In a section discussing Miller indices, my textbook says the following:
The rules for determining the Miller indices of a direction or an orientation in a crystal are as follows: translate the orientation to the origin of the unit cell, and take the normalized coordinates of its other vertex.
What I'm confused about is how one translates the orientation to the origin of the unit cell?
Since the textbook just mentions this without elaboration or illustration, it is not clear precisely what this means or how one would go about it. I would appreciate it if people could please take the time to explain and demonstrate how this is (mathematically) done. Sources would be appreciated, if you have them.