Interpolation of multivariable function for dynamic programming

Hello,

I have a multivariable function, Φ, that I am trying to update numerically using dynamic programming (value function iteration). More specifically, I have three state variables, X1(3 grids), X2(2 GRIDS) and X3(2) grids. (Number of grids given as example)

Based on this grid i construct a grid space (3*3*2) which gives me the values of a function (Φ) at those grid space as:

I am curious if i can interpolate this function using interp3

something like interp3(X,Y,X0,'linear','extrap') where X are the columns of the grid and Y are the functional values corresponding to that grid and X0 is a 1*3 matrix,