Abstract: Based on Lasserre's algorithm for volume, the concretecalculating method for shape functions and their derivatives in twointerpolation schemes are presented. The problems for caseswhere the calculation fails are discussed. Numerical simulationsillustrate that the smoothness of the shape functions in Sibson interpolantand Laplace interpolant are different. The NEM shape functions varylinearly on convex boundary, so it is easy to impose essential boundaryconditions exactly.