ACM Transactions on Graphics · SIGGRAPH Asia 2026 · Conditionally accepted

Field Optimization for Scalable and Distortion-Aware Process Planning in Hybrid Additive-Subtractive Manufacturing

Yongxue Chen · Tao Liu · Aoran Lyu · Yu Jiang · Neelotpal Dutta · Charlie C.L. Wang^†

Digital Manufacturing Laboratory · The University of Manchester

^†Corresponding author

Overview figure web-assets/fig-01-overview.webp · recommended 16:7

By formulating hybrid manufacturing (HM) process planning as an optimization problem over continuous fields, our method reduces the estimated fabrication time by 68.3% on the GE-Bracket model and controls distortion in intermediate structures, as indicated by the displacements and the histograms obtained from finite element analysis. Owing to the continuous field representation, our method gives much smaller geometric approximation errors (see the color map in the left) and preserves small geometric features (see the zoom-views) while maintaining a computation time comparable to that of the voxel-based method [Chen et al. 2025] in low-resolution. The frequency spectra of local tool-motion velocities further demonstrate the improved continuity of the operations generated by our approach. Moreover, the proposed formulation naturally extends to advanced HM platforms with 3-axis additive and 5-axis subtractive-manufacturing capabilities.

Abstract

This paper presents a field-based optimization method for process planning in hybrid manufacturing, where the goal is to determine a feasible and efficient sequence of additive and subtractive operations for fabricating a target shape. Existing approaches rely on deterministic or discretized formulations, which lead to unoptimized fabrication time and make planning sensitive to voxel resolution. They also do not explicitly account for distortion in intermediate structures formed during manufacturing. To address these limitations, we represent manufacturing states using continuous fields, which scale naturally to models with large dimensions and fine geometric features while enabling smoother fabrication sequences. Based on this representation, we formulate process planning as a numerical optimization problem under multiple objectives, including final shape conformance, intermediate structural strength, manufacturing time, self-supporting and collision-free. Experimental results show that our method can generate distortion-aware process plans on a variety of models while substantially reducing fabrication time through up to a 72.6% reduction in the volume of extra support.

Video

Method

Computational pipeline web-assets/fig-03-pipeline.webp · recommended 2:1

Illustration of the computational pipeline of our field-optimization-based HM process planning approach. The sequence of AM/SM operations for an input model M is determined by five implicit fields: (t_AM(x), t_SM(x), p_AM(x), p_SM(x), N_CC(x)). The optimization of these fields is driven by minimizing loss terms associated with shape-conformance L_shp, support volume L_vol, structural distortion L_str, self-supporting constraints L_spt, and AM/SM collision avoidance, denoted by L_cAM and L_cSM, respectively. After the implicit fields are determined, the AM layers and SM sequences are extracted and sorted in the post-processing step, followed by toolpath generation.

Experiments

Fig. 4 · Complex geometry web-assets/fig-04-femur.webp

Fabrication of a Femur model with complex geometry (genus 98). (a) SM-only: using only SM operations cannot form the internal porous structures. (b) AM-only: when using only AM operations, the internal support structures cannot be removed after fabrication. The results in (a) and (b) are both generated by Autodesk Fusion. (c) HM: the exact target model can be fabricated through the interlaced AM and SM operations generated by our approach, with the corresponding AM layers and SM sequences shown on the right.

Fig. 10 · Distortion ablation web-assets/fig-10-distortion-ablation.webp

Ablation study of the structural distortion loss L_str on the Fertility model. The loss L_str penalizes excessive deformation in intermediate structures during fabrication. Panel (a) shows the result optimized with L_str, where distortion at the evaluated fabrication height is controlled. Panel (b) shows the result optimized without L_str; a floating component is formed, as highlighted in the zoomed view. Panel (c) compares the maximum-displacement histograms over all intermediate structures and shows substantially larger distortion when the loss is disabled.

Fig. 15 · Scalability web-assets/fig-15-scalability.webp

Scalability study on the GE-Bracket model at different dimensions. Comparison of (a) the voxel-based method [Chen et al. 2025] and (b) our field-based method. The four plots report support-volume ratio (top left), maximum and mean geometric error (top right), operation jumps (bottom left), and total AM+SM manufacturing time (bottom right). As model size increases, the field-based method produces fewer jumps and requires less manufacturing time.

Fig. 17 · Physical validation web-assets/fig-17-physical-models.webp

Physical models fabricated using a desktop hybrid manufacturing machine, with fabrication times shown in parentheses. (a) GE-Bracket (16 hours), (b) MBB Beam (5 hours), (c) Femur (23 hours), and (d) Cantilever Bracket (6 hours).

Citation

@article{chen2026fieldoptimization,
  title   = {Field Optimization for Scalable and Distortion-Aware
             Process Planning in Hybrid Additive-Subtractive Manufacturing},
  author  = {Chen, Yongxue and Liu, Tao and Lyu, Aoran and Jiang, Yu
             and Dutta, Neelotpal and Wang, Charlie C. L.},
  journal = {ACM Transactions on Graphics (SIGGRAPH Asia)},
  year    = {2026},
  note    = {Conditionally accepted}
}

Contact

Digital Manufacturing Laboratory · The University of Manchester

Yongxue Chen yongxue.chen@manchester.ac.uk Charlie C.L. Wang charlie.wang@manchester.ac.uk