Recording ceramic potsherds recovered during archeological excavation is an essential task for both the archeological interpretation and conservation because of the evidence they represent. However, complete vessels provide additional data such as food storage capacity, and physical dimensions that surpasses the information that can be extracted from a single potsherd. This paper proposes a novel digital approach intended to improve the archeological registration and interpretation by the complete 3D shape reconstruction of pottery with axial symmetry based on the 2D recordings of single potsherds. A 3D laser scanner and photogrammetry are used to acquire the mesh models of potsherds and complete vessels, respectively. Subsequently, 2D generator profiles are extracted from the models by calculating the contour, axis of symmetry, and diameter of the rim's potsherd. Then, a database of profile contours of complete vessels was established, classified and utilized in the reconstruction algorithm using Principal Component Analysis (PCA) in order to obtain a 3D complete representation of pottery estimated from a single potsherd. The proposed method was applied in the study of pottery developed by Pre-Hispanic civilizations on the north coast of Peru for the preparation and consumption of a maize-based alcoholic beverage. Accuracy experiments report errors of less than 6.25% for the 3D reconstruction of complete vessels from single potsherds. Nevertheless, experiments demonstrate that the use of a large enough database in the reconstruction algorithm leads to accuracy errors less than 0.66%.