  Identifying Blaschke-Santal\'o diagrams is an important topic that
essentially consists in determining the image $Y=F(X)$ of a map
$F:X\to{\mathbb{R}}^d$, where the dimension of the source space $X$ is much
larger than the one of the target space. In some cases, that occur for instance
in shape optimization problems, $X$ can even be a subset of an
infinite-dimensional space. The usual Monte Carlo method, consisting in
randomly choosing a number $N$ of points $x_1,\dots,x_N$ in $X$ and plotting
them in the target space ${\mathbb{R}}^d$, produces in many cases areas in $Y$
of very high and very low concentration leading to a rather rough numerical
identification of the image set. On the contrary, our goal is to choose the
points $x_i$ in an appropriate way that produces a uniform distribution in the
target space. In this way we may obtain a good representation of the image set
$Y$ by a relatively small number $N$ of samples which is very useful when the
dimension of the source space $X$ is large (or even infinite) and the
evaluation of $F(x_i)$ is costly. Our method consists in a suitable use of {\it
Centroidal Voronoi Tessellations} which provides efficient numerical results.
Simulations for two and three dimensional examples are shown in the paper.

Numerical Analysis;Numerical Analysis