#quaternions #rotation #3d #algebra #linear-interpolation

no-std num-quaternion

Quaternion numbers implementation for Rust

20 releases

new 0.2.17 Jul 21, 2024
0.2.16 Jul 16, 2024
0.2.9 Jun 26, 2024
0.1.2 May 25, 2024

#86 in Math

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Quaternions for Rust.

num-quaternion is a Rust library designed for robust, efficient and easy to use quaternion arithmetic and operations. Quaternions are used extensively in computer graphics, robotics, and physics for representing rotations and orientations.


  • Basic Quaternion Operations: Addition, subtraction, multiplication, division, and conjugation.
  • Unit Quaternions: Special support for unit quaternions with optimized operations.
  • Conversion Functions: Convert to/from Euler angles, rotation vectors, and more.
  • Interpolation: Spherical linear interpolation (SLERP) for smooth rotations.
  • Comprehensive Documentation: Detailed documentation with examples to help you get started quickly.


Add num-quaternion to your Cargo.toml:

num-quaternion = "0.2.17"

For #![no_std] environments, disable the default std feature and enable libm to benefit from the advanced mathematical functions of num-quaternion:

num-quaternion = { version = "0.2.17", default-features = false, features = ["libm"] }

Then, include it in your crate:

use num_quaternion::{Quaternion, UnitQuaternion, Q32, Q64, UQ32, UQ64};


Creating Quaternions

// Create a quaternion with explicit components
let q1 = Q32::new(1.0, 2.0, 3.0, 4.0);  // = 1 + 2i + 3j + 4k

// Create a quaternion using shorthand notation
let q2 = 1.0 + Q32::I;  // = 1 + i

Basic Operations

let q3 = q1 + q2;        // Quaternion addition
let q4 = q1 * q2;        // Quaternion multiplication
let q_conj = q1.conj();  // Quaternion conjugation

Unit Quaternions

let uq1 = q1.normalize().expect("Normalization failed"); // Normalize quaternion
let uq2 = UQ32::I;  // Unit quaternion representing the imaginary unit

Conversion Functions

// From Euler angles
let (roll, pitch, yaw) = (1.5, 1.0, 3.0);
let uq = UnitQuaternion::from_euler_angles(roll, pitch, yaw);

// To Euler angles
let euler_angles = uq.to_euler_angles();

// From rotation vector
let rotation_vector = [1.0, 0.0, 0.0]; // x axis rotation, 1 radian
let uq = UnitQuaternion::from_rotation_vector(&rotation_vector);

// To rotation vector
let rotation_vector = uq.to_rotation_vector();

Spherical Linear Interpolation (SLERP)

let uq1 = UQ32::ONE;  // Create a unit quaternion
let uq2 = UQ32::I;    // Create another unit quaternion
let interpolated = uq1.slerp(&uq2, 0.3);  // Perform SLERP with t=0.3


Comprehensive documentation with examples can be found on docs.rs.


Detailed release notes are provided in RELEASES.md.


Contributions are welcome! Please fork the repository and submit pull requests. By contributing, you agree that your contributions will be dual-licensed under the Apache-2.0 and MIT licenses.

If you have any questions or need help, feel free to open an issue on GitHub.

Further instructions can be found in the CONTRIBUTING.md guidelines.


Licensed under either of

at your option.


Special thanks to @cuviper for the num-complex crate which served as a model for this crate. num-quaternion is designed to integrate seamlessly with the rust-num family of crates.