#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
#endif
module SpatialMath ( Euler(..)
, rotateXyzAboutX
, rotateXyzAboutY
, rotateXyzAboutZ
, euler321OfQuat
, euler321OfDcm
, quatOfEuler321
, dcmOfQuat
, dcmOfQuatB2A
, dcmOfEuler321
, quatOfDcm
, quatOfDcmB2A
, rotVecByDcm
, rotVecByDcmB2A
, rotVecByQuat
, rotVecByQuatB2A
, rotVecByEuler
, rotVecByEulerB2A
, M33
, V3(..)
, Quaternion(..)
) where
import Data.Data ( Data )
import Data.Foldable ( Foldable )
import Data.Traversable ( Traversable )
import Data.Typeable ( Typeable1 )
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
import GHC.Generics (Generic)
#endif
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706
import GHC.Generics (Generic1)
#endif
import Linear
normalize' :: Floating a => Quaternion a -> Quaternion a
normalize' q = fmap (* normInv) q
where
normInv = 1/(norm q)
data Euler a = Euler { eYaw :: a
, ePitch :: a
, eRoll :: a
} deriving (Eq, Show, Functor, Foldable, Traversable, Ord
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
, Generic
#endif
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706
, Generic1
#endif
)
deriving instance Typeable1 Euler
deriving instance Data a => Data (Euler a)
rotateXyzAboutX :: Floating a => V3 a -> a -> V3 a
rotateXyzAboutX (V3 ax ay az) rotAngle = V3 bx by bz
where
cosTheta = cos rotAngle
sinTheta = sin rotAngle
bx = ax
by = ay*cosTheta az*sinTheta
bz = ay*sinTheta + az*cosTheta
rotateXyzAboutY :: Floating a => V3 a -> a -> V3 a
rotateXyzAboutY (V3 ax ay az) rotAngle = V3 bx by bz
where
cosTheta = cos rotAngle
sinTheta = sin rotAngle
bx = ax*cosTheta + az*sinTheta
by = ay
bz = ax*sinTheta + az*cosTheta
rotateXyzAboutZ :: Floating a => V3 a -> a -> V3 a
rotateXyzAboutZ (V3 ax ay az) rotAngle = V3 bx by bz
where
cosTheta = cos rotAngle
sinTheta = sin rotAngle
bx = ax*cosTheta ay*sinTheta
by = ax*sinTheta + ay*cosTheta
bz = az
euler321OfQuat :: RealFloat a => Quaternion a -> Euler a
euler321OfQuat (Quaternion q0 (V3 q1 q2 q3)) = Euler yaw pitch roll
where
r11 = q0*q0 + q1*q1 q2*q2 q3*q3
r12 = 2.0*(q1*q2 + q0*q3)
mr13' = 2.0*(q1*q3 q0*q2)
mr13
| mr13' > 1 = 1
| mr13' < 1 = 1
| otherwise = mr13'
r23 = 2.0*(q2*q3 + q0*q1)
r33 = q0*q0 q1*q1 q2*q2 + q3*q3
yaw = atan2 r12 r11
pitch = asin mr13
roll = atan2 r23 r33
quatOfDcm :: RealFloat a => M33 a -> Quaternion a
quatOfDcm = quatOfEuler321 . euler321OfDcm
quatOfDcmB2A :: (Conjugate a, RealFloat a) => M33 a -> Quaternion a
quatOfDcmB2A = conjugate . quatOfDcm
euler321OfDcm :: RealFloat a => M33 a -> Euler a
euler321OfDcm
(V3
(V3 r11 r12 r13)
(V3 _ _ r23)
(V3 _ _ r33)) = Euler yaw pitch roll
where
mr13' = r13
mr13
| mr13' > 1 = 1
| mr13' < 1 = 1
| otherwise = mr13'
yaw = atan2 r12 r11
pitch = asin mr13
roll = atan2 r23 r33
quatOfEuler321 :: (Floating a, Ord a) => Euler a -> Quaternion a
quatOfEuler321 (Euler yaw pitch roll) = normalize' q
where
sr2 = sin $ 0.5*roll
cr2 = cos $ 0.5*roll
sp2 = sin $ 0.5*pitch
cp2 = cos $ 0.5*pitch
sy2 = sin $ 0.5*yaw
cy2 = cos $ 0.5*yaw
q0 = cr2*cp2*cy2 + sr2*sp2*sy2
q1 = sr2*cp2*cy2 cr2*sp2*sy2
q2 = cr2*sp2*cy2 + sr2*cp2*sy2
q3 = cr2*cp2*sy2 sr2*sp2*cy2
q' = Quaternion q0 (V3 q1 q2 q3)
q
| q0 < 0 = Quaternion (q0) (V3 (q1) (q2) (q3))
| otherwise = q'
dcmOfQuat :: Num a => Quaternion a -> M33 a
dcmOfQuat (Quaternion q0 (V3 q1 q2 q3)) = V3 (V3 r0 r1 r2)
(V3 r3 r4 r5)
(V3 r6 r7 r8)
where
r0 = q0*q0 + q1*q1 q2*q2 q3*q3
r3 = 2*(q1*q2 q0*q3)
r6 = 2*(q1*q3 + q0*q2)
r1 = 2*(q1*q2 + q0*q3)
r4 = q0*q0 q1*q1 + q2*q2 q3*q3
r7 = 2*(q2*q3 q0*q1)
r2 = 2*(q1*q3 q0*q2)
r5 = 2*(q2*q3 + q0*q1)
r8 = q0*q0 q1*q1 q2*q2 + q3*q3
dcmOfEuler321 :: (Floating a, Ord a) => Euler a -> M33 a
dcmOfEuler321 = dcmOfQuat . quatOfEuler321
dcmOfQuatB2A :: (Conjugate a, RealFloat a) => Quaternion a -> M33 a
dcmOfQuatB2A = dcmOfQuat . conjugate
rotVecByDcm :: Num a => M33 a -> V3 a -> V3 a
rotVecByDcm dcm vec = dcm !* vec
rotVecByDcmB2A :: Num a => M33 a -> V3 a -> V3 a
rotVecByDcmB2A dcm vec = vec *! dcm
rotVecByQuat :: Num a => Quaternion a -> V3 a -> V3 a
rotVecByQuat q = rotVecByDcm (dcmOfQuat q)
rotVecByQuatB2A :: Num a => Quaternion a -> V3 a -> V3 a
rotVecByQuatB2A q = rotVecByDcmB2A (dcmOfQuat q)
rotVecByEuler :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a
rotVecByEuler = rotVecByDcm . dcmOfEuler321
rotVecByEulerB2A :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a
rotVecByEulerB2A = rotVecByDcmB2A . dcmOfEuler321