System and method for performing undo and redo operations during machining simulation

A method associates a cell in the cADF with a machining instruction that changes a type of the cell or a type of a distance field in the cell in forming a composite surface of the workpiece to produce at least part of an association, and associates the distance field in the cell with the machining instruction changing the type of the distance field in forming the composite surface of the workpiece to produce at least part of the association. In response to receiving a command to undo a simulation of the machining to the intermediate machining instruction, a subset of cells and a subset of distance fields forming the composite surface of the workpiece at time of the simulation by the intermediate machining instruction are identified using the associate and the intermediate representation of the workpiece is determined using the subsets of cells and distance fields.