B-splines locally controlled I have read that in contrast of the thin-plate splines, B-splines are locally controlled, which makes them computationally efficient even for large number of control points. 
I didn't understand what does it mean by saying that B-splines are locally controlled. Can anyone help with this?

It means that value of B-spline at a point depends just on few control points localized nearby. And vice versa, if you modify a control point, or coefficient of one basisfunction it will affect just some local nighborhood.
In case of cubic B-spline (which is most common e.g. in computer graphics )  in 1D value $f(x)$ at any point depends on value of 4 control points (resp. basisfunctions ) as
$ f(x) = \sum_{i=1..3} \alpha_i \phi ( x - i ) $
It is nice visible here
http://www.brnt.eu/phd/ucbs-basis.png 
or here
http://www.cs.berkeley.edu/~sequin/CS284/IMGS/bsplinebasics.gif
