Generation of lattices of points for bivariate interpolation

Principal lattices in the plane are distributions of points particularly simple to use Lagrange, Newton or Aitken–Neville interpolation formulae. Principal lattices were generalized by Lee and Phillips, introducing three-pencil lattices, that is, points which are the intersection of three lines, each one belonging to a different pencil. In this contribution, a semicubical parabola is used to construct lattices of points with similar properties. For the construction of new lattices we use cubic pencils of lines and an addition of lines on them. AMS subject classification 41A05, 65D05, 41A63Research partially supported by the Spanish Research Grant BFM2003-03510, by Gobierno de Aragón and Fondo Social Europeo.