Have you heard anything about quaternions? Do you know how they are used in computer graphics?

Quaternions are an extension of complex numbers, representing numbers with four components: one scalar and three imaginary units (i, j, k). In computer graphics, they are widely used for representing and computing rotations in 3D space.

Advantages of quaternions over matrices or Euler angles:

• No gimbal lock problem (loss of degrees of freedom at certain angles).
• Compact and efficient storage of rotations (4 numbers instead of 9 in a matrix).
• Ease of interpolation (slerp) for smooth animations.

Example of use: to rotate an object in 3D, we can create a quaternion describing a rotation around an axis by a certain angle and apply it to a position vector.

In Go, you can use third-party libraries such as gonum or go-gl/mathgl to work with quaternions.

import (
    "fmt"
    "github.com/go-gl/mathgl/mgl32"
)

func main() {
    // Create a quaternion for a 90-degree rotation around the Y axis
    q := mgl32.QuatRotate(mgl32.DegToRad(90), mgl32.Vec3{0, 1, 0})

    // The vector we want to rotate
    v := mgl32.Vec3{1, 0, 0}

    // Apply the rotation
    rotated := q.Rotate(v)

    fmt.Println(rotated) // Expect approximately (0, 0, -1)
}