Улучшение документации по кватернионам и версорам

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Andrey Pokidov 2025-02-07 23:46:30 +07:00
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[Quaternions](./quaternion-eng.md) are hypercomplex numbers that have one real component and three imaginary components:
q = w + ix + jy + kz, where w is the real component, x, y, z are the imaginary components, and i, j, k are the imaginary units
q = w + ix + jy + kz
i<sup>2</sup> = j<sup>2</sup> = k<sup>2</sup> = ijk = -1
where:
w, x, y, z &isin; R
- w, x, y, z &isin; 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. Hamilton later proposed a special class of quaternions, which he called versors.
@ -18,11 +20,10 @@ It is sufficient to add the equation of the modulus being equal to one to the fo
q = w + ix + jy + kz
i<sup>2</sup> = j<sup>2</sup> = k<sup>2</sup> = -1
w, x, y, z &isin; R
w<sup>2</sup> + x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 1
- w, x, y, z &isin; 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
- w<sup>2</sup> + x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 1
The name comes from the Latin verb "versare", meaning "to turn", "to rotate", to which the Latin ending -or is added, denoting the subject performing the action. Literally, the Latin word "versor" can be translated as "rotator" or "turner".
@ -55,6 +56,7 @@ The BGC library provides a separate implementation for versors in the form of st
} BgcVersorFP64;
```
Fields:
- s0 is the real part of the versor.
- x1, x2, x3 are the imaginary components of the versor.