> V2 -> V2 Source #

liftV2 :: (Double# -> Double#) -> V2 -> V2 Source #

data V3 Source #

Constructors

V3 Double# Double# Double#

Instances

Show V3 Source #
Methods showsPrec :: Int -> V3 -> ShowS # show :: V3 -> String # showList :: [V3] -> ShowS #
Arbitrary V3 Source #
Methods arbitrary :: Gen V3 # shrink :: V3 -> [V3] #

toListV3 :: V3 -> [Double] Source #

fromListV3 :: [Double] -> V3 Source #

dotV3 :: V3 -> V3 -> Double# Source #

lift2V3 :: (Double# -> Double# -> Double#) -> V3 -> V3 -> V3 Source #

liftV3 :: (Double# -> Double#) -> V3 -> V3 Source #

data V6 Source #

Constructors

V6 Double# Double# Double# Double# Double# Double#

Instances

Show V6 Source #
Methods showsPrec :: Int -> V6 -> ShowS # show :: V6 -> String # showList :: [V6] -> ShowS #
Arbitrary V6 Source #
Methods arbitrary :: Gen V6 # shrink :: V6 -> [V6] #
Unbox V6 Source #

Vector Vector V6 Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) V6 -> m (Vector V6) # basicUnsafeThaw :: PrimMonad m => Vector V6 -> m (Mutable Vector (PrimState m) V6) # basicLength :: Vector V6 -> Int # basicUnsafeSlice :: Int -> Int -> Vector V6 -> Vector V6 # basicUnsafeIndexM :: Monad m => Vector V6 -> Int -> m V6 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) V6 -> Vector V6 -> m () # elemseq :: Vector V6 -> V6 -> b -> b #
MVector MVector V6 Source #
Methods basicLength :: MVector s V6 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s V6 -> MVector s V6 # basicOverlaps :: MVector s V6 -> MVector s V6 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) V6) # basicInitialize :: PrimMonad m => MVector (PrimState m) V6 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V6 -> m (MVector (PrimState m) V6) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) V6 -> Int -> m V6 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) V6 -> Int -> V6 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) V6 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) V6 -> V6 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) V6 -> MVector (PrimState m) V6 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) V6 -> MVector (PrimState m) V6 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) V6 -> Int -> m (MVector (PrimState m) V6) #
data Vector V6 Source #
data Vector V6 = V_V6 (Vector (Double, Double, Double, Double, Double, Double))
data MVector s V6 Source #
data MVector s V6 = MV_V6 (MVector s (Double, Double, Double, Double, Double, Double))

toListV6 :: V6 -> [Double] Source #

fromListV6 :: [Double] -> V6 Source #

dotV6 :: V6 -> V6 -> Double# Source #

lift2V6 :: (Double# -> Double# -> Double#) -> V6 -> V6 -> V6 Source #

liftV6 :: (Double# -> Double#) -> V6 -> V6 Source #

data M2x2 Source #

Constructors

M2x2 Double# Double# Double# Double#

Instances

Show M2x2 Source #
Methods showsPrec :: Int -> M2x2 -> ShowS # show :: M2x2 -> String # showList :: [M2x2] -> ShowS #
Arbitrary M2x2 Source #
Methods arbitrary :: Gen M2x2 # shrink :: M2x2 -> [M2x2] #

mulT2x2 :: V2 -> V2 -> M2x2 Source #

mul2x2d :: M2x2 -> V2 -> M2x2 Source #

muld2x2 :: V2 -> M2x2 -> M2x2 Source #

mulr2x2 :: V2 -> M2x2 -> V2 Source #

mul2x2c :: M2x2 -> V2 -> V2 Source #

toListM2x2 :: M2x2 -> [Double] Source #

fromListM2x2 :: [Double] -> M2x2 Source #

lift2M2x2 :: (Double# -> Double# -> Double#) -> M2x2 -> M2x2 -> M2x2 Source #

liftM2x2 :: (Double# -> Double#) -> M2x2 -> M2x2 Source #

data M3x3 Source #

Constructors

M3x3 Double# Double# Double# Double# Double# Double# Double# Double# Double#

Instances

Show M3x3 Source #
Methods showsPrec :: Int -> M3x3 -> ShowS # show :: M3x3 -> String # showList :: [M3x3] -> ShowS #
Arbitrary M3x3 Source #
Methods arbitrary :: Gen M3x3 # shrink :: M3x3 -> [M3x3] #

mulT3x3 :: V3 -> V3 -> M3x3 Source #

mul3x3d :: M3x3 -> V3 -> M3x3 Source #

muld3x3 :: V3 -> M3x3 -> M3x3 Source #

mulr3x3 :: V3 -> M3x3 -> V3 Source #

mul3x3c :: M3x3 -> V3 -> V3 Source #

toListM3x3 :: M3x3 -> [Double] Source #

fromListM3x3 :: [Double] -> M3x3 Source #

lift2M3x3 :: (Double# -> Double# -> Double#) -> M3x3 -> M3x3 -> M3x3 Source #

liftM3x3 :: (Double# -> Double#) -> M3x3 -> M3x3 Source #

data M6x6 Source #

Instances

Show M6x6 Source #
Methods showsPrec :: Int -> M6x6 -> ShowS # show :: M6x6 -> String # showList :: [M6x6] -> ShowS #
Arbitrary M6x6 Source #
Methods arbitrary :: Gen M6x6 # shrink :: M6x6 -> [M6x6] #

mulT6x6 :: V6 -> V6 -> M6x6 Source #

mul6x6d :: M6x6 -> V6 -> M6x6 Source #

muld6x6 :: V6 -> M6x6 -> M6x6 Source #

mulr6x6 :: V6 -> M6x6 -> V6 Source #

mul6x6c :: M6x6 -> V6 -> V6 Source #

toListM6x6 :: M6x6 -> [Double] Source #

fromListM6x6 :: [Double] -> M6x6 Source #

lift2M6x6 :: (Double# -> Double# -> Double#) -> M6x6 -> M6x6 -> M6x6 Source #

liftM6x6 :: (Double# -> Double#) -> M6x6 -> M6x6 Source #

mul2x2x2 :: M2x2 -> M2x2 -> M2x2 Source #

mul3x3x3 :: M3x3 -> M3x3 -> M3x3 Source #

split3v3 :: V6 -> (V3, V3) Source #

join3v3 :: V3 -> V3 -> V6 Source #

newtype Diag6 Source #

Constructors

Diag6 V6

Instances

Show Diag6 Source #
Methods showsPrec :: Int -> Diag6 -> ShowS # show :: Diag6 -> String # showList :: [Diag6] -> ShowS #

newtype P2 Source #

Constructors

P2 V2

Instances

Show P2 Source #
Methods showsPrec :: Int -> P2 -> ShowS # show :: P2 -> String # showList :: [P2] -> ShowS #
Generic P2 Source #
Associated Types type Rep P2 :: * -> * # Methods from :: P2 -> Rep P2 x # to :: Rep P2 x -> P2 #
NFData P2 Source #
Methods rnf :: P2 -> () #
Unbox P2 Source #

WorldTransformable P2 Source #
Methods transform :: WorldTransform -> P2 -> P2 Source # untransform :: WorldTransform -> P2 -> P2 Source # wExtract :: LocalT P2 -> WorldT P2 Source # wExtract_ :: LocalT P2 -> P2 Source # wInject :: WorldTransform -> WorldT P2 -> LocalT P2 Source # wInject_ :: WorldTransform -> P2 -> P2 Source #
Vector Vector P2 Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) P2 -> m (Vector P2) # basicUnsafeThaw :: PrimMonad m => Vector P2 -> m (Mutable Vector (PrimState m) P2) # basicLength :: Vector P2 -> Int # basicUnsafeSlice :: Int -> Int -> Vector P2 -> Vector P2 # basicUnsafeIndexM :: Monad m => Vector P2 -> Int -> m P2 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) P2 -> Vector P2 -> m () # elemseq :: Vector P2 -> P2 -> b -> b #
MVector MVector P2 Source #
Methods basicLength :: MVector s P2 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s P2 -> MVector s P2 # basicOverlaps :: MVector s P2 -> MVector s P2 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) P2) # basicInitialize :: PrimMonad m => MVector (PrimState m) P2 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> P2 -> m (MVector (PrimState m) P2) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) P2 -> Int -> m P2 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) P2 -> Int -> P2 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) P2 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) P2 -> P2 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) P2 -> MVector (PrimState m) P2 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) P2 -> MVector (PrimState m) P2 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) P2 -> Int -> m (MVector (PrimState m) P2) #
type Rep P2 Source #
type Rep P2 = D1 * (MetaData "P2" "Physics.Linear" "shapes-0.1.0.0-E6UUiYRpOc15rGTlEn6KOE" True) (C1 * (MetaCons "P2" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * V2)))
data Vector P2 Source #
data Vector P2 = V_P2 (Vector V2)
data MVector s P2 Source #
data MVector s P2 = MV_P2 (MVector s V2)

append2 :: V2 -> Double -> V3 Source #

split3 :: V3 -> (V2, Double) Source #

smulV2 :: Double -> V2 -> V2 Source #

smulV2' :: V2 -> Double -> V2 Source #

sdivV2 :: Double -> V2 -> V2 Source #

smulV6 :: Double -> V6 -> V6 Source #

smulV6' :: V6 -> Double -> V6 Source #

smulM2x2 :: Double -> M2x2 -> M2x2 Source #

smulM2x2' :: M2x2 -> Double -> M2x2 Source #

plusV2 :: V2 -> V2 -> V2 Source #

plusV6 :: V6 -> V6 -> V6 Source #

zeroV2 :: V2 Source #

zeroP2 :: P2 Source #

minusV2 :: V2 -> V2 -> V2 Source #

crossV2 :: V2 -> V2 -> Double Source #

crosszV2 :: V2 -> Double -> V2 Source #

zcrossV2 :: Double -> V2 -> V2 Source #

unitV2 :: Double -> V2 Source #

crossV2V2 :: V2 -> V2 -> V2 -> V2 Source #

vmulDiag6 :: V6 -> Diag6 -> V6 Source #

vmulDiag6' :: Diag6 -> V6 -> V6 Source #

flip3v3 :: V6 -> V6 Source #

afdot :: P2 -> V2 -> Double Source #

afdot' :: V2 -> P2 -> Double Source #

clockwiseV2 :: V2 -> V2 Source #

normalizeV2 :: V2 -> V2 Source #

lengthV2 :: V2 -> Double Source #

Length of a vector.

sqLengthV2 :: V2 -> Double Source #

Squared length of a vector.

diffP2 :: P2 -> P2 -> V2 Source #

midpointP2 :: P2 -> P2 -> P2 Source #

vplusP2 :: V2 -> P2 -> P2 Source #

pminusV2 :: P2 -> V2 -> P2 Source #

pplusV2 :: P2 -> V2 -> P2 Source #

invM2x2 :: M2x2 -> M2x2 Source #

negateV2 :: V2 -> V2 Source #

identity2x2 :: M2x2 Source #

identity3x3 :: M3x3 Source #

afmul :: M3x3 -> V2 -> V2 Source #

afmul' :: M3x3 -> P2 -> P2 Source #

data Line2 Source #

Constructors

Line2
Fields linePoint :: !P2 lineNormal :: !V2

toLine2 :: P2 -> P2 -> Line2 Source #

perpLine2 :: P2 -> P2 -> Line2 Source #

intersect2 :: Line2 -> Line2 -> P2 Source #

data ClipResult a Source #

Constructors

ClipLeft !a	clip the left side to this new endpoint
ClipRight !a	clip the right side to this new endpoint
ClipBoth !a	the entire segment was out-of-bounds
ClipNone	the entire segment was in-bounds

applyClip :: ClipResult a -> SP a a -> Either a (SP a a) Source #

Apply a ClipResult to a line segment. Replaces clipped endpoints. If both endpoints (entire segment) clipped, use Lefted clip point.

TODO: Delete this function?

applyClip' :: ClipResult a -> SP a a -> Maybe (SP a a) Source #

Alternate form of applyClip. Nothing if entire segment clipped.

applyClip'' :: ClipResult a -> SP s s -> Maybe (Either s (SP s s)) Source #

Alternate form of applyClip. Removes clipped points.

lApplyClip Source #

Arguments

:: ASetter' s a	lens to access the "point" data to apply the clipping
-> ClipResult a	clipping
-> SP s s	line segment with endpoints that contain "point" data
-> Either s (SP s s)

Alternate form of applyClip. Applies clipping using the given lens.

If ClipBoth, then use only the first vertex of the line segment and change it to use the clipping point. (TODO: Why?)

TODO: Delete this function?

lApplyClip' :: ASetter' s a -> ClipResult a -> SP s s -> Maybe (SP s s) Source #

Alternate form of lApplyClip. If the entire segment was behind the bound, use Nothing.

clipSegment Source #

Arguments

:: Line2	bounding plane
-> SP Line2 (SP P2 P2)	(plane of the line segment, endpoints of the line segment)
-> ClipResult P2	which endpoint(s) to clip, and what point to clip to

Given a bounding plane (expressed as a point and a normal), figure out how to clip a line segment so it is on the positive side of the plane.

rotate22_ :: Double# -> Double# -> M2x2 Source #

rotate22 :: Double# -> M2x2 Source #

afmat33 :: M2x2 -> M3x3 Source #

aftranslate33 :: V2 -> M3x3 Source #

afrotate33 :: Double# -> M3x3 Source #

afscale33 :: V2 -> M3x3 Source #