Convexity of Bẻzier nets on sub-triangles

This note generalizes a result of Goodman[3], where it is shown that the convexity of Bèzier nets defined on a base triangle is preserved on sub-triangles obtained from a mid-point subdivision process. Here we show that the convexity of Bèzier nets is preserved on and only on sub-triangles that are "parallel" to the base triangle

On a class of polynomial triangular macro-elements

AbstractIn this paper we present a new class of polynomial triangular macro-elements of arbitrary degree which are an extension of the classical Clough-Tocher cubic scheme. Their most important property is that the degree plays the role of a tension parameter, since these macro elements tend to the plane interpolating the vertices data. Graphical examples showing their use in scattered data interpolation are reported