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 ${\displaystyle O(\log ^{2}n)}$. Their name is due to the University of Padua, where they were originally discovered.

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.

We can see the Padua point as a "sampling" of a parametric curve, called generating curve, which is slightly different for each of the four families, so that the points for interpolation degree ${\displaystyle n}$ and family ${\displaystyle s}$ can be defined as

Actually, the Padua points lie exactly on the self-intersections of the curve, and on the intersections of the curve with the boundaries of the square ${\displaystyle [-1,1]^{2}}$. The cardinality of the set ${\displaystyle \operatorname {Pad} _{n}^{s}}$ is ${\textstyle |\operatorname {Pad} _{n}^{s}|={\frac {(n+1)(n+2)}{2}}}$. Moreover, for each family of Padua points, two points lie on consecutive vertices of the square ${\displaystyle [-1,1]^{2}}$, ${\displaystyle 2n-1}$ points lie on the edges of the square, and the remaining points lie on the self-intersections of the generating curve inside the square.

The four generating curves are closed parametric curves in the interval ${\displaystyle [0,2\pi ]}$, and are a special case of Lissajous curves.

The generating curve of Padua points of the first family is

If we sample it as written above, we have:

where ${\displaystyle \delta _{j}=0}$ when ${\displaystyle n}$ is even or odd but ${\displaystyle j}$ is even, ${\displaystyle \delta _{j}=1}$ if ${\displaystyle n}$ and ${\displaystyle k}$ are both odd