A family of C1 Clough-Tocher spline spaces on C0 piecewise quadratic domain partitions

The paper addresses the construction of C1 splines on a curved domain that is parametrized by a C0 piecewise geometry mapping composed of quadratic B & eacute;zier triangles. The C1 splines are assembled from polynomials of a chosen total degree greater than or equal to four, and their construction is based on the Clough-Tocher splitting technique that ensures locality. In particular, the splines are locally characterized by an interpolation problem described by Hermite data, which resembles the standard macro-element concepts developed for C1 splines on triangulations.