HMath.Rotation¶

Description

SO(3), SE(3), and rigid dual quaternions. Active right-handed transforms act on column vectors; compose a b applies b first. Translation shares the coordinate unit of points, angles are radians, and twists are (omega,v). SO(3) logs choose angles in [0,pi]; pi-axis sign is the quaternion convention. SE(3) exp/log use the SO(3) left Jacobian, with series near identity. Dual quaternion interpolation is screw-linear ScLERP through SE(3), including the pure-translation limit. These APIs model rigid transforms, not scale/shear.

On this page¶

API	Purpose
SO3	Normalized representative of SO(3).
so3	Normalize a nonzero quaternion into SO(3).
rotationQuaternion	Underlying unit Hamilton quaternion.
identityRotation	Identity rotation.
composeRotation	Composition applying the right rotation first.
inverseRotation	Inverse of a unit rotation.
rotate	Apply a rotation to a finite three-vector.
expSO3	Exponential of a rotation vector; vector norm is the angle in radians.
logSO3	Principal logarithm as a rotation vector.
SE3	Rigid transformation x -> R*x+t.
se3	Construct a rigid transform from a rotation and finite translation.
rotationPart	Rotation component.
translationPart	Translation component.
identityTransform	Identity rigid transform.
compose	Compose transforms; b acts first.
inverse	Inverse rigid transform.
transformPoint	Apply a rigid transform.
expSE3	SE(3) exponential.
logSE3	Principal SE(3) logarithm, stable at identity and at rotations near pi.
toHomogeneous	Row-major homogeneous 4x4 matrix, bottom row [0,0,0,1].
fromHomogeneous	Validate a homogeneous rigid matrix (bottom row tolerance 1e-12, rotation 1e-9).
DualQuaternion	Unit real part and Study-orthogonal dual part.
dualQuaternion	Construct a rigid dual quaternion.
dualParts	Real and dual Hamilton parts.
toDualQuaternion	Encode translation as 0.5(0,t)r.
fromDualQuaternion	Decode translation from 2dconjugate(r).
multiplyDual	Rigid dual-quaternion product.
inverseDual	Inverse rigid dual quaternion.
interpolateDual	Shortest-rotation screw-linear interpolation on [0,1].

Documentation

SO3

data SO3 Source #

Normalized representative of SO(3).

Instances

Instances details

Show SO3 Source #
Instance details Defined in HMath.Rotation Methods showsPrec :: Int -> SO3 -> ShowS # show :: SO3 -> String # showList :: [SO3] -> ShowS #
Eq SO3 Source #
Instance details Defined in HMath.Rotation Methods (==) :: SO3 -> SO3 -> Bool # (/=) :: SO3 -> SO3 -> Bool #

so3

so3 :: Quaternion -> Either MathError SO3 Source #

Normalize a nonzero quaternion into SO(3).

rotationQuaternion

rotationQuaternion :: SO3 -> Quaternion Source #

Underlying unit Hamilton quaternion.

identityRotation

identityRotation :: SO3 Source #

Identity rotation.

composeRotation

composeRotation :: SO3 -> SO3 -> Either MathError SO3 Source #

Composition applying the right rotation first.

inverseRotation

inverseRotation :: SO3 -> SO3 Source #

Inverse of a unit rotation.

rotate

rotate :: SO3 -> [Double] -> Either MathError [Double] Source #

Apply a rotation to a finite three-vector.

expSO3

expSO3 :: [Double] -> Either MathError SO3 Source #

Exponential of a rotation vector; vector norm is the angle in radians.

logSO3

logSO3 :: SO3 -> Either MathError [Double] Source #

Principal logarithm as a rotation vector.

SE3

data SE3 Source #

Rigid transformation x -> R*x+t.

Instances

Instances details

Show SE3 Source #
Instance details Defined in HMath.Rotation Methods showsPrec :: Int -> SE3 -> ShowS # show :: SE3 -> String # showList :: [SE3] -> ShowS #
Eq SE3 Source #
Instance details Defined in HMath.Rotation Methods (==) :: SE3 -> SE3 -> Bool # (/=) :: SE3 -> SE3 -> Bool #

se3

se3 :: SO3 -> [Double] -> Either MathError SE3 Source #

Construct a rigid transform from a rotation and finite translation.

rotationPart

rotationPart :: SE3 -> SO3 Source #

Rotation component.

translationPart

translationPart :: SE3 -> [Double] Source #

Translation component.

identityTransform

identityTransform :: SE3 Source #

Identity rigid transform.

compose

compose :: SE3 -> SE3 -> Either MathError SE3 Source #

Compose transforms; b acts first.

inverse

inverse :: SE3 -> Either MathError SE3 Source #

Inverse rigid transform.

transformPoint

transformPoint :: SE3 -> [Double] -> Either MathError [Double] Source #

Apply a rigid transform.

expSE3

expSE3 :: ([Double], [Double]) -> Either MathError SE3 Source #

SE(3) exponential. The translational twist v is integrated by J(omega).

logSE3

logSE3 :: SE3 -> Either MathError ([Double], [Double]) Source #

Principal SE(3) logarithm, stable at identity and at rotations near pi.

toHomogeneous

toHomogeneous :: SE3 -> Either MathError (Matrix Double) Source #

Row-major homogeneous 4x4 matrix, bottom row [0,0,0,1].

fromHomogeneous

fromHomogeneous :: Matrix Double -> Either MathError SE3 Source #

Validate a homogeneous rigid matrix (bottom row tolerance 1e-12, rotation 1e-9).

DualQuaternion

data DualQuaternion Source #

Unit real part and Study-orthogonal dual part.

Instances

Instances details

Show DualQuaternion Source #
Instance details Defined in HMath.Rotation Methods showsPrec :: Int -> DualQuaternion -> ShowS # show :: DualQuaternion -> String # showList :: [DualQuaternion] -> ShowS #
Eq DualQuaternion Source #
Instance details Defined in HMath.Rotation Methods (==) :: DualQuaternion -> DualQuaternion -> Bool # (/=) :: DualQuaternion -> DualQuaternion -> Bool #