The problem of reconstruction of broken surface objects embedded in 3-D space is handled. A coordinate independent representation for the crack curves is developed. A new robust matching algorithm is proposed which serves for finding matching pieces even when some brittle pieces are missing. A prototype system having an X-based GUI has been developed. This system generates artifical wire-frame data of broken pieces (with some noise) for a pot-shaped 3-D object and then recombines it using the proposed algorithms. (C) 1999 Elsevier Science Ltd. All rights reserved.