Traversing x direction:

\[ f(x, y_1) = \frac{x_2-x}{x_2-x_1}f(x_1,y_1)+\frac{x-x_1}{x_2-x_1}f(x_2,y_1) \]

\[ f(x,y_2)=\frac{x_2-x}{x_2-x_1}f(x_1,y_2)+\frac{x-x_1}{x_2-x_1}f(x_2,y_2) \]

Traversing y direction:

\[ f(x, y) = \frac{y_2-y}{y_2-y_1}f(x,y_1)+\frac{y-y_1}{y_2-y_1}f(x,y_2) \]