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Additive Manufacturing (AM) has emerged as an innovative technology that gives designers several advantages, such as geometric freedom of design and less waste. However, the quality of the parts produced is affected by different design and manufacturing parameters, such as the part orientation, the nozzle temperature and speed, the support material, and the layer thickness. In this context, the layer thickness is considered an important AM parameter affecting the part quality and accuracy. Thus, in this paper, a new adaptative slicing method based on the cusp vector and the surface deviation is proposed with the aim of minimizing the dimensional defects of FFF printed parts and investigate the impact on the dimensional part tolerancing. An algorithm is developed to automatically extract data from the STL file, select the build orientation, and detect intersection points between the initial slicing and the STL mesh. The innovation of this algorithm is exhibited via adapting the slicing according to the surface curvature based on two factors: the cusp vector and the surface deviation. The suggested slicing technique guarantees dimensional accuracy, especially for complex feature shapes that are challenging to achieve using a uniform slicing approach. Finally, a preview of the slicing is displayed, and the G-code is generated to be used by the FFF machine. The case study consists of the dimensional tolerance inspection of prototypes manufactured using the conventional and adaptive slicing processes. The proposed method's effectiveness is investigated using RE and CMM processes. The method demonstrates its reliability through the observed potential for accuracy improvements exceeding 0.6% and cost savings of up to 4.3% in specific scenarios. This reliability is substantiated by comparing the resulting dimensional tolerances and manufacturing costs. [ABSTRACT FROM AUTHOR]