The availability of 3D scanning devices allows to perform the process of digitisation of a growing number of diverse museum artefacts. After the properly conducted processing of the acquired point cloud, we get a photorealistic digital copy that can be presented in many ways. With regard to objects from archaeological excavations, the vast majority are artefacts that are more or less damaged or only partially preserved. Their state of preservation, specialised archaeological knowledge and the use of appropriate 3D computer technologies allow their complete digital reconstruction. The present work concerns the development of alternative methods and algorithms of conduct, the selection of programs and tools to recreate the surface of the outer and inner side and the bottom of a 12th century pitcher from the Afrasiab excavations in Uzbekistan.