Simplified calculation of rHCT basis functions for an arbitrary splitting

Reduced Hsieh-Clough-Tocher elements are triangular C1-elements with only nine degrees of freedom. Simple formulas for the basis functions of reduced Hsieh-Clough-Tocher elements based on the edge vectors of the triangle have been given recently for a barycentric splitting. We generalise these formulas to the case of an arbitrary splitting point.:1 Introduction 2 Basic definitions 3 Mapping to the reference triangle 4 Construction of the rHCT shape function