Let $f_1, \ldots, f_s$ be polynomials in $\Q[X_1, \ldots, X_n]$ that generate a radical ideal and let $V$ be their complex zero-set. Suppose that $V$ is smooth and equidimensional; then we show that computing suitable sections of the polar varieties associated to generic projections of $V$ gives at least one point in each connected component of $V\cap\R^n$. We deduce an algorithm that extends that of Bank, Giusti, Heintz and Mbakop to non-compact situations. Its arithmetic complexity is polynomial in the complexity of evaluation of the input system, an intrinsic algebraic quantity and a combinatorial quantity.