Local Hermite Interpolation by Bivariate C¹ Cubic Splines on Checkerboard Triangulations.

Given a so-call checkerboard quadrangulation ◊̄, 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 C¹ cubic splines on …. By enforcing some additional smoothness conditions across the interior edges of …, a C¹ piecewise cubic polynomial function based on … is constructed by interpolating only the function values and derivatives of first order at the vertices of ◊̄ and none of the normal derivatives at the midpoints of edges in ◊̄ is needed. It is shown that the new interpolation method produces optimal order approximation of smooth functions. [ABSTRACT FROM AUTHOR]