Error Analysis of 3D Simplex Interpolation Method

The three-dimensional (3D) simplex interpolation method, which only uses the same shape and size of tetrahedrons for all points, is proposed. The maximum and root-means-square (RMS) errors are analyzed for the proposed simplex, traditional simplex and Lagrange interpolations. The interpolation regions are chosen basing on the smallest interpolation error or simpler numerical implementation. Numerical results verified that the proposed simplex interpolation makes the interpolation simple, easy to be implemented, and more efficient.