In a method and apparatus for cutting either a single sheet or a lay-up of sheets of material to derive pattern pieces or the like from the material, the material is cut segment-by-segment by bringing a fresh segment to a cutting station after a preceding segment has been entirely cut. Discontinuities, which may translate into points of non-clean cutting, which might otherwise occur in cut lines as they pass to one segment to another, because of accidental shifting or mispositioning of the material during advancement, are avoided or reduced by acquiring the start and finish X and Y coordinates of an index point on the material and then using such coordinates with the cutting instructions used in the cutting of the subsequent segment, the use of the coordinates being such that accidental shifting or mispositioning of the material is taken into account and compensated for in the cutting of the second segment.