Padua points

In polynomial interpolation of two variables, the Padua points are the first known example (and up to now the only one) of a unisolvent point set (that is, the interpolating polynomial is unique) with minimal growth of their Lebesgue constant, proven to be ${\displaystyle O(\log ^{2}n)}$.^[1] Their name is due to the University of Padua, where they were originally discovered.^[2]

The points are defined in the domain ${\displaystyle [-1,1]\times [-1,1]\subset \mathbb {R} ^{2}}$. It is possible to use the points with four orientations, obtained with subsequent 90-degree rotations: this way we get four different families of Padua points.