A survey on bivariate Lagrange interpolation on Lissajous nodes

Abstract

This article is a survey on recent research on bivariate polynomial interpolation on the node points of Lissajous curves. The resulting theory is a generalization of the generating curve approach developed for Lagrange interpolation on the Padua points. After classifying the different types of Lissajous curves, we give a short overview on interpolation and quadrature rules defined on the node points of the Lissajous curves. Further, we summarize some convergence results and show how the interpolating polynomials can be computed efficiently. Finally, the developed theory is applied to a practical problem from a medical imaging modality called Magnetic Particle Imaging.