Machine contouring of irregularly spaced observations can be performed in three basic steps: (1) In large areas with no data points, control values are interpolated by a specified mathematical rule. These values keep the next step “well behaved.” (2) A regional polynomial surface is fitted by least squares to the original and interpolated points. (3) The surface of step (2) is deformed smoothly to pass through the original observations. The final product is similar in appearance to hand‐drawn maps. The complete mathematical theory is developed in an appendix.