  Consider an $s$-dimensional function being evaluated at $n$ points of a low
discrepancy sequence (LDS), where the objective is to approximate the
one-dimensional functions that result from integrating out $(s-1)$ variables.
Here, the emphasis is on accurately approximating the shape of such
\emph{one-dimensional} functions. Approximating this shape when the function is
evaluated on a set of grid points instead is relatively straightforward.
However, the number of grid points needed increases exponentially with $s$. LDS
are known to be increasingly more efficient at integrating $s$-dimensional
functions compared to grids, as $s$ increases. Yet, a method to approximate the
shape of a one-dimensional function when the function is evaluated using an
$s$-dimensional LDS has not been proposed thus far. We propose an approximation
method for this problem. This method is based on an $s$-dimensional integration
rule together with fitting a polynomial smoothing function. We state and prove
results showing conditions under which this polynomial smoothing function will
converge to the true one-dimensional function. We also demonstrate the
computational efficiency of the new approach compared to a grid based approach.
