Rotating vector by an angle and by given direction vector of the axis and there is a point of the axis. (3 dimensions)

Question

1. The 3D coordinates of the vector.

2. The rotation angle in radians.

3. The 3D coordinates of a point of the axis.

4. The 3D coordinates of the direction vector of the axis.

The length of the direction vector is greater than 1e-8.

how I should rotate input vector?

First of all, I need to move my coordinate system into another start point? I don't understand how I should rotate my vector around a direction one. And then.. I should rotate at first around x axis, then y, and then z?

Answer 1

There is effective approach - using Rodrigues formula

To rotate vector V about axis with unit direction vector k by angle theta:

Vrot = V * cos(theta) + (k x v) * sin(theta) + k * (k.dot.v) * (1 - cos(theta))