A Unique Multivariate Hermite Interpolant on the Simplex

The objective of this paper is to construct a Hermite interpolant for arbitrary regular simplices as simple and as well-behaving as possible. The presented interpolant is unique under the given conditions and has a polynomial degree of only 3, but is the identity for quadratic polynomials-this property is not only nice, but very useful for, e.g., optimization. Last but not least the representation of the interpolant is quite simple and allows a fast implementation on a computer.