I'm reading the following paper by Hsu et al (here).
Say I've got a trivariate uniform cubic B-spline volume of the form: $$ \mathbf{q}_{ijk}(s,t,u) =\sum_{l,m,n=-3}^{0}\mathbf{P}_{i+l,j+m,k+n}B_{i}(s)B_{j}(t)B_{k}(u) $$
Questions:
Given a point $(x,y,z)$, how can one obtain its translation in the coordinate space of the spline? And more specifically, to which segment of the spline it belongs?
Suppose that I wish to move said vertex (possibly having been previously moved) to a new position $(x',y',z')$. Before using the technique in the paper to modify the control points, one needs to find out (again) the segment to which it belongs. How can it be done?