Machine contouring must not introduce information which is not present in the data. The one‐dimensional spline fit has well defined smoothness properties. These are duplicated for two‐dimensional interpolation in this paper, by solving the corresponding differential equation. Finite difference equations are deduced from a principle of minimum total curvature, and an iterative method of solution is outlined. Observations do not have to lie on a regular grid. Gravity and aeromagnetic surveys provide examples which compare favorably with the work of draftsmen.