Quaternion

Quaternion represents $q_1 + q_2 \bm{i} + q_3 \bm{j} + q_4 \bm{k}$. The salar part and vector part can be accessed by q.scalar and q.vector, respectively.

quaternion(θ, x::Vec; [normalize = true, degree = false])
quaternion(T, θ, x::Vec; [normalize = true, degree = false])

Construct Quaternion from angle θ and direction x. The constructed quaternion is normalized such as norm(q) ≈ 1 by default.

julia> q = quaternion(π/4, Vec(0,0,1))
0.9238795325112867 + 0.0𝙞 + 0.0𝙟 + 0.3826834323650898𝙠

julia> v = rand(Vec{3})
3-element Tensor{Tuple{3},Float64,1,3}:
 0.5908446386657102
 0.7667970365022592
 0.5662374165061859

julia> (q * v / q).vector ≈ rotmatz(π/4) ⋅ v
true

rotate(x::Vec, q::Quaternion)

Rotate x by quaternion q.

Examples

julia> v = Vec(1.0, 0.0, 0.0)
3-element Tensor{Tuple{3},Float64,1,3}:
 1.0
 0.0
 0.0

julia> rotate(v, quaternion(π/4, Vec(0,0,1)))
3-element Tensor{Tuple{3},Float64,1,3}:
 0.7071067811865475
 0.7071067811865476
 0.0