{"ID":2824783,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22502","arxiv_id":"2512.22502","title":"Topology-Preserving Scalar Field Optimization for Boundary-Conforming Spiral Toolpaths on Multiply Connected Freeform Surfaces","abstract":"Multiply connected freeform surface features are widely encountered in industrial components, where toolpath generation often suffers from discontinuities, sharp turns, non-uniform scallop heights, and incomplete boundary coverage. This paper proposes a scalar-field variational optimization method for milling that produces continuous, boundary-conforming, and non-self-intersecting toolpaths with smoother transitions, more uniform spacing, and reduced redundant path length. A feasible singularity-free initial scalar field with boundary-conforming iso-level sets is first constructed via conformal slit mapping. The optimization is then reformulated as a topology-preserving mesh deformation process governed by boundary-synchronous updates, whereby the continuity, boundary-conformity, and non-self-intersection requirements of the toolpath are converted into mesh-shape constraints maintained throughout the iterative optimization. As a result, the proposed method achieves globally optimized path spacing and improved scallop-height uniformity while preserving trajectory smoothness. Milling experiments show that, compared with a state-of-the-art conformal slit mapping-based method, the proposed approach improves machining efficiency by 14.24%, enhances scallop-height uniformity by 5.70%, and reduces milling impact-induced vibrations by over 10%. The proposed strategy provides an effective solution for high-performance machining of complex multiply connected freeform components.","short_abstract":"Multiply connected freeform surface features are widely encountered in industrial components, where toolpath generation often suffers from discontinuities, sharp turns, non-uniform scallop heights, and incomplete boundary coverage. This paper proposes a scalar-field variational optimization method for milling that prod...","url_abs":"https://arxiv.org/abs/2512.22502","url_pdf":"https://arxiv.org/pdf/2512.22502v3","authors":"[\"Shen Changqing\",\"Xu Bingzhou\",\"Qi Bosong\",\"Zhang Xiaojian\",\"Yan Sijie\",\"Ding Han\"]","published":"2025-12-27T07:05:51Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"cs.GR\"]","methods":"[]","has_code":false}