TPMS2STEP: error-controlled and C2 continuity-preserving translation of TPMS models to STEP files based on constrained-PIA
<|reference_start|>TPMS2STEP: error-controlled and C2 continuity-preserving translation of TPMS models to STEP files based on constrained-PIA: Triply periodic minimal surface (TPMS) is emerging as an important way of designing microstructures. However, there has been limited use of commercial CAD/CAM/CAE software packages for TPMS design and manufacturing. This is mainly because TPMS is consistently described in the functional representation (F-rep) format, while modern CAD/CAM/CAE tools are built upon the boundary representation (B-rep) format. One possible solution to this gap is translating TPMS to STEP, which is the standard data exchange format of CAD/CAM/CAE. Following this direction, this paper proposes a new translation method with error-controlling and $C^2$ continuity-preserving features. It is based on an approximation error-driven TPMS sampling algorithm and a constrained-PIA algorithm. The sampling algorithm controls the deviation between the original and translated models. With it, an error bound of $2\epsilon$ on the deviation can be ensured if two conditions called $\epsilon$-density and $\epsilon$-approximation are satisfied. The constrained-PIA algorithm enforces $C^2$ continuity constraints during TPMS approximation, and meanwhile attaining high efficiency. A theoretical convergence proof of this algorithm is also given. The effectiveness of the translation method has been demonstrated by a series of examples and comparisons.<|reference_end|>
@article{zhao2024tpms2step:,
    title={TPMS2STEP: error-controlled and C2 continuity-preserving translation of
  TPMS models to STEP files based on constrained-PIA},
    author={Yaonaiming Zhao, Qiang Zou, Guoyue Luo, Jiayu Wu, Sifan Chen, Depeng
  Gao, Minghao Xuan, Fuyu Wang},
    journal={arXiv preprint arXiv:2405.07946},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.07946},
    primaryClass={cs.CG}
}