Computerized control systems for machine tools must generate coordinated movements of the separately driven axes of motion in order to trace accurately a predetermined path of the cutting tool relative to the workpiece. However, since the dynamic properties of the individual machine axes are not exactly equal, undesired contour errors are generated. The contour error is defined as the distance ...

Recent progress is described on the unsolved problem of unfolding the surface of an orthogonal polyhedron to a single non-overlapping planar piece by cutting edges of the polyhedron. Although this is in general not possible, partitioning the faces into the natural vertex-grid may render it always achievable. Advances that have been made on various weakenings of this central problem are summariz...