Discretization of Unit Vector in 3D I cant think of a thing that I think is supposed to be easy... =/
Im glad if you could help me.
Im working with a regular discretization of a 3d euclidean space. Cubic cells. Then, after a black-box-like process, I have a unit vector that is related to a specific cell. I know that it must be pointing to any of the 26 neighbors (9 in upper and bottom level, 8 in the same). But, which cell is it pointing? 
In 2D, using square cells, was easy to develop a code to do that... but I cant think how it should be in 3D.

Im solving a BVP of a 3D Elliptic PDE with finite difference scheme. After I solve it, since in the specific PDE Im using I have a property of just having on local minimum, which is the global minimum, I wanna trace a path from a random point, going along gradient descendant lines, until the global minimum. So, the discretization arises because of FDS, and my vector field are just the inverse of the gradient field (ie, gradient descendant) of my solved BVP/PDE. 
Some formalities that I forgot and DavidK pointed out.
Let 
$$v \in R^3, \quad with \quad ||v||=1$$
be a vector.
Also, consider a regular discretization of a region of R^3, with
$$ \Delta_x = \Delta_y = \Delta_z = 1  $$
Ie, cubic cells, with 0=(0,0,0) being its initial point. 
Example1:
Lets consider one cubic-cell inside the domain. Without loss of generalization, let it be the closest one to the origin, ie, since the one centered at (0.5,0.5,0.5) is in the border, lets choose the one centered at (1.5,1.5,1.5). 
If v=(1,0,0), it is pointing to the cell centered in (2.5,1.5,1.5).
If v=(2^(1/2),-2^(1/2),0), it is pointing to the cell centered in (2.5,0.5,1.5).


Why don't you try this?
Extend your unit vector $v$ to a ray from its origin $o$,
$r=o + \alpha v$ where $\alpha \in \mathbb{R}$.
Now iterate over the $26$ neighboring cells, computing the closet
approach of $r$ to the center of each cell.
(I am assuming you know how to perform this computation. E.g, see
Wikipedia's Distance from a point to a line.)
Select the cell with the minimum distance to the ray. 
