The geometrical performance of Additive Manufactured (AM) parts, particularly the influence of printing orientation on geometrical properties, is an open topic of investigation. The task of understanding geometry deviations across different printing orientations can be laborious, involving a multitude of experiments and the measurement of deviation fields. This study introduces a three-stage comprehensive methodology to address this issue. (i) An experimental investigation is conducted at varying printing orientation and the printed parts are captured by laser scanning; (ii) an automatic 3-2-1 alignment procedure of the scanned geometries is implemented, accurately replicating real positioning procedures; and (iii), Reduced-Order Modelling (ROM) is applied for the parametric mapping of deviation fields to orientation angles, creating a surrogate model of the non-nominal parts. Demonstrated with PET-G specimens, this approach can be applied to various geometries. Thanks to the surrogate model, the deviation field for any orientation can be obtained in real-time. As a result, the efficiency and accuracy of the AM process can be improved by reducing setup and scanning time when investigating different printing configurations. This allows manufacturers to focus more on part design and optimization, potentially leading to significant advancements in AM.