package OCADml

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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