A computer-implemented method for providing a visual representation of material removal from an object by a cutting tool during a cut procedure is described. The method may comprise tracking consecutive cuts a cut trajectory of the cutting tool during the cut procedure, shape sweeping the consecutive poses of the cutting tool, and, for example, accumulating a union of the cut trajectory in a voxelized constructive solid geometry (CSG) grid to produce an object space representation of the union of the cut trajectory. The computer-implemented method may further comprise performing a CSG operation on object space representation of the union of the cut trajectory and a model of the object, and displaying a result of the CSG operation at a display screen.
