Local Hermite Interpolation by Bivariate C1 Cubic Splines on Checkerboard Triangulations

Given a so-call checkerboard quadrangulation 0, a checkerboard triangulation can be obtained by adding two diagonals of all quadrilaterals in In this paper, we develop a local Hermite interpolation method for bivariate C-1 cubic splines on (sic) By enforcing some additional smoothness conditions across the interior edges of (sic), a C-1 piecewise cubic polynomial function based on (sic) is constructed by interpolating only the function values and derivatives of first order at the vertices of (sic) and none of the normal derivatives at the midpoints of edges in (sic) is needed. It is shown that the new interpolation method produces optimal order approximation of smooth functions.