Deriving an expression for minimum arc length along a 3D surface between any two points.

Question

Consider a 3D surface, defined by the function $z = f(x, y)$. Assuming the surface is differentiable (no kinks), is there a function that expresses the minimum arc length traced along the surface between any two points $(x_0, y_0)$ and $(x_1, y_1)$?