Abstract: A polishing machine is described in which a surface treatment tool is moved across the surface of a workpiece in accordance with a predefined tool-path, in order to carry out the desired treatment process. The tool-path is non-periodic and preferably pseudo-random. Various techniques are described for generating data representing the tool-path to be followed. A technique is also described for determining optimum control parameters used to control the polishing machine for a given tool-path. The surface treatment may be a shaping technique in which material is removed from the surface, or a technique for adding material to the surface of the workpiece, or a technique for modifying the surface or a region under the surface of the workpiece.