A computer simulation of machining of an object by a motion of a tool is described. The object is represented by a boundary representation (BP) object, wherein the BP object includes a boundary representation of a surface of the object, wherein the motion is represented by a set of swept volumes, wherein the set of swept volumes includes a first set of implicit functions defining a surface of the set of swept volumes. The simulation includes determining a proxy object having a second set of implicit functions defining a surface of the proxy object; simulating the machining of the proxy object with the set of swept volumes to produce a machined proxy (MP) object having a third set of implicit functions defining a surface of the MP object; rendering an image of a Boolean intersection between the MP object and the BP object.