Add new way to represent a rotation matrix (vector rotation)

[zhy91]

Introduction

Now, Rotations.jl contains two ways to represent rotation matrices: Euler Angles and Rotating around an axis.

However, vector rotation, i.e., rotating from one vector to another, is sometimes needed. Is it possible to add this way?

Mathematical method

References:

1. https://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Rotation_matrix.html#Vector_rotation
2. https://math.stackexchange.com/questions/180418/calculate-rotation-matrix-to-align-vector-a-to-vector-b-in-3d/476311#476311

By the way, such rotation has infinite solutions. The above method gives only one of them.

Simple example

This is a simple example written by myself:

function vector_rotate(f::T, t::T) where T<:AbstractVector{Float64}
    v = f × t
    c = f ⋅ t
    u = [   0 -v[3]  v[2];
         v[3]     0 -v[1];
        -v[2]  v[1]     0]
    E = Matrix{Float64}(I, 3, 3)
    R = (c ≈ -1.0) ? (-E) : (E + u + u * u / (1 + c))
    return R
end

Thank you all!

[zhy91]

Sorry for my stupid issue. :<

I soon realize that u and c in the above example are actually the axis and angle in the way "Rotating around an axis".
Therefore, the new way is not necessary.

[tamasgal]

Sorry for digging this out but I just wanted to create a similar issue and now scratching my head how you solved it.

I guess that we can use RotationVecGenerator with f × t as an axis, something like: R = RotationVecGenerator((a × b)...) but how do we pass the angle?

[hyrodium]

If you need to create a rotation from an angle a and its axis [v1, v2, v3], you can use AngleAxis(a, v1, v2, v3).
If you need to create a rotation that rotates a vector u to a vector v, you can use rotation_between(u,v).

• https://juliageometry.github.io/Rotations.jl/dev/functionreference/#Rotations.AngleAxis
• https://juliageometry.github.io/Rotations.jl/dev/functionreference/#Rotations.rotation_between

[tamasgal]

Ah yes, makes sense, thanks!