Numerical Optimization of Polygon Tessellation for Generating Machine-producible Crochet Patterns

Jan Lukas Storck; Bjarte Alexander Feldmann; Johannes Fiedler; Yordan Kyosev

doi:10.14502/tekstilec.66.2023062

Authors

Jan Lukas Storck Hochschule Bielefeld – University of Applied Sciences and Arts, Bielefeld, Faculty of Engineering and Mathematics, Germany Author https://orcid.org/0000-0002-6841-8791
Bjarte Alexander Feldmann Hochschule Bielefeld – University of Applied Sciences and Arts, Bielefeld, Faculty of Engineering and Mathematics, Germany Author https://orcid.org/0009-0008-3117-9783
Johannes Fiedler Hochschule Bielefeld – University of Applied Sciences and Arts, Bielefeld, Faculty of Engineering and Mathematics, Germany Author
Yordan Kyosev Technische Universität Dresden, Faculty of Mechanical Science and Engineering, Institute of Textile Machinery and High Performance Material Technology, Dresden, Germany Author https://orcid.org/0000-0003-3376-1423

DOI:

https://doi.org/10.14502/tekstilec.66.2023062

Keywords:

crochet, design, tessellation, crocheting machine, numerical optimization

Abstract

The automation of current crocheting technology offers many possibilities. To fully exploit this potential, it is necessary to develop not only hardware, but also methods that enable the design of novel machine-crocheted fabrics. In the case of manual crocheting, approaches for an automated generation of crochet patterns according to 3D shapes have already been presented in the literature. However, the most technically advanced crocheting machine prototype currently proposed automates the crocheting of flat fabrics starting from a chain row. Given the limitations and operation of this so-called CroMat crocheting machine, a tool for shaping flat machine-crocheted fabrics according to 2D convex polygons is presented here. With this, surfaces can be divided into crochet stitches using a tessellation process and numerical optimization. The rules of the automated crocheting process were thus followed to ensure the machine manufacturability of generated patterns. Computer models of the fabrics were used as previews. In addition, the shaping possibilities of the CroMat crocheting machine, in particular with respect to increase and decrease stitches, are presented and discussed by means of the tessellation optimization of exemplary polygon shapes. Generally speaking, the algorithm extends the toolbox for designing machine-crocheted fabrics through the automated generation of valid crochet patterns corresponding to input shapes and according to the possibilities of the CroMat crocheting machine prototype.

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References

GRIMMELSMANN, Nils, FIEDLER, Johannes, EHRMANN, Andrea. Häkelmaschine. DE patent, no. 102016015204A1. 2018-06-21.

GRIMMELSMANN Nils, DÖPKE Christoph, WEHLAGE, Svea, EHRMANN Andrea. The largest crocheting machine in the world. Melliand International, 2019, 25(2), 99–100.

STORCK, Jan Lukas, FELDMANN, Bjarte Alexander, KYOSEV, Yordan. Design tool for automated crocheting of fabrics. Communications in Development and Assembling of Textile Products, 2023, 4(2), 254–272, doi: 10.25367/cdatp.2023.4.p254-272.

PERRY, Gabriella. Croche-Matic – building a robot for crocheting 3D spherical form. Master's thesis. Harvard Graduate School of Design, 2022, https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37372333. DOI: https://doi.org/10.1109/ICRA48891.2023.10160345

SEITZ, Klara, LINCKE, Jens, REIN, Patrick, HIRSCHFELD, Robert. Language and Tool Support for 3D Crochet Patterns. Potsdam : Universitätsverlag Potsdam, 2021.

SEITZ, Klara, REIN, Patrick, LINCKE, Jens, HIRSCHFELD, Robert. Digital crochet: toward a visual language for pattern description. In Proceedings of the 2022 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software, 2022, 48–62, doi: 10.1145/3563835.3567657. DOI: https://doi.org/10.1145/3563835.3567657

NAKJAN, Pikanate, RATANOTAYANON, Sukanya, PORWONGSAWANG, Natchayar. Automatic crochet pattern generation from 2D sketching. In 10th International Conference on Knowledge and Smart Technology (KST). IEEE, 2018, 170–175, doi: 10.1109/KST.2018.8426123. DOI: https://doi.org/10.1109/KST.2018.8426123

GUO, Runbo, LIN, Jenny, NARAYANAN, Vidya and MCCANN, James. Representing crochet with stitch meshes. In SCF '20: Proceedings of the 5th Annual ACM Symposium on Computational Fabrication. Edited by E. Whiting, J. Hart, C. Sung, N. Peek, M. Akbarzadeh, D. Aukes, A. Schulz, H. Taylor and J. Kim. New York : ACM, 2020, 1–8, doi: 10.1145/3424630.3425409. DOI: https://doi.org/10.1145/3424630.3425409

ÇAPUNAMAN, Özgüç B., BINGÖL, Cemal K., GÜRSOY, Benay. Computing stitches and crocheting geometry. In Computer-Aided Architectural Design. Future Trajectories. 17th International Conference, CAAD Futures 2017, Istanbul, Turkey, July 12-14, 2017, Selected Papers. Communications in Computer and Information Science, vol 724. Edited by G. Çağdaş, M. Özkar and L. F. Gül. Singapore : Springer, 2017, 289–305, doi: 10.1007/978-981-10-5197-5_16. DOI: https://doi.org/10.1007/978-981-10-5197-5_16

ZAHARIEVA-STOYANOVA, Elena, BOZOV, Stefan. Application of XML-based language for digital representation of crochet symbols. Digital Presentation and Preservation of Cultural and Scientific Heritage, 2017, 7, 181–190, doi: 10.55630/dipp.2017.7.16. DOI: https://doi.org/10.55630/dipp.2017.7.16

ZAHARIEVA-STOYANOVA, Elena, BESHEVLIEV, Damyan. Digital representation of crochet symbols sets. Digital Presentation and Preservation of Cultural and Scientific Heritage, 2018, 8, 159–164, doi: 10.55630/dipp.2018.8.14. DOI: https://doi.org/10.55630/dipp.2018.8.14

JIANG, Chen, WANG, Kan, LIU, Yi, ZHANG, Chuck and WANG, Ben. Textile-based sandwich scaffold using wet electrospun yarns for skin tissue engineering. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 119, 1–9, doi: 10.1016/j.jmbbm.2021.104499. DOI: https://doi.org/10.1016/j.jmbbm.2021.104499

SHI, Linyan, WANG, Sihan, LIANG, Nanyue, ZHANG, Xinyu, NIU, Lizhong, CHENG, Deshan and TANG, Xiaoning. Sound absorption of crochet fabrics with multi-plied yarns. Applied Acoustics, 2022, 199, 1–7, doi: 10.1016/j.apacoust.2022.109017. DOI: https://doi.org/10.1016/j.apacoust.2022.109017

BOBIN, Maxence, AMROUN, Hamdi, COQUILLART, Sabine, BIMBARD, Franck, AMMI, Mehdi. SVM based approach for the assessment of elbow flexion with smart textile sensor. In 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC), 2017, 2129–2134, doi: 10.1109/SMC.2017.8122934. DOI: https://doi.org/10.1109/SMC.2017.8122934

EMERY, Irene. The primary structures of fabrics: an illustrated classification. New York : Watson-Guptill Publications, 1995.

KARP, Cary. Defining crochet. Textile History, 2018, 49(2), 208–223, doi: 10.1080/00404969.2018.1491689. DOI: https://doi.org/10.1080/00404969.2018.1491689

HENDERSON, David W., TAIMINA, Daina. Crocheting the hyperbolic plane. Mathematical Intelligencer, 2001, 23(2), 17–28, doi: 10.1007/BF03026623. DOI: https://doi.org/10.1007/BF03026623

OSINGA, Hinke M., KRAUSKOPF, Bernd. Crocheting the Lorenz manifold. Mathematical Intelligencer, 2004, 26(4), 25–37, doi 10.1007/BF02985416. DOI: https://doi.org/10.1007/BF02985416

POPESCU, Mariana, RIPPMAN, Matthias, VAN MELE, Tom, BLOCK, Philippe. Automated generation of knit patterns for non-developable surfaces. In Humanizing Digital Reality: Design Modelling Symposium Paris 2017. Singapore : Springer, 2018, 271–284, doi: 10.1007/978-981-10-6611-5_24. DOI: https://doi.org/10.1007/978-981-10-6611-5_24

WU, Kui, SWAN, Hannah and YUKSEL, Cem. Knittable stitch meshes. ACM Transactions on Graphics, 2019, 38(1), 1–13, doi: 10.1145/3292481. DOI: https://doi.org/10.1145/3292481

NARAYANAN, Vidya, WU, Kai and YUKSEL, Cem, MCCANN, James. Visual knitting machine programming. ACM Transactions on Graphics, 2019, 38(4), 1–13, doi: 10.1145/3306346.3322995. DOI: https://doi.org/10.1145/3306346.3322995

MCCANN, James, ALBAUGH, Lea, NARAYANAN, Vidya, GROW, April, MATUSIK, Wojciech, MANKOFF, Jennifer, HODGINS, Jessica. A compiler for 3D machine knitting. ACM Transactions on Graphics, 2016, 35(4), 1–11, doi: 10.1145/2897824.2925940. DOI: https://doi.org/10.1145/2897824.2925940

NARAYANAN, Vidya, ALBAUGH, Lea, HODGINS, Jessica, COROS, Stelian, McCANN, James. Automatic machine knitting of 3D meshes. ACM Transactions on Graphics, 2018, 37(3), 1–15, doi: 10.1145/3186265. DOI: https://doi.org/10.1145/3186265

KASPAR, Alexandre, MAKATURA, Liane, MATUSIK, Wojciech. Knitting skeletons: A computer-aided design tool for shaping and patterning of knitted garments. In UIST '19: Proceedings of the 32nd Annual ACM Symposium on User Interface Software and Technology. New York : Association for Computing Machinery, 2019, 53–65, doi: 10.1145/3332165.3347879. DOI: https://doi.org/10.1145/3332165.3347879

Standards and guidelines for crochet and knitting [online]. Craft Yarn Council [accessed 30.07.2023]. Available on World Wide Web: <https://www.craftyarncouncil.com/standards>.

Crochet chart symbols [online]. Craft Yarn Council [accessed 30.07.2023]. Available on World Wide Web: <https://www.craftyarncouncil.com/standards/crochet-chart-symbols>.

STORCK, Jan L., GERBER, Dennis, STEENBOCK, Liska, KYOSEV, Yordan. Topology based modelling of crochet structures. Journal of Industrial Textiles, 2022, 52, doi: 10.1177/15280837221139250. DOI: https://doi.org/10.1177/15280837221139250

TexMind textile viewer (free) [online]. TexMind [accessed 30.07.2023]. Available on World Wide Web: <http://texmind.com/wp/products/neues-produkt/>.

LEE, Y.C., LI, Zhi-lin, LI, Y.L. Taxonomy of space tessellation. ISPRS Journal of Photogrammetry and Remote Sensing, 2000, 55(3), 139–149, doi: 10.1016/S0924-2716(00)00015-0. DOI: https://doi.org/10.1016/S0924-2716(00)00015-0

DU, Qiang, FABER, Vance, GUNZBURGER, Max. Centroidal Voronoi tessellations: applications and algorithms. SIAM Review, 1999, 41(4), 637–676, doi: 10.1137/S0036144599352836. DOI: https://doi.org/10.1137/S0036144599352836

CHU, C., ANTONIO, J. Approximation algorithms to solve real-life multicriteria cutting stock problems. Operations Research, 1999, 47(4), 495–508, doi: 10.1287/opre.47.4.495. DOI: https://doi.org/10.1287/opre.47.4.495

PapDesigner [online]. Friedrich Folkmann [accessed 30.07.2023]. Available on World Wide Web: <http://friedrich-folkmann.de/papdesigner/Hauptseite.html>.

HOPPER, E., TURTON, B.C. A review of the application of meta-heuristic algorithms to 2D strip packing problems. Artificial Intelligence Review, 2001, 16, 257–300, doi: 10.1023/A:1012590107280. DOI: https://doi.org/10.1023/A:1012590107280

ISRANI, Sharat, SANDERS, Jerry. Two-dimensional cutting stock problem research: a review and a new rectangular layout algorithm. Journal of Manufacturing Systems, 1982, 1(2), 169–182, doi: 10.1016/S0278-6125(82)80027-7. DOI: https://doi.org/10.1016/S0278-6125(82)80027-7

About SymPy [online]. SymPy [accessed 30.07.2023]. Available on World Wide Web: <https://www.sympy.org/en/index.html>.

NumPy – main page [online]. NumPy [accessed 30.07.2023]. Available on World Wide Web: <https://numpy.org>.

Pytexlib library [online]. GitHub [accessed 30.07.2023]. Available on World Wide Web: <https://github.com/virtualtextiles/pytexlib/>.

Matplotlib documentation [online]. Matplotlib [accessed on 30.07.2023]. Available on World Wide Web: <https://matplotlib.org/stable/index.html>.

KAPLLANI, Levi, AMANATIDES, Chelsea, DION, Genevieve, SHAPIRO, Vadim, BREEN, David E. TopoKnit: a process-oriented representation for modeling the topology of yarns in weft-knitted textiles. Graphical Models, 2021, 118, 1–19 doi: 10.1016/j.gmod.2021.101114. DOI: https://doi.org/10.1016/j.gmod.2021.101114

SPENCER, David J. The straight bar frame and full-fashioning. In Knitting Technology: a Comprehensive Handbook and Practical Guide. Woodhead Publishing, 2001, 194–206, doi: 10.1533/9781855737556.194.

References to Supplementary materials:

STORCK, Jan Lukas, FELDMANN, Bjarte Alexander, KYOSEV, Yordan. Design tool for automated crocheting of fabrics. Communications in Development and Assembling of Textile Products, 2023, 4(2), 254–272, doi: 10.25367/cdatp.2023.4.p254-272. DOI: https://doi.org/10.25367/cdatp.2023.4.p254-272

SPENCER, David J. Electronics in knitting. In Knitting technology: a comprehensive handbook and practical guide. 3th ed. Cambridge : Woodhead Publishing, 2001, 134–144. DOI: https://doi.org/10.1533/9781855737556.134

SPENCER, David J. The straight bar frame and full-fashioning. In Knitting technology: a comprehensive handbook and practical guide. 3th ed. Cambridge : Woodhead Publishing, 2001, 194–206. DOI: https://doi.org/10.1533/9781855737556.194