Analysis of three-dimensional grids: Cubic equations for nine-point prismatic arrays

Four polynomial equations for interpolating the nine-point cube are compared. All of the equations estimate first-, second- and third-order coefficients. Fidelity to monotonic test surfaces, as measured by sums-of-squares of deviations, depends on the distribution of the center point datum among the coefficients. Linear-term coefficients rendered by the equations are often more accurate than the like coefficients rendered by main-effects formulas.