Crate quaternion_core

Expand description

Quaternion library written in Rust.

This crate provides Quaternion operations and conversions between several rotation representations. Functions are generic and support f32 and f64.

§Generics

Functions implementing the QuaternionOps trait can take both Quaternion<T> and Vector3<T> types as arguments (How convenient…!!).

For example:

use quaternion_core::{Vector3, Quaternion, add};
 
// --- Vector3 --- //
let v1: Vector3<f32> = [1.0, 2.0, 3.0];
let v2: Vector3<f32> = [0.1, 0.2, 0.3];
 
let added_v = add(v1, v2);  // <--- [1.1, 2.2, 3.3]
 
// --- Quaternion --- //
let q1: Quaternion<f64> = (1.0, [2.0, 3.0, 4.0]);
let q2: Quaternion<f64> = (0.1, [0.2, 0.3, 0.4]);
 
let added_q = add(q1, q2);  // <--- (1.1, [2.2, 3.3, 4.4])

§What is Versor?

Versor denotes a Quaternion representing rotation, with a norm of 1. This is precisely what is meant by a Unit Quaternion.

The documentation for this crate basically writes Versor instead of Unit Quaternion, but the difference in usage is not clear. Please think Versor = Unit Quaternion.

Enums§

RotationSequence: Specifies the rotation sequence of Euler angles.
RotationType: Specifies the rotation type of Euler angles.

Traits§

QuaternionOps: This trait provides operations common to Quaternions and Pure Quaternions (Vector3).

Functions§

add: Addition of two Quaternions or Vector3s: a + b
conj: Calculate the conjugate of a Quaternion.
cross: Cross product of two Quaternions or Vector3s: a × b
dot: Dot product of two Quaternions or Vector3s: a · b
exp: Exponential function of a Quaternion or Pure Quaternion (Vector3).
frame_rotation: Rotates a frame by the Versor (Frame Rotation - Point Fixed)
from_axis_angle: Generate Versor by specifying rotation angle[rad] and axis vector.
from_dcm: Converts a Direction Cosine Matrix (DCM) into a Versor
from_euler_angles: Converts a Euler Angles into a Versor.
from_rotation_vector: Converts a Rotation Vector into a Versor.
hadamard: Calculate the element-wise product of two Quaternions or Vector3s.
hadamard_add: Hadamard product and addition in one step.
identity: Generate identity quaternion.
inv: Calculate the inverse of a Quaternion or Pure Quaternion (Vector3).
lerp: Lerp (Linear interpolation)
ln: Natural logarithm of a Quaternion.
ln_versor: Natural logarithm of a Versor.
matrix_product: Product of Direction Cosine Matrix (DCM) and Vector3
mul: Multiplication of two Quaternions or Pure Quaternoins (Vector3).
negate: Invert the sign of a Vector3s or Quaternions.
norm: Calculate L2 norm of Vector3s or Quaternions.
normalize: Normalize a Vector3 or Quaternion.
point_rotation: Rotates a point by the Versor (Point Rotation - Frame Fixed)
pow: Power function of a Quaternion.
pow_versor: Power function of a Versor.
rotate_a_to_b: Calculate the Versor to rotate from vector a to vector b (Without singularity!).
rotate_a_to_b_shortest: Calculate the versor to rotate from vector a to vector b by the shortest path.
scale: Scaling a Quaternion or Vector3 by a scalar factor: s * a
scale_add: Scaling and addition in one step: s * a + b
slerp: Slerp (Spherical linear interpolation)
sqrt: Square root of a Quaternion.
sqrt_versor: Square root of a Versor.
sub: Subtraction of two Quaternions or Vector3s: a - b
sum: Sum all elements of a Quaternion or Vector3.
to_axis_angle: Extracts the rotation axis and the rotation angle around the axis from the Versor.
to_dcm: Converts a Versor into a Direction Cosine Matrix (DCM).
to_euler_angles: Converts a Versor into a Euler Angles.
to_rotation_vector: Converts a Versor into a Rotation Vector.

Type Aliases§

DCM: Direction Cosine Matrix
Quaternion: Quaternion
Vector3: Three dimensional vector (Pure Quaternion)