44 lines
1.3 KiB
Markdown
44 lines
1.3 KiB
Markdown
# Quaternions
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[Ðóññêàÿ âåðñèÿ / Russian version](quaternion-rus.md)
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Quaternions are hypercomplex numbers that extend the concept of complex numbers.
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They consist of one real component and three imaginary components:
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q = s + ix + jy + kz
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where:
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- s, x, y, z ∈ R are real numbers
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- i, j, k are imaginary units that satisfy the following conditions:
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- i<sup>2</sup> = j<sup>2</sup> = k<sup>2</sup> = ijk = -1
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Quaternions were discovered by mathematician William Hamilton and introduced
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to the public in 1843. They have found wide application in computer graphics,
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robotics, and physics to describe rotations in three-dimensional space.
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## Quaternion implementation in the library
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There are two types of quaternions in the library:
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- **BGC_FP32_Quaternion** - a quaternion using single-precision floating-point
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numbers
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- **BGC_FP64_Quaternion** - a quaternion using double-precision floating-point
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numbers
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Structure definitions:
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```c
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typedef struct {
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float s, x, y, z;
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} BGC_FP32_Quaternion;
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typedef struct {
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double s, x, y, z;
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} BGC_FP64_Quaternion;
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```
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Fields:
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- **s** is the real part of the quaternion. It is named after the word Scalar.
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- **x**, **y**, **z** - Imaginary components of the quaternion.
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[Documentation](intro-eng.md)
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