  In this article, we study bivariate polynomial interpolation on the node
points of degenerate Lissajous figures. These node points form Chebyshev
lattices of rank $1$ and are generalizations of the well-known Padua points. We
show that these node points allow unique interpolation in appropriately defined
spaces of polynomials and give explicit formulas for the Lagrange basis
polynomials. Further, we prove mean and uniform convergence of the
interpolating schemes. For the uniform convergence the growth of the Lebesgue
constant has to be taken into consideration. It turns out that this growth is
of logarithmic nature.
