“Helix-Free Stripes for Knit Graph Design” by Mitra, Makatura, Whiting and Chien

  • ©Rahul Mitra, Liane Makatura, Emily Whiting, and Edward (Ed) Chien




    Helix-Free Stripes for Knit Graph Design

Session/Category Title: Fabulous Fabrication: From Knitting to Circuits




    The problem of placing evenly-spaced stripes on a triangular mesh mirrors that of having evenly-spaced course rows and wale columns in a knit graph for a given geometry. This work presents strategies for producing helix-free stripe patterns and traces them to produce helix-free knit graphs suitable for machine knitting. We optimize directly for the discrete differential (1-form) of the stripe texture function, i.e., the spinning form, and demonstrate the knitting-specific advantages of this framework. In particular, we note how simple linear constraints allow us to place stitch irregularities, align course rows and wale columns to boundary/feature curves, and eliminate helical stripes. Two mixed-integer optimization strategies using these constraints are presented and applied to several mesh models. The results are smooth, globally-informed, helix-free stripe patterns that we trace to produce machine-knittable graphs. We further provide an explicit characterization of helical stripes and a theoretical analysis of their elimination constraints.


    1. David Bommes, Timm Lempfer, and Leif Kobbelt. 2011. Global Structure Optimization of Quadrilateral Meshes. Computer Graphics Forum 30, 2 (2011), 375–384.
    2. Keenan Crane, Fernando de Goes, Mathieu Desbrun, and Peter Schröder. 2013. Digital Geometry Processing with Discrete Exterior Calculus. In ACM SIGGRAPH 2013 courses (Anaheim, California) (SIGGRAPH ’13). ACM, New York, NY, USA, 126 pages.
    3. Gurobi Optimization, LLC. 2022. Gurobi Optimizer Reference Manual. https://www.gurobi.com
    4. Allen Hatcher. 2000. Algebraic topology. Cambridge Univ. Press, Cambridge.
    5. Yuki Igarashi, Takeo Igarashi, and Hiromasa Suzuki. 2008. Knitting a 3D Model. Computer Graphics Forum 27, 7 (2008), 1737–1743.
    6. Benjamin Jones, Yuxuan Mei, Haisen Zhao, Taylor Gotfrid, Jennifer Mankoff, and Adriana Schulz. 2022. Computational Design of Knit Templates. ACM Transactions on Graphics 41, 2 (April 2022), 1–16.
    7. Alexandre Kaspar, Liane Makatura, and Wojciech Matusik. 2019. Knitting Skeletons: Computer-Aided Design Tool for Shaping and Patterning of Knitted Garments. Proceedings of the ACM Symposium on User Interface Software and Technology (UIST).
    8. Alexandre Kaspar, Kui Wu, Yiyue Luo, Liane Makatura, and Wojciech Matusik. 2021. Knit Sketching: from Cut & Sew Patterns to Machine-Knit Garments. ACM Transactions on Graphics (Proc. SIGGRAPH) 40, 4 (2021).
    9. Felix Knöppel, Keenan Crane, Ulrich Pinkall, and Peter Schröder. 2015. Stripe patterns on surfaces. ACM Transactions on Graphics 34, 4 (July 2015), 39:1–39:11.
    10. Georges Nader, Quek-Yu Han, Chia-Pei Zhi, Oliver Weeger, and Sai-Kit Yeung. 2021. KnitKit. ACM Transactions on Graphics (TOG) (July 2021).
    11. Vidya Narayanan, Lea Albaugh, Jessica Hodgins, Stelian Coros, and James Mccann. 2018. Automatic Machine Knitting of 3D Meshes. ACM Transactions on Graphics 37, 3 (Aug. 2018), 35:1–35:15.
    12. Vidya Narayanan, Kui Wu, Cem Yuksel, and James McCann. 2019. Visual knitting machine programming. ACM Transactions on Graphics 38, 4 (July 2019), 63:1–63:13.
    13. Yuta Noma, Nobuyuki Umetani, and Yoshihiro Kawahara. 2022. Fast Editing of Singularities in Field-Aligned Stripe Patterns. In SIGGRAPH Asia 2022 Conference Papers (Daegu, Republic of Korea) (SA ’22). Association for Computing Machinery, New York, NY, USA, Article 37, 8 pages.
    14. Thibault Tricard, Vincent Tavernier, Cédric Zanni, Jonàs Martínez, Pierre-Alexandre Hugron, Fabrice Neyret, and Sylvain Lefebvre. 2020. Freely orientable microstructures for designing deformable 3D prints.ACM Trans. Graph. 39, 6 (2020), 211–1.
    15. Kui Wu, Xifeng Gao, Zachary Ferguson, Daniele Panozzo, and Cem Yuksel. 2018. Stitch meshing. ACM Transactions on Graphics 37, 4 (Aug. 2018), 1–14.
    16. Kui Wu, Hannah Swan, and Cem Yuksel. 2019. Knittable Stitch Meshes. ACM Transactions on Graphics 38, 1 (Feb. 2019), 1–13.
    17. Cem Yuksel, Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2012. Stitch meshes for modeling knitted clothing with yarn-level detail. ACM Transactions on Graphics (TOG) (July 2012).

ACM Digital Library Publication:

Overview Page: