SpatialMath

Documentation

data Euler a

3-2-1 Euler angle rotation sequence

Constructors

Euler

Fields

eYaw :: a

ePitch :: a

eRoll :: a

Instances

Functor Euler

Typeable1 Euler

Foldable Euler

Traversable Euler

Generic1 Euler

Eq a => Eq (Euler a)

Data a => Data (Euler a)

Ord a => Ord (Euler a)

Show a => Show (Euler a)

Generic (Euler a)

rotateXyzAboutX :: Floating a => V3 a -> a -> V3 a

Rotate a vector about the X axis

>>> rotateXyzAboutX (V3 0 1 0) (pi/2)
V3 0.0 6.123233995736766e-17 1.0

>>> rotateXyzAboutX (V3 0 0 1) (pi/2)
V3 0.0 (-1.0) 6.123233995736766e-17

rotateXyzAboutY :: Floating a => V3 a -> a -> V3 a

Rotate a vector about the Y axis

>>> rotateXyzAboutY (V3 0 0 1) (pi/2)
V3 1.0 0.0 6.123233995736766e-17

>>> rotateXyzAboutY (V3 1 0 0) (pi/2)
V3 6.123233995736766e-17 0.0 (-1.0)

rotateXyzAboutZ :: Floating a => V3 a -> a -> V3 a

Rotate a vector about the Z axis

>>> rotateXyzAboutZ (V3 1 0 0) (pi/2)
V3 6.123233995736766e-17 1.0 0.0

>>> rotateXyzAboutZ (V3 0 1 0) (pi/2)
V3 (-1.0) 6.123233995736766e-17 0.0

euler321OfQuat :: RealFloat a => Quaternion a -> Euler a

Convert quaternion to Euler angles

>>> euler321OfQuat (Quaternion 1.0 (V3 0.0 0.0 0.0))
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 0.0}

>>> euler321OfQuat (Quaternion (sqrt(2)/2) (V3 (sqrt(2)/2) 0.0 0.0))
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 1.5707963267948966}

>>> euler321OfQuat (Quaternion (sqrt(2)/2) (V3 0.0 (sqrt(2)/2) 0.0))
Euler {eYaw = 0.0, ePitch = 1.5707963267948966, eRoll = 0.0}

>>> euler321OfQuat (Quaternion (sqrt(2)/2) (V3 0.0 0.0 (sqrt(2)/2)))
Euler {eYaw = 1.5707963267948966, ePitch = -0.0, eRoll = 0.0}

euler321OfDcm :: RealFloat a => M33 a -> Euler a

Convert DCM to euler angles

>>> euler321OfDcm $ V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
Euler {eYaw = 0.0, ePitch = -0.0, eRoll = 0.0}

>>> euler321OfDcm $ V3 (V3 0 1 0) (V3 (-1) 0 0) (V3 0 0 1)
Euler {eYaw = 1.5707963267948966, ePitch = -0.0, eRoll = 0.0}

>>> let s = sqrt(2)/2 in euler321OfDcm $ V3 (V3 s s 0) (V3 (-s) s 0) (V3 0 0 1)
Euler {eYaw = 0.7853981633974483, ePitch = -0.0, eRoll = 0.0}

quatOfEuler321 :: (Floating a, Ord a) => Euler a -> Quaternion a

Convert Euler angles to quaternion

>>> quatOfEuler321 (Euler 0 0 0)
Quaternion 1.0 (V3 0.0 0.0 0.0)

>>> quatOfEuler321 (Euler (pi/2) 0 0)
Quaternion 0.7071067811865476 (V3 0.0 0.0 0.7071067811865475)

>>> quatOfEuler321 (Euler 0 (pi/2) 0)
Quaternion 0.7071067811865476 (V3 0.0 0.7071067811865475 0.0)

>>> quatOfEuler321 (Euler 0 0 (pi/2))
Quaternion 0.7071067811865476 (V3 0.7071067811865475 0.0 0.0)

dcmOfQuat :: Num a => Quaternion a -> M33 a

convert a quaternion to a DCM

>>> dcmOfQuat $ Quaternion 1.0 (V3 0.0 0.0 0.0)
V3 (V3 1.0 0.0 0.0) (V3 0.0 1.0 0.0) (V3 0.0 0.0 1.0)

>>> let s = sqrt(2)/2 in dcmOfQuat $ Quaternion s (V3 0.0 0.0 s)
V3 (V3 0.0 1.0000000000000002 0.0) (V3 (-1.0000000000000002) 0.0 0.0) (V3 0.0 0.0 1.0000000000000002)

>>> dcmOfQuat $ Quaternion 0.9238795325112867 (V3 0.0 0.0 0.3826834323650898)
V3 (V3 0.7071067811865475 0.7071067811865476 0.0) (V3 (-0.7071067811865476) 0.7071067811865475 0.0) (V3 0.0 0.0 1.0)

dcmOfQuatB2A :: (Conjugate a, RealFloat a) => Quaternion a -> M33 a

dcmOfEuler321 :: (Floating a, Ord a) => Euler a -> M33 a

Convert DCM to euler angles

>>> dcmOfEuler321 $ Euler {eYaw = 0.0, ePitch = 0, eRoll = 0}
V3 (V3 1.0 0.0 0.0) (V3 0.0 1.0 0.0) (V3 0.0 0.0 1.0)

>>> dcmOfEuler321 $ Euler {eYaw = pi/2, ePitch = 0, eRoll = 0}
V3 (V3 2.220446049250313e-16 1.0 0.0) (V3 (-1.0) 2.220446049250313e-16 0.0) (V3 0.0 0.0 1.0)

>>> dcmOfEuler321 $ Euler {eYaw = pi/4, ePitch = 0, eRoll = 0}
V3 (V3 0.7071067811865475 0.7071067811865476 0.0) (V3 (-0.7071067811865476) 0.7071067811865475 0.0) (V3 0.0 0.0 1.0)

quatOfDcm :: RealFloat a => M33 a -> Quaternion a

convert a DCM to a quaternion

>>> quatOfDcm $ V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)
Quaternion 1.0 (V3 0.0 0.0 0.0)

>>> quatOfDcm $ V3 (V3 0 1 0) (V3 (-1) 0 0) (V3 0 0 1)
Quaternion 0.7071067811865476 (V3 0.0 0.0 0.7071067811865475)

>>> let s = sqrt(2)/2 in quatOfDcm $ V3 (V3 s s 0) (V3 (-s) s 0) (V3 0 0 1)
Quaternion 0.9238795325112867 (V3 0.0 0.0 0.3826834323650898)

quatOfDcmB2A :: (Conjugate a, RealFloat a) => M33 a -> Quaternion a

rotVecByDcm :: Num a => M33 a -> V3 a -> V3 a

vec_b = R_a2b * vec_a

rotVecByDcmB2A :: Num a => M33 a -> V3 a -> V3 a

vec_a = R_a2b^T * vec_b

rotVecByQuat :: Num a => Quaternion a -> V3 a -> V3 a

vec_b = q_a2b * vec_a * q_a2b^(-1) vec_b = R(q_a2b) * vec_a

rotVecByQuatB2A :: Num a => Quaternion a -> V3 a -> V3 a

rotVecByEuler :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a

rotVecByEulerB2A :: (Floating a, Ord a) => Euler a -> V3 a -> V3 a

re-exported from linear

type M33 a = V3 (V3 a)

A 3x3 matrix with row-major representation

data V3 a

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Monad V3

Functor V3

Typeable1 V3

Applicative V3

Foldable V3

Traversable V3

Distributive V3

R3 V3

R2 V3

R1 V3

Core V3

Metric V3

Additive V3

Traversable1 V3

Foldable1 V3

Apply V3

Bind V3

Eq a => Eq (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)

Storable a => Storable (V3 a)

Epsilon a => Epsilon (V3 a)

data Quaternion a

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion

Functor Quaternion

Typeable1 Quaternion

Applicative Quaternion

Foldable Quaternion

Traversable Quaternion

Distributive Quaternion

Complicated Quaternion

Hamiltonian Quaternion

Core Quaternion

Metric Quaternion

Additive Quaternion

Apply Quaternion

Bind Quaternion

Eq a => Eq (Quaternion a)

RealFloat a => Floating (Quaternion a)

RealFloat a => Fractional (Quaternion a)

Data a => Data (Quaternion a)

RealFloat a => Num (Quaternion a)

Ord a => Ord (Quaternion a)

Read a => Read (Quaternion a)

Show a => Show (Quaternion a)

Ix a => Ix (Quaternion a)

Storable a => Storable (Quaternion a)

(Conjugate a, RealFloat a) => Conjugate (Quaternion a)

(RealFloat a, Epsilon a) => Epsilon (Quaternion a)