  We present effective algorithms for uniform approximation of multivariate
functions satisfying some prescribed inner structure. We extend in several
directions the analysis of recovery of ridge functions $f(x)=g(\langle
a,x\rangle)$ as performed earlier by one of the authors and his coauthors. We
consider ridge functions defined on the unit cube $[-1,1]^d$ as well as
recovery of ridge functions defined on the unit ball from noisy measurements.
We conclude with the study of functions of the type
$f(x)=g(\|a-x\|_{l_2^d}^2)$.
