Module OCADml.Quaternion

Provides functions for the creation of and operations between quaternions. These can be used to create composable and interpolatable rotations to be applied to 3d vectors (V3.t), and shapes.

type t
val id : t

The identity quaternion: { x = 0.; y = 0.; z = 0.; w = 1. }

val make : V3.t -> float -> t

make ax angle

Create a quaternion representing a rotation of angle (in radians) around the vector ax.

Basic Arithmetic

val add : t -> t -> t

add a b

Hadamard (element-wise) addition of quaternions a and b.

val sub : t -> t -> t

sub a b

Hadamard (element-wise) subtraction of quaternion b from a.

val mul : t -> t -> t

mul a b

Quaternion multiplication of a and b.

val neg : t -> t

neg t

Negation of all elements of t.

val sadd : t -> float -> t

sadd t s

Add s to the magnitude of t, leaving the imaginary parts unchanged.

val ssub : t -> float -> t

ssub t s

Subtract s from the magnitude of t, leaving the imaginary parts unchanged.

val ssub_neg : t -> float -> t

ssub_neg t s

Negate the imaginary parts of t, and subtract the magnitude from s to obtain the new magnitude.

val smul : t -> float -> t

smul t s

Element-wise multiplication of t by s.

val sdiv : t -> float -> t

div_scalar t s

Element-wise division of t by s.

Vector Math

val norm : t -> float

norm t

Calculate the vector norm (a.k.a. magnitude) of t.

val normalize : t -> t

normalize t

Normalize t to a quaternion for which the magnitude is equal to 1. e.g. norm (normalize t) = 1.

val dot : t -> t -> float

dot a b

Vector dot product of a and b.

val conj : t -> t

conj t

Take the conjugate of the quaternion t, negating the imaginary parts (x, y, and z) of t, leaving the magnitude unchanged.

val distance : t -> t -> float

distance a b

Calculate the magnitude of the difference (Hadamard subtraction) between a and b.

Conversions

val of_euler : V3.t -> t

of_euler v

Create a quaternion equivalent to the Euler angle rotations represented by v.

val to_euler : t -> V3.t

to_euler t

Convert the quaternion t to equivalent Euler angles.

val to_affine : ?trans:V3.t -> t -> Affine3.t

to_affine ?trans t

Convert quaternion t into an Affine3.t, optionally providing a translation vector trans to tack on.

Vector Transformations

val align : V3.t -> V3.t -> t

align a b

Calculate a quaternion that would bring a into alignment with b.

val transform : ?about:V3.t -> t -> V3.t -> V3.t

transform ?about t v

Rotate v with the quaternion t around the origin (or the point about if provided).

Utilities

val slerp : t -> t -> float -> t

slerp a b step

Spherical linear interpotation. Adapted from pyquaternion.

val to_string : t -> string