Module Quaternions.Q

type ('a, 'b) t
val create : float -> Owl.Mat.mat -> ([ `unit ], _) t

create theta u creates a unit quaternion correponsing to a rotation of angle theta around axis u. Note that u is first normalised so only its direction matters.

val create_real : float -> (_, [ `real ]) t
val create_imag : Owl.Mat.mat -> (_, [ `imaginary ]) t
val unpack : (_, _) t -> float * Owl.Mat.mat

Extracts the real (scalar) and imaginary (vector) part of a quaternion

val unpack_flt : (_, _) t -> float * (float * float * float)
val of_ypr : (float * float * float) -> ([ `unit ], _) t

Create a unit quaternion from the yaw, pitch, and roll angles.

val to_ypr : ([ `unit ], _) t -> float * float * float

Extract (yaw, pitch, roll) from a quaternion; these are the conventions used by J Wilson et al 2018, corresponding to the intrinsic Tait-Bryan angles following the (x'' - y' - z) convention -- cf wikipedia.

val to_vec : (_, _) t -> Owl.Mat.mat

Packs a quaternion as a 4D vector.

val of_vec : Owl.Mat.mat -> (_, _) t

Unpacks a 4D vector into a quaternion.

val renormalize : (_, _) t -> ([ `unit ], _) t

Renormalises a quaternion (so it becomes a unit quaternion)

val dot_prod : (_, _) t -> (_, _) t -> float

Quaternion dot product

val sqr_norm : (_, _) t -> float

Squared norm of a quaternion

val (+) : (_, 'a) t -> (_, 'a) t -> (_, 'a) t

Addition of two quaternions

val (-) : (_, 'a) t -> (_, 'a) t -> (_, 'a) t

Subtraction of two quaternions

val (*) : (_, _) t -> (_, _) t -> (_, _) t

Quaternion product.

val ($*) : float -> (_, 'a) t -> (_, 'a) t

Multiplication by a scalar

val (/$) : (_, 'a) t -> float -> (_, 'a) t

Division by a scalar

val conj : ('a, 'b) t -> ('a, 'b) t
val geodesic_distance : ([ `unit ], _) t -> ([ `unit ], _) t -> float

Geodesic distance on SO(3)

val to3D : ([ `unit ], _) t -> Owl.Mat.mat

place a quaternion inside the 3D ball used to visualise them

val sample : unit -> ([ `unit ], _) t

sample quaternions from a geodesic-uniform distribution on SO(3)