Support structure generation is a critical requirement in additive manufacturing (AM) to prevent material collapse in overhanging regions. However, it increases print time, material waste, and overall production cost, especially in extrusion-based AM. To mitigate these problems, design engineers often resort to manually finetuning or even redesigning prototype geometry to minimise support structures, which is time-consuming and inefficient. A direct geometric optimisation that preserves locality of shape changes whilst corresponding to the part orientation remains an underdetermined problem. In this paper, we present a novel alternating optimisation framework that finds the corresponding part geometry and orientation to minimise support structures under minimal geometric deviation. Whilst global-level support structure reduction is realised by the part orientation change, we introduce an efficient energy minimisation-based geometric optimisation framework, which is governed by saliency-aware elementwise projections and a set of manufacturing constraints. The proposed framework is validated through extensive computational and physical printing experiments employing multiple 3D printers and support structure types, on a diverse set of complex models including topologically non-trivial parts such as gyroid structures. Our results show an average reduction of 50 % in support structure print time, 27 % in material usage and 25 % in total print time, demonstrating the effectiveness of the proposed framework and its potential as a paradigm shift in manufacturing-oriented design.

• A new salient feature map is proposed to find critical points with respect to multi-axis tool orientation. • A relationship between the tool orientation compliance and the part orientation is revealed through a vector field-based approach. • A direct technique to compute a volumetric iso-tool orientation vector field for multi-axis tool path design. Part orientation is a crucial element that governs the impact of several manufacturing constraints in material extrusion-based additive manufacturing (AM). Although part orientation optimisation has been extensively investigated to improve the manufacturability in 2.5-axis AM configuration, its influence on material extrusion-based multi-axis AM remains underdetermined. In this paper, we propose a computational framework to find the optimal part orientation that maximises the compliance of the tool orientation vector field with respect to several constraints required for support-free multi-axis AM. By combining topological significance, mesh saliency and curvedness metrics, we introduce a new salient feature map to formulate the link between the part orientation and the tool orientation vector field compliance. Once the optimal orientation is computed, our method enables a direct computation of a compliant iso-tool orientation vector field for a set of input iso-tool path points. We demonstrate that the part orientation can indeed be changed to minimise tool angle variation whilst adhering to overhang angle constraints for a range of 3D mesh models. The effectiveness of the proposed method is validated by comparing our method with existing tool orientation vector field design methods. Our promising results reveal the potential in part orientation optimisation as a means to address manufacturing constraints in multi-axis tool path design.