Local Lagrange interpolation by quintic C1C1 splines on type-6 tetrahedral partitions

We develop a Lagrange interpolation method for quintic C1C1 splines on cube partitions with 24 tetrahedra in each cube. The construction of the interpolation points is based on a new priority principle by decomposing the tetrahedral partition into special classes of octahedra such that no tetrahedron has to be refined. It follows that the interpolation method is local and stable, and has optimal approximation order six and linear complexity. The interpolating splines are uniquely determined by data values, but no derivatives are needed.