References
- C. C. L. Wang, Geometric Modeling and Reasoning of Human-Centered Freeform Products. London: Springer-Verlag, 2013. https://doi.org/10.1007/978-1-4471-4360-4
- M. P. Carmo, Differential Geometry of Curves and Surfaces. Englewood Cliffs: Prentice-Hall, 1976.
- H. S. Abdul-Rahman, S. Lou, W. Zeng, X. Jiang, and P. J. Scott, “Freeform texture representation and characterisation based on triangular mesh projection techniques,” Measurement, vol. 92, pp. 172–182, Oct. 2016. https://doi.org/10.1016/j.measurement.2016.06.005
- P. Azariadis and N. Sapidis, “Planar development of digital free-form surfaces,” in Advances in Geometric Modeling, M. Sarfraz, Ed. Wiley, Jan. 2004. https://doi.org/10.1002/0470860448.ch2
- M. Eigensatz, M. Kilian, A. Schiftner, N. J. Mitra, H. Pottmann, and M. Pauly, “Paneling architectural freeform surfaces,” ACM Trans. Graph., vol. 29, no. 4, Jul. 2010, Art. no. 45. https://doi.org/10.1145/1833351.1778782
- Y. J. Yang, W. Zeng, and X. X. Meng, “Conformal freeform surfaces,” Computer-Aided Design, vol. 81, pp. 48–60, Dec. 2016. https://doi.org/10.1016/j.cad.2016.09.003
- W. Zhan, “Research on pattern flattening for parts with complex surfaces,” M.S. thesis, Nanjing Univ. Aeronautics & Astronautics, Nanjing, China, 2007.
- R. Xu, X. Liu, and J. Chen, “Development and status of surfaces flattening method,” Die and Mould Technology, no. 5, pp. 15–18, 2002.
- R. Sawhney and K. Crane, “Boundary first flattening,” ACM Trans. Graph. (ToG), vol. 37, no. 1, pp. 1–14, Dec. 2017. https://doi.org/10.1145/3132705
- Q. Zhang, J. Hou, Y. Qian, Y. Zeng, J. Zhang, and Y. He, “Flattening-net: Deep regular 2D representation for 3D point cloud analysis,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 45, no. 8, pp. 9726–9742, Feb. 2023. https://doi.org/10.1109/TPAMI.2023.3244828
- M. Xiao, Z. Qi, and H. Shi, “The surface flattening based on mechanics revision of the tunnel 3D point cloud data from laser scanner,” Procedia Computer Science, vol. 131, pp. 1229–1237, 2018. https://doi.org/10.1016/j.procs.2018.04.335
- X. Ji, G. Wen, H. Gong, R. Sun, and H. Li, “Three-dimensional wound flattening method for mapping skin mechanical properties based on finite element method,” Comput. Methods Biomech. Biomed. Engin., vol. 27, no. 2, pp. 237–250, Feb. 2023. https://doi.org/10.1080/10255842.2023.2183347
- P. Zheng, Q. Liu, J. Lou, C. Lian, and D. Lin, “A free-form surface flattening algorithm that minimizes geometric deformation energy,” IET Image Processing, vol. 16, no. 9, pp. 2544 –2556, Jul. 2022. https://doi.org/10.1049/ipr2.12508
- B. Yi, Y. Yang, R. Zheng, X. Li, and M. Yi, “Triangulated surface flattening based on the physical shell model,” J. Mech. Sci. Technol., vol. 32, pp. 2163–2171, May 2018. https://doi.org/10.1007/s12206-018-0425-0
- J. McCartney, B. K. Hinds, B. L. Seow, and D. Gong, “An energy based model for the flattening of woven fabrics,” J. Mater. Process. Technol., vol. 107, no. 1–3, pp. 312–318, Nov. 2000. https://doi.org/10.1016/S0924-0136(00)00694-4
- C. H. Lee and H. Huh, “Blank design and strain estimates for sheet metal forming processes by a finite element inverse approach with initial guess of linear deformation,” J. Mater. Process. Technol., vol. 82, no. 1–3, pp. 145–155, 1998. https://doi.org/10.1016/S0924-0136(98)00034-X
- J. Lan, X. Dong, and Z. Li, “Blank and strain estimates for sheet metal forming processes by an inverse approach of FE,” J. Plast. Eng., vol. 8, pp. 60–62, 2001.
- K. Chung and O. Richmond, “Ideal forming–I. Homogeneous deformation with minimum plastic work,” Int. J. Mech. Sci., vol. 34, no. 7, pp. 575–591, Jul. 1992. https://doi.org/10.1016/0020-7403(92)90032-C
- K. Chung and O. Richmond, “Ideal forming–II. Sheet forming with optimum deformation,” Int. J. Mech. Sci., vol. 34, no. 8, pp. 617–633, Aug. 1992. https://doi.org/10.1016/0020-7403(92)90059-P
- K. Chung, J. W. Yoon, and O. Richmond, “Ideal sheet forming with frictional constraints,” Int. J. Plasticity, vol. 16, no. 6, pp. 595–610, May 2000. https://doi.org/10.1016/S0749-6419(99)00068-6
- W. Chung, S. H. Kim, and K. H. Shin, “A method for planar development of 3D surfaces in shoe pattern design,” J. Mech. Sci. Technol., vol. 22, no. 8, pp. 1510–1519, 2008. https://doi.org/10.1007/s12206-008-0609-0
- Q. L. Zhang and X. Q. Luo, “Finite element method for developing arbitrary surfaces to flattened forms,” Finite Elem. Anal. Des., vol. 39, no. 10, pp. 977–984, Jul. 2003. https://doi.org/10.1016/S0168-874X(02)00142-7
- J. W. Yoon, K. Chung, F. Pourboghrat, and F. Barlat, “Design optimization of extruded preform for hydroforming processes based on ideal forming design theory,” Int. J. Mech. Sci., vol. 48, no. 12, pp. 1416–1428, Dec. 2006. https://doi.org/10.1016/j.ijmecsci.2006.07.003
- H. Wang and C. C. Wang, “A general surface development algorithm based on energy model,” J. Comput.-Aided Des. Comput. Graph., vol. 13, no. 6, p. 556, 2001.
- Z. Cai, M. Li, and W. Guo, “Calculating blank of shell-like parts based on triangular mesh system,” Eng. Technol. Ed., vol. 32, no. 2, 2002.
- C. C. Wang, S. S. Smith, and M. M. Yuen, “Surface flattening based on energy model,” Comput.-Aided Des., vol. 34, no. 11, pp. 823–833, Sep. 2002. https://doi.org/10.1016/S0010-4485(01)00150-6
- S. Li, X. Liu, X. Zheng, and H. Lu, “An overview of flattening methods for complex surface,” J. Inf. Comput. Sci., vol. 11, no. 1, pp. 323–333, 2014.
- K. H. Shin, “A method for planar development of free-form surfaces made of anisotropic materials,” J. Mech. Sci. Technol., vol. 25, no. 11, pp. 2817–2825, Nov. 2011. https://doi.org/10.1007/s12206-011-0726-z
- Q. Liu, J. Xi, and Z. Wu, “An energy-based surface flattening method for flat pattern development of sheet metal components,” Int. J. Adv. Manuf. Technol., vol. 68, no. 5–8, pp. 1155–1166, Apr. 2013. https://doi.org/10.1007/s00170-013-4908-y
- E. Yavuz and R. Yazici, “A dynamic neural network model for accelerating preliminary parameterization of 3D triangular mesh surfaces,” Neural Comput. Appl., vol. 31, no. 8, pp. 3691–3701, Jan. 2018. https://doi.org/10.1007/s00521-017-3332-x
- E. Yavuz, R. Yazici, M. C. Kasapbasi, and T. T. Bilgin, “Improving initial flattening of convex-shaped free-form mesh surface patches using a dynamic virtual boundary,” Comput. Syst. Sci. Eng., vol. 34, no. 6, pp. 339–355, 2019. https://doi.org/10.32604/csse.2019.34.339
- D. N. Metaxas, Physics-Based Deformable Models. Dordrecht: Kluwer Academic, 1997. https://doi.org/10.1007/978-1-4615-6335-8