# Quaternions

[Русская версия / Russian version](quaternion-rus.md)

Quaternions are hypercomplex numbers that extend the concept of complex numbers.
They consist of one real component and three imaginary components:

q = s + ix + jy + kz

where:

- s, x, y, z ∈ R are real numbers
- i, j, k are imaginary units that satisfy the following conditions:
   - i<sup>2</sup> = j<sup>2</sup> = k<sup>2</sup> = ijk = -1

Quaternions were discovered by mathematician William Hamilton and introduced
to the public in 1843. They have found wide application in computer graphics,
robotics, and physics to describe rotations in three-dimensional space.

## Quaternion implementation in the library

There are two types of quaternions in the library:
- **BGC_FP32_Quaternion** - a quaternion using single-precision floating-point
numbers
- **BGC_FP64_Quaternion** - a quaternion using double-precision floating-point
numbers

Structure definitions:

```c
    typedef struct {
        float s, x, y, z;
    } BGC_FP32_Quaternion;

    typedef struct {
        double s, x, y, z;
    } BGC_FP64_Quaternion;
```

Fields:
- **s** is the real part of the quaternion. It is named after the word Scalar.
- **x**, **y**, **z** - Imaginary components of the quaternion.

[Documentation](intro-eng.md)