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Innovative Surface Merging Method for Generating Point-Based Skin Model Shapes Considering Processing Features

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Abstract

Virtual prototypes have been appealing in the early design stage of computer aided tolerancing, because it is less expensive to evaluate and modify tolerances numerically. Derived from the machining processes, form uncertainties are simulated, controlled and analyzed in virtual prototypes using parametric and intuitive surface patches. The generation of a complete virtual prototype often involves combining surface patches with different patterns to one complete model. To overcome possible geometric defects in this process, a surface merging method is proposed in this paper. Skin Model Shapes is first introduced as the geometric foundation. The whole part surface is segmented based on the geometric shape and machining type. Then point-based patches are generated accordingly. Interpolation implicit surfaces based on radial basis function networks are constructed in patch boundaries based on spatial-constrained homogeneous transformation matrices. A feature augmentation process is then introduced to preserve processing features after resampling the blend patch. The proposed method is proved to be efficient in feature retaining as well as surface smoothing, through numerical experiments and analysis on an example mechanical part. The results show that the generated virtual prototype would become 62.5% more smooth while retaining a 91.6% feature similarity after using the proposed method. Moreover, the proposed method could preserve 174% more features at a cost of 9.0% smoothness than using a conventional modified trimmed filtering method.

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References

  1. Wang, G. G. (2002). Definition and review of virtual prototyping. Journal of Computing and Information Science in Engineering, 2(3), 232–236.

    Google Scholar 

  2. Zhu, Z., Qiao, L., & Anwer, N. (2016). An improved tolerance analysis method based on skin model shapes of planar parts. Procedia CIRP, 56, 237–242.

    Google Scholar 

  3. Zeng, W., & Rao, Y. (2019). Modeling of assembly deviation with considering the actual working conditions. International Journal of Precision Engineering and Manufacturing, 20(5), 791–803.

    Google Scholar 

  4. Morse, E., Dantan, J. Y., Anwer, N., Söderberg, R., Moroni, G., Qureshi, A., et al. (2018). Tolerancing: Managing uncertainty from conceptual design to final product. CIRP Annals, 67(2), 695–717.

    Google Scholar 

  5. Calvo, R., Gómez, E., & Domingo, R. (2014). Vectorial method of minimum zone tolerance for flatness, straightness, and their uncertainty estimation. International Journal of Precision Engineering and Manufacturing, 15(1), 31–44.

    Google Scholar 

  6. Anselmetti, B., Chavanne, R., Yang, J. X., & Anwer, N. (2010). Quick GPS: A new CAT system for single-part tolerancing. CAD Computer Aided Design, 42(9), 768–780.

    Google Scholar 

  7. Heling, B., Aschenbrenner, A., Walter, M. S. J., & Wartzack, S. (2016). On connected tolerances in statistical tolerance-cost-optimization of assemblies with interrelated dimension chains. In Procedia CIRP, vol. 43, pp. 262–267. Elsevier B.V.

  8. Mujezinović, A., Davidson, J. K., & Shah, J. J. (2004). A new mathematical model for geometric tolerances as applied to polygonal faces. Journal of Mechanical Design, Transactions of the ASME, 126(3), 504–518.

    Google Scholar 

  9. Ameta, G., Davidson, J. K., & Shah, J. J. (2007). Tolerance-maps applied to a point-line cluster of features. Journal of Mechanical Design, Transactions of the ASME, 129(8), 782–792.

    Google Scholar 

  10. Ameta, G., Davidson, J. K., & Shah, J. (2010). Influence of form on tolerance-map-generated frequency distributions for 1D clearance in design. Precision Engineering, 34(1), 22–27.

    Google Scholar 

  11. Giordano, M., Samper, S., & Petit, J. P. (2007). Tolerance analysis and synthesis by means of deviation domains, axi-symmetric cases. In Models for computer aided tolerancing in design and manufacturing - selected conference papers from the 9th CIRP international seminar on computer-aided Tolerancing, CAT 2005, pp. 85–94.

  12. Chen, H., Jin, S., Li, Z., & Lai, X. (2015). A modified method of the unified Jacobian–Torsor model for tolerance analysis and allocation. International Journal of Precision Engineering and Manufacturing, 16(8), 1789–1800.

    Google Scholar 

  13. Chitale, A. N., Davidson, J. K., & Shah, J. J. (2019). Statistical tolerance analysis with sensitivities established from tolerance-maps and deviation spaces. Journal of Computing and Information Science in Engineering, 19(4).

  14. Desrochers, A., Ghie, W., & Laperrière, L. (2003). Application of a unified Jacobian–Torsor model for tolerance analysis. Journal of Computing and Information Science in Engineering, 3(1), 2–14.

    MATH  Google Scholar 

  15. Chen, W., Xie, W., Huo, D., & Yang, K. (2018). A novel 3D surface generation model for micro milling based on homogeneous matrix transformation and dynamic regenerative effect. International Journal of Mechanical Sciences, 144, 146–157.

    Google Scholar 

  16. Jeevanantham, A. K., Chaitanya, S. V., & Rajeshkannan, A. (2019). Tolerance analysis in selective assembly of multiple component features to control assembly variation using matrix model and genetic algorithm. International Journal of Precision Engineering and Manufacturing, 20(10), 1801–1815.

    Google Scholar 

  17. Song, C., Zhou, Y., & Luo, C. (2019). Geometric tolerance modeling method based on B-spline parameter space envelope. In Proceedings of 2019 IEEE international conference on mechatronics and automation, ICMA 2019, pp. 2058–2063. IEEE.

  18. Luo, C., Franciosa, P., Ceglarek, D., Ni, Z., & Jia, F. (2018). A novel geometric tolerance modeling inspired by parametric space envelope. IEEE Transactions on Automation Science and Engineering, 15(3), 1386–1398.

    Google Scholar 

  19. Lin, E. E. (2000). Graph-matrix-based automated tolerance analysis and setup planning in computer-aided process planning. Ph.D. thesis, Texas Tech University.

  20. Zhang, K., Li, Y., & Tang, S. (2010). An integrated modeling method of unified tolerance representation for mechanical product. International Journal of Advanced Manufacturing Technology, 46(1–4), 217–226.

    Google Scholar 

  21. Schleich, B., Wartzack, S., Anwer, N., & Mathieu, L. (2015). Skin model shapes: Offering new potentials for modelling product shape variability. Proceedings of the ASME Design Engineering Technical Conference, 1A–2015, 1–9.

    Google Scholar 

  22. Schleich, B., & Wartzack, S. (2013). How to determine the influence of geometric deviations on elastic deformations and the structural performance? Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 227(5), 754–764.

    Google Scholar 

  23. Ameta, G., Serge, S., & Giordano, M. (2011). Comparison of spatial math models for tolerance analysis: Tolerance-maps, deviation domain, and TTRS. Journal of Computing and Information Science in Engineering, 11(2),

  24. Anwer, N., Ballu, A., & Mathieu, L. (2013). The skin model, a comprehensive geometric model for engineering design. CIRP Annals - Manufacturing Technology, 62, 143–146.

    Google Scholar 

  25. Anwer, N., Schleich, B., Mathieu, L., & Wartzack, S. (2014). From solid modelling to skin model shapes: Shifting paradigms in computer-aided tolerancing. CIRP Annals - Manufacturing Technology, 63(1), 137–140.

    Google Scholar 

  26. Schleich, B., Anwer, N., Mathieu, L., & Wartzack, S. (2016). Status and prospects of skin model shapes for geometric variations management. Procedia CIRP, 43, 154–159.

    Google Scholar 

  27. Pottmann, H., Leopoldseder, S., Hofer, M., Steiner, T., & Wang, W. (2005). Industrial geometry: Recent advances and applications in CAD. CAD Computer Aided Design, 37(7), 751–766.

    Google Scholar 

  28. Schleich, B., & Wartzack, S. (2015). Tolerance analysis of rotating mechanism based on skin model shapes in discrete geometry. Procedia CIRP, 27, 10–15.

    Google Scholar 

  29. Homri, L., Goka, E., Levasseur, G., & Dantan, J. Y. (2017). Tolerance analysis: Form defects modeling and simulation by modal decomposition and optimization. CAD Computer Aided Design, 91, 46–59.

    Google Scholar 

  30. Yan, X., & Ballu, A. (2016). Toward an automatic generation of part models with form error. Procedia CIRP, 43, 23–28.

    Google Scholar 

  31. Yan, X., & Ballu, A. (2017). Generation of consistent skin model shape based on FEA method. International Journal of Advanced Manufacturing Technology, 92(1–4), 789–802.

    Google Scholar 

  32. Corrado, A., & Polini, W. (2018). FEA integration in the tolerance analysis using Skin Model Shapes. In Procedia CIRP.

  33. Liu, T., Zhao, Q., Cao, Y., & Yang, J. (2018). A generic approach for analysis of mechanical assembly. Precision Engineering, 54, 361–370.

    Google Scholar 

  34. Ting, L., Zuowei, Z., Yanlong, C., Anwer, N., & Jiangxin, Y. (2018). Consideration of working conditions in assembly tolerance analysis. Procedia CIRP, 75, 226–231.

    Google Scholar 

  35. Yacob, F., Semere, D., & Nordgren, E. (2018). Octree-based generation and variation analysis of skin model shapes. Journal of Manufacturing and Materials Processing, 2(3), 52.

    Google Scholar 

  36. Yacob, F., Semere, D., & Nordgren, E. (2019). Anomaly detection in Skin Model Shapes using machine learning classifiers. International Journal of Advanced Manufacturing Technology, pp. 3677–3689.

  37. Corrado, A., & Polini, W. (2017). A comprehensive study of tolerance analysis methods for rigid parts with manufacturing signature and operating conditions. Journal of Advanced Mechanical Design, Systems and Manufacturing, 11(2), 1–21.

    Google Scholar 

  38. Corrado, A., Polini, W., Moroni, G., & Petrò, S. (2018). A variational model for 3D tolerance analysis with manufacturing signature and operating conditions. Assembly Automation, 38(1), 10–19.

    Google Scholar 

  39. Garaizar, O. R., Qiao, L., Anwer, N., & Mathieu, L. (2016). Integration of thermal effects into tolerancing using skin model shapes In Procedia CIRP.

  40. Schleich, B., & Wartzack, S. (2015). Approaches for the assembly simulation of skin model shapes. CAD Computer Aided Design, 65, 18–33.

    Google Scholar 

  41. Liu, J., Zhang, Z., Ding, X., & Shao, N. (2018). Integrating form errors and local surface deformations into tolerance analysis based on skin model shapes and a boundary element method. CAD Computer Aided Design, 104, 45–59.

    Google Scholar 

  42. Zhang, Z., Liu, J., Ding, X., & Shao, N. (2018). Tolerance analysis of annular surfaces considering form errors and local surface deformations. Procedia CIRP, 75, 291–296.

    Google Scholar 

  43. Yan, X., & Ballu, A. (2018). Tolerance analysis using skin model shapes and linear complementarity conditions. Journal of Manufacturing Systems, 48(July), 140–156.

    Google Scholar 

  44. Yan, H., Cao, Y., & Yang, J. (2016). Statistical tolerance analysis based on good point set and homogeneous transform matrix. Procedia CIRP, 43, 178–183.

    Google Scholar 

  45. Schleich, B., & Wartzack, S. (2016). A quantitative comparison of tolerance analysis approaches for rigid mechanical assemblies. Procedia CIRP, 43, 172–177.

    Google Scholar 

  46. Samper, S., Adragna, P. A., Favreliere, H., & Pillet, M. (2009). Modeling of 2D and 3D assemblies taking into account form errors of plane surfaces. Journal of Computing and Information Science in Engineering, 9(4), 1–12.

    Google Scholar 

  47. Corrado, A., Polini, W., Moroni, G., & Petrò, S. (2016). 3D tolerance analysis with manufacturing signature and operating conditions. Procedia CIRP, 43, 130–135.

    Google Scholar 

  48. Polini, W., & Moroni, G. (2015). Manufacturing signature for tolerance analysis. Journal of Computing and Information Science in Engineering, 15(1).

  49. Corrado, A., & Polini, W. (2017). Manufacturing signature in variational and vector-loop models for tolerance analysis of rigid parts. International Journal of Advanced Manufacturing Technology, 88(5–8), 2153–2161.

    Google Scholar 

  50. Henke, R. P., Summerhays, K. D., Baldwin, J. M., Cassou, R. M., & Brown, C. W. (1999). Methods for evaluation of systematic geometric deviations in machined parts and their relationships to process variables. Precision Engineering.

  51. Summerhays, K. D., Henke, R. P., Baldwin, J. M., Cassou, R. M., & Brown, C. W. (2002). Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations. Precision Engineering, 26(1), 105–121.

    Google Scholar 

  52. Xiaokai, M., Sun, Q., Jiawen, X., Chai, Z., Sun, W., & Zhao, B. (2019). Feasibility analysis of the replacement of the actual machining surface by a 3D numerical simulation rough surface. International Journal of Mechanical Sciences, 150(2018), 135–144.

    Google Scholar 

  53. Jin, J., & Shi, J. (1999). Feature-preserving data compression of stamping tonnage information using wavelets. Technometrics, 41(4), 327–339.

    Google Scholar 

  54. Zahouani, H., Mezghani, S., Vargiolu, R., & Dursapt, M. (2008). Identification of manufacturing signature by 2D wavelet decomposition. Wear, 264(5–6), 480–485.

    Google Scholar 

  55. Roy, U., & Li, B. (1999). Representation and interpretation of geometric tolerances for polyhedral objects- I. Form tolerances. CAD Computer Aided Design, 31(4), 273–285.

    MATH  Google Scholar 

  56. Roy, U., & Li, B. (1999). Representation and interpretation of geometric tolerances for polyhedral objects. II. Size, orientation and position tolerances. CAD Computer Aided Design, 31(4), 273–285.

    MATH  Google Scholar 

  57. Weckenmann, A., Eitzert, H., Garmer, M., & Weber, H. (1995). Functionality-oriented evaluation and sampling strategy in coordinate metrology. Precision Engineering, 17(4), 244–252.

    Google Scholar 

  58. Zhang, T., Liu, Z. Q., Shi, Z. Y., & Xu, C. H. (2013). Size effect on surface roughness in micro turning. International Journal of Precision Engineering and Manufacturing.

  59. Yuan, Y., Zhang, D., Jing, X., Hanyu Zhu, W., Zhu, L., Cao, J., et al. (2019). Fabrication of hierarchical freeform surfaces by 2D compliant vibration-assisted cutting. International Journal of Mechanical Sciences, 152(2018), 454–464.

    Google Scholar 

  60. Subramanya Udupa, N. G., Shunmugam, M. S., & Radhakrishnan, V. (1987). Optimizing workpiece position in centreless grinding by roundness profile analysis. Precision Engineering, 9(1), 23–30.

    Google Scholar 

  61. Cho, N., & Tu, J. (2001). Roundness modeling of machined parts for tolerance analysis. Precision Engineering, 25(1), 35–47.

    Google Scholar 

  62. Cai, M., Yang, J. X., & Zhao Tong, W. (2004). Mathematical model of cylindrical form tolerance. Journal of Zhejiang University: Science, 5(7), 890–895.

    Google Scholar 

  63. Turk, G., O’Brien, J.F. (2005). Shape transformation using variational implicit functions. In ACM SIGGRAPH, 2005, courses, SIGGRAPH, 2005

  64. Moroni, G., & Pacella, M. (2008). An approach based on process signature modeling for roundness evaluation of manufactured items. Journal of Computing and Information Science in Engineering, 8(2), 0210031–02100310.

    Google Scholar 

  65. Teixeira, C. A. R., & Cavalca, K. L. (2008). Reliability as an added-value factors in an automotive clutch system. Quality and Reliability Engineering International, 24(2007), 229–248.

    Google Scholar 

  66. Colosimo, B. M., Semeraro, Q., & Pacella, M. (2008). Statistical process control for geometric specifications: On the monitoring of roundness profiles. Journal of Quality Technology, 40(1), 1–18.

    Google Scholar 

  67. Masoudi, S., Esfahani, M. J., Jafarian, F., & Mirsoleimani, S. A. (2019). Comparison the effect of MQL, wet and dry turning on surface topography, cylindricity tolerance and sustainability. International Journal of Precision Engineering and Manufacturing-Green Technology, 6(2), 100–113.

    Google Scholar 

  68. Ranganath Nayak, P. (1971). Random process model of rough surfaces. Journal of Tribology, 93(3), 398–407.

    Google Scholar 

  69. Du, S., & Fei, L. (2016). Co-kriging method for form error estimation incorporating condition variable measurements. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 138(4).

  70. Zhou, W., Tang, J., Chen, H., & Shao, W. (2019). A comprehensive investigation of surface generation and material removal characteristics in ultrasonic vibration assisted grinding. International Journal of Mechanical Sciences, 156, 14–30.

    Google Scholar 

  71. Grandgirard, J., Poinsot, D., Krespi, L., Nénon, J. P., & Cortesero, A. M. (2002). Costs of secondary parasitism in the facultative hyperparasitoid Pachycrepoideus dubius: Does host size matter? Entomologia Experimentalis et Applicata, 103(3), 239–248.

    Google Scholar 

  72. Moroni, G., & Rasella, M. (2007). Application of regression spline to reverse modeling. Journal of Computing and Information Science in Engineering, 7(1), 95–101.

    Google Scholar 

  73. Na, D. H., & Lee, Y. (2013). A study to predict the creation of surface defects on material and suppress them in caliber rolling process. International Journal of Precision Engineering and Manufacturing, 14(10), 1727–1734.

    Google Scholar 

  74. Frerichs, F., Sölter, J., Lübben, T., Brinksmeier, E., & Zoch, H. W. (2016). A simulation based development of process signatures for manufacturing processes with thermal loads. Procedia CIRP, 45, 327–330.

    Google Scholar 

  75. Pereira, A. M. B., De Arruda, M. C., Antônio, A. C., Lira, W. W. M., & Martha, L. F. (2012). Boolean operations on multi-region solids for mesh generation. In Engineering with Computers, vol. 28, pp. 225–239.

  76. Wang, K., Shichang, D., & Xi, L. (2019). Three-dimensional tolerance analysis modelling of variation propagation in multi-stage machining processes for general shape workpieces. International Journal of Precision Engineering and Manufacturing, 15(9), 1883–1888.

    Google Scholar 

  77. Le Goic, G., Favrelière, H., Samper, S., & Formosa, F. (2011). Multi scale modal decomposition of primary form, waviness and roughness of surfaces. Scanning, 33(5), 332–341.

    Google Scholar 

  78. Capello, E., & Semeraro, Q. (2001). The harmonic fitting method for the assessment of the substitute geometry estimate error. Part I: 2D and 3D theory. International Journal of Machine Tools and Manufacture, 41(8), 1071–1102.

    Google Scholar 

  79. Capello, E., & Semeraro, Q. (2001). The harmonic fitting method for the assessment of the substitute geometry estimate error. Part II: Statistical approach, machining process analysis and inspection plan optimisation. International Journal of Machine Tools and Manufacture, 41(8), 1103–1129.

    Google Scholar 

  80. Maharshi, K., Mukhopadhyay, T., Roy, B., Roy, L., & Dey, S. (2018). Stochastic dynamic behaviour of hydrodynamic journal bearings including the effect of surface roughness. International Journal of Mechanical Sciences, 142–143(April), 370–383.

    Google Scholar 

  81. Bubna, K., & Stewart, C. V. (1998). Model selection and surface merging in reconstruction algorithms. In Proceedings of the IEEE international conference on computer vision.

  82. Sheng, W., Xi, N., Song, M., & Chen, Y. (2001). Graph-based surface merging in CAD-guided dimensional inspection of automotive parts.

  83. Huang, H., Wu, S., Gong, M., Cohen-Or, D., Ascher, U., & Zhang, H. R. (2013). Edge-aware point set resampling. ACM Transactions on Graphics, 32(1).

  84. Öztireli, A. C., Guennebaud, G., & Gross, M. (2009). Feature preserving point set surfaces based on non-linear kernel regression. Computer Graphics Forum, 28(2), 493–501.

    Google Scholar 

  85. Xiao, C., Zheng, W., Miao, Y., Zhao, Y., & Peng, Q. (2007). A unified method for appearance and geometry completion of point set surfaces. Visual Computer, 23(6), 433–443.

    Google Scholar 

  86. Harary, G., Tal, A., & Grinspun, E. (2014). Context-based coherent surface completion. ACM Transactions on Graphics, 33(1).

  87. Park, S., Guo, X., Shin, H., & Qin, H. (2005). Shape and appearance repair for incomplete point surfaces. Proceedings of the IEEE International Conference on Computer Vision, II, 1260–1267.

    Google Scholar 

  88. Weyrich, T., Pauly, M., Heinzle, S., Keiser, R., Scandella, S., & Gross, M. (2004). Post-processing of Scanned 3D surface data.

  89. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., & Silva, C. T. (2013). Point set surfaces. Proceedings of the IEEE Visualization Conference, 21–28, 2001.

    Google Scholar 

  90. Zwicker, M., Pfister, H., Van Baar, J., & Gross, M. (2001). Surface splatting. In Proceedings of the 28th annual conference on computer graphics and interactive techniques, SIGGRAPH 2001, pp. 371–378.

  91. Davis, J., Marschner, S. R., Garr, M., & Levoy, M. (2002). Filling holes in complex surfaces using volumetric diffusion. In Proceedings 1st international symposium on 3D data processing visualization and transmission, 3DPVT 2002, pp. 428–441.

  92. Sederberg, T. W., Zheng, J., Bakenov, A., & Nasri, A. (2003). T-splines and T-NURCCs. In ACM SIGGRAPH 2003 papers, SIGGRAPH ’03, pp. 477–484.

  93. Lai, J., Jianzhong, F., Shen, H., Gan, W., & Chen, Z. (2015). Machining error inspection of T-spline surface by on-machine measurement. International Journal of Precision Engineering and Manufacturing, 16(3), 433–439.

    Google Scholar 

  94. Turk, G., & O’Brien, J. F. (2002). Modelling with implicit surfaces that interpolate. ACM Transactions on Graphics.

  95. Kazhdan, M., & Hoppe, H. (2013). Screened poisson surface reconstruction. In ACM transactions on graphics, vol. 32.

  96. Fleishman, S., Cohen-Or, D., Alexa, M., & Silva, C. T. (2003). Progressive point set surfaces. ACM Transactions on Graphics, 22(4), 997–1011.

    Google Scholar 

  97. Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., & Evans, T. R. (2001). Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of the 28th annual conference on computer graphics and interactive techniques, SIGGRAPH 2001, pp. 67–76.

  98. Zhong, D., Zhang, J., & Wang, L. (2019). Fast implicit surface reconstruction for the radial basis functions interpolant. Applied Sciences, (9):5535.

  99. Amenta, N., Bern, M., & Kamvysselis, M. (1998). A new voronoi-based surface reconstruction algorithm. In Proceedings of the 25th annual conference on computer graphics and interactive techniques, SIGGRAPH 1998, (March): 415–422.

  100. Steinke, F., Schölkopf, B., & Blanz, V. (2005). Support vector machines for 3D shape processing. Computer Graphics Forum, 24(3), 285–294.

    Google Scholar 

  101. Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., & Seidel, H. P. (2003). Multi-level partition of unity implicits. In ACM transactions on graphics, vol. 22, pp. 463–470.

  102. Kanai, T., Suzuki, H., & Kimura, F. (2000). Metamorphosis of arbitrary triangular meshes. IEEE Computer Graphics and Applications, 20(2), 62–75.

    Google Scholar 

  103. Zhou, X. Y., Du, Z., & Kim, H. A. (2019). A level set shape metamorphosis with mechanical constraints for geometrically graded microstructures. Structural and Multidisciplinary Optimization, 60(1).

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Acknowledgements

The work is supported by the National Science Foundation of China under Grant No. 51875516.

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  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Ci He, Shuyou Zhang, Lemiao Qiu, Zili Wang & Xiaojian Liu

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  1. Ci He
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He, C., Zhang, S., Qiu, L. et al. Innovative Surface Merging Method for Generating Point-Based Skin Model Shapes Considering Processing Features. Int. J. Precis. Eng. Manuf. 21, 2117–2138 (2020). https://doi.org/10.1007/s12541-020-00396-8

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