Polynomial interpolation in R2 and on the unit sphere in R3

We construct new Hermite interpolation schemes in , and Lagrange and Hermite interpolation schemes on the unit sphere in . We show that the Hermite projectors in are the limits of Lagrange projectors at Bos configurations distributed on lines and circles in . Using this result we prove that the Lagrange projectors on the unit sphere converge to the Hermite projectors when the interpolation points coalesce.