The Support Flow Tensor Field for Build-Orientation Candidate Search: Algorithm, External Audit, and a Hybrid Budget Allocation

Build orientation strongly affects support material and postprocessing in additive manufacturing; however, dense orientation sweeps with support-structure tomography (TOMO) or repeated slicer runs are expensive. This study presents the Support Flow Tensor Field (SFTF), a support-aware candidate generator that ranks directions before accurate verification by following ray-cast support paths from overhanging faces to receiving faces or to the build plate and concentrating a fixed verification budget around promising basins. Candidate generation for 2048 directions took 6.2 s per mesh (direct end-to-end measurement); against the budget-matched uniform baseline, this is pure overhead, larger than the TOMO cost of the entire 2400-cell primary budget but about 5% (CuraEngine) and 21% (PrusaSlicer) of a 10-direction slicer budget. The method was externally audited on 60 independently selected Thingi10K meshes with dense TOMO references, 30 of them also with CuraEngine 5.13 and PrusaSlicer 2.9.6, and then in a preregistered prospective confirmation on 70 further complex meshes. At 2400 cells, uniform search was near-saturated and SFTF did not establish noninferiority; as a replacement for uniform coverage at a 10-direction budget, it was not confirmed either (mean contrasts +0.003 and +0.016, intervals spanning zero). SFTF located the panel-best direction three to four times as often as uniform search but failed badly when its ranking was uninformative. Splitting the same budget, five uniform directions for coverage and five SFTF directions for exploitation, reduced that adverse tail: in an exploratory analysis of the 70 meshes the hybrid lowered mean normalized regret against uniform-10 by 0.040 (CuraEngine) and 0.058 (PrusaSlicer), and in a prespecified reanalysis of the previously analyzed 30-mesh slicer panel by 0.062 and 0.094. The hybrid allocation is therefore proposed as a candidate rule for small slicer budgets, supported on two separate samples but pending an untouched prospective test.