OUYANG Jingxuan ^{1, 2}, YANG Xue ³, XU Shengliang ³, SHI Zhonglou ⁴

(1. Gannan University of Science and Technology, Ganzhou 341000, Jiangxi, China; 2. Gongqing College of Nanchang University, Jiujiang 332020, Jiangxi, China; 3. Nanchang University, Nanchang 330031, Jiangxi, China;

4. Jianghan University, Wuhan 430090, Hubei, China)

Extended abstract:

[Background and purposes] As a vital carrier of Chinese civilization heritage, ancient stone inscriptions embody irreplaceable historical information and artistic value. However, their preservation faces severe challenges, due to natural deterioration (e.g., biodeterioration, weathering, and cracking) and human-induced interventions. In response to this conservation crisis, scholars have progressively shifted their focus from traditional documentation methods toward digital restoration, with research priorities increasingly centered on morphological reconstruction and semantic content recovery. In the transition from digital models to physical restoration, the layer-by-layer fabrication accuracy of 3D printing technology emerges as one of the decisive factors governing faithful physical reproduction. Against this backdrop, the integrated application of digital sculpting and 3D printing technologies offers a transformative solution for the restoration of ancient stone inscriptions. This paper is aimed to present a comprehensive, end-to-end digital restoration framework—from data acquisition to physical re-creation—applied specifically to the ancient stone inscriptions of Mount Lu.

[Methods] A full-process digital workflow was adopted. (1) High-precision laser scanning (SeeScan TrackScan-P542 spherical scanner with an i-Tracker optical tracker) is employed to acquire point-cloud data of the Diyishan inscription, while Geomagic Wrap software is then used for noise removal, gap filling and mesh optimization to establish a NURBS-based base surface model. (2) Using Zbrush's Alpha brush library and integrating historical documentation with curvature analysis, the weathered calligraphic strokes are digitally restored, yielding a morphologically authentic restoration model (Model A). (3) Model A is 3D printed to produce physical stone-carving specimens with a Tuozhu Lab X1 3D printer. (4) The printed specimens are re-scanned using a 3D scanner to generate reconstructed digital models (Model B). (5) Finally, PolyWorks software is utilized to perform quantitative accuracy analysis, i.e., measuring deviation errors between Model A (digital restoration) and Model B (physical reconstruction).

[Results]

1. Accuracy Analysis of Dimensional Deviations in 3D-Printed Ancient Stone Inscription Specimens

The character "Di" (第), exhibiting pronounced morphological distortion, is selected as the representative subject for analysis. Forty-one characteristic nodes are systematically distributed along its contour curve and the contour deviation at each node is computed. In the vertical direction, nodes No. 1–22 (top region of the character) exhibit negative normal deviations, indicating localized material loss, whereas nodes No.23–41 (lower region) show positive normal deviations, reflecting localized material excess. After measuring all contour deviations, the maximum and minimum deviation values per specimen are extracted, while their arithmetic difference, the total contour deviation, is calculated. It is found that Sample 1 [Fig. 10 (a)] achieves the smallest total deviation (0.293 mm), while Sample 5 [Fig. 10 (e)] exhibits the largest value (0.788 mm).

2.Range Analysis of the Orthogonal Experiment and Identification of the Optimal Parameter Combination

An experimental matrix is constructed based on the L₉(3⁴) orthogonal array, with total contour deviation adopted as the quantitative evaluation metric. For each parameter combination, the arithmetic mean and range (R) of total contour deviation are calculated. This enables systematic analysis of how process parameters influence dimensional accuracy of polymer-based stone-carving specimens, revealing both the relative significance of each factor and the optimal parameter configuration.

Range analysis yields the factor importance ranking of C>A>B>D, i.e., print orientation (C) exerts the strongest influence on total contour deviation, followed by print temperature (A), print speed (B) and infill density (D), confirming that print orientation is the dominant determinant of morphological fidelity. The minimal total contour deviation of 0.218 mm is achieved under the settings, including print temperature=210 ℃, print speed=10 mm·s⁻¹, print orientation=45° and infill density=15%. The optimized combination ensures superior printing performance.

3. Verification Experiment for the Optimal Parameter Combination

To validate the robustness and generalizability of the identified optimal parameters, a verification experiment is conducted using a locally scanned and digitally restored section of Huang Tingjian's ancient stone inscription Verses of the Seven Buddhas (七佛偈). Using the same optimal parameter combination and printing machine, a physical specimen is fabricated and subsequently rescanned to obtain its reconstructed model (Model B). Co-registration and deviation analysis between Model A (the restoration model of Verses of the Seven Buddhas) and Model B yield a total contour deviation of 0.270 mm, only 0.052 mm higher than the minimal deviation (0.218 mm) observed for the "第" character in the Diyishan inscription. This close agreement strongly confirms the effectiveness and transferability of the optimized printing parameters.

[Conclusions] The following conclusions have been arrived. (1) A complete technical workflow has been established, "Authentic- State Restoration Model of the Ancient Stone Inscription (Model A)→Polymer-based 3D-Printed Stone-Carving Specimen→ Reconstructed Digital Model of the Printed Specimen (Model B)→Quantitative Deviation and Accuracy Analysis via Co-Registration of Models A and B." This pipeline provides a robust technical foundation for digital replication and parametric optimization of ancient stone inscriptions. (2) Following surface restoration of the Diyishan inscription, the maximum deviation between Model A and Model B falls within the range of −0.3126 mm to +0.3126 mm, demonstrating high fidelity in geometric reproduction of the original inscription’s morphology. (3) The contour profile of the printed specimens exhibits pronounced regional variation, where the top region shows localized thickness reduction, while the bottom region displays localized thickness increase, revealing distinct regional forming characteristics (i.e., differential material deposition and solidification behavior) across the print volume during fabrication. (4) Across all orthogonal parameter combinations, the total contour deviation of printed specimens ranges from 0.293 mm to 0.788 mm. The most influential process parameters, ranked by impact magnitude on total deviation, are print orientation>print temperature>print speed, whereas infill density exerts a negligible effect on printing accuracy. (5) With minimization of total contour deviation as the optimization objective, the optimal parameter combination is identified as A₁B₁C₂D₁, corresponding to print temperature of 210 ℃, print speed of 10 mm·s⁻¹, print orientation of 45° and infill density of 15%.

Key words: ancient stone inscriptions; 3D printing; 3D scanning; restoration model; reconstructed