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https://github.com/rawify/quaternion.cpp

A C++ Quaternion library
https://github.com/rawify/quaternion.cpp

angle complex conjugate cpp math numbers quaternion rotation

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A C++ Quaternion library

Host: GitHub
URL: https://github.com/rawify/quaternion.cpp
Owner: rawify
License: mit
Created: 2023-08-30T11:09:09.000Z (over 1 year ago)
Default Branch: main
Last Pushed: 2024-04-04T16:38:43.000Z (10 months ago)
Last Synced: 2024-04-04T17:45:16.789Z (10 months ago)
Topics: angle, complex, conjugate, cpp, math, numbers, quaternion, rotation
Language: C++
Homepage:
Size: 12.7 KB
Stars: 1
Watchers: 1
Forks: 1
Open Issues: 0
Metadata Files:
- Readme: README.md
- License: LICENSE

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README

# Quaternion.cpp - ℍ in C++

Quaternion.c is a well tested C++ library for 3D rotations. Quaternions are a compact representation of rotations and can be used everywhere, from the attitude of a dron over to computer games to the rotation of satellites and all by avoiding the [Gimbal lock](https://en.wikipedia.org/wiki/Gimbal_lock). The library is a port of [Quaternion.js](https://github.com/rawify/Quaternion.js)

## Examples

```cpp
#include

Quaternion x(1, 2, 3, 4);
x.normalize();
```

Converting Euler angles to a quaternion is as easy as

```cpp
Quaternion q = Quaternion::fromAxisAngle(1, 0, 0, 0.4);
```

## Operators

### Quaternion q1 + q2

Adds two quaternions Q1 and Q2

### Quaternion q1 - q2

Subtracts a quaternions Q2 from Q1

### Quaternion -q

Calculates the additive inverse, or simply it negates the quaternion

### Quaternion q1 * q2

Calculates the Hamilton product of two quaternions. **Note:** This function is not commutative, i.e. order matters!

### Quaternion q1 * scale

Scales a quaternion by a scalar

## Functions

### Quaternion norm()

Calculates the length/modulus/magnitude or the norm of a quaternion

### Quaternion normSq()

Calculates the squared length/modulus/magnitude or the norm of a quaternion

### Quaternion normalize()

Normalizes the quaternion to have |Q| = 1 as long as the norm is not zero. Alternative names are the signum, unit or versor

### Quaternion dot()

Calculates the dot product of two quaternions

### Quaternion conjugate()

Calculates the conjugate of a quaternion. If the quaternion is normalized, the conjugate is the inverse of the quaternion - but faster.

### rotateVector(&x, &y, &z)

Rotates a 3 component vector, represented as three arguments passed as reference

### Quaternion::fromAxisAngle(x, y, z, angle)

Static method gets a quaternion by a rotation given as an axis (x, y, z) and angle

### Quaternion::fromEuler(ϕ, θ, ψ)

Euler angles are probably the reason to use quaternions. The definition is mostly sloppy and you can only decide how it was defined based on the matrix representation. A `ZXY` in one definition is the multiplication order read from right to left and in another the execution order from left to right.

So for `fromEuler(ϕ, θ, ψ)` with `QUATERNION_EULER_ZYX`, for example means first rotate around Y by ψ then around X by θ and then around Z by ϕ (`RotZ(ϕ)RotX(θ)RotY(ψ)`).

The order of `fromEuler()` can be defined at compile time by defining `QUATERNION_EULER_ORDER`. The value can be `ZXY, XYZ / RPY, YXZ, ZYX / YPR (default), YZX, XZY, ZYZ, ZXZ, YXY, YZY, XYX, XZX`, using the constants such as `QUATERNION_EULER_ZYX`.