Unisolvent point set

In approximation theory, a finite collection of points X in $R^{n}$ is said to be unisolvent for a space W if any element $w\in W$ is uniquely determined by its values on X.
i.e. X is unisolvent for $W=\Pi _{n}^{m}$ (polynomials in n variables of degree at most m) if there exists a unique polynomial in W of lowest possible degree which interpolates the data X.

Simple examples in $R^{2}$ would be the fact that two distinct points determine a line, three points determine a parabola, etc. It is clear that over $R^{2}$, any collection of k+1 distinct points will uniquely determine $\Pi ^{k}$.