Transforming 2D Materials into 3D Objects: Flexing and Stretching the Rules
Year: 2025 Authors: Alison Martin
Core claim
Traditional weaving strategies can generate free-form, high-genus 3D geometries from straight-edged strips while preserving structural efficiency and elegance.
Topics
weaving, 3D form generation, complex surfaces, basket-making, minimal surfaces
Domains
geometry, topology, surface morphology, craft, textile design, material art, fabrication
Methods
woven mesh transformation, basket-making rules, triaxial weaving, curved ribbon weaving
Media
woven paper, straight edge strips, woven mesh
Paper text
The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.
Martin
Transforming 2D Materials into 3D Objects: Flexing and Stretching the Rules
Alison Martin
Livorno, Italy; alisonmartin57@gmail.com
Weaving is an orderly entanglement; it has long been a way to deal with complexity and unorganized components and aims to introduce geometric characteristics and physical properties such as structural efficiency and elegance into a fabric of entwined strands. Weaving embeds a fundamental construction principle of transformational properties through which a 2D woven mesh can become a 3D network. The traditional basket-making strategy provides a clear set of rules for achieving a broad range of complex doubly curved morphologies (including free-form and high genus topology) while only using straight edge strips of material in fabrication.
The versatility of weaving patterns and form-related components relating to three-dimensional geometry of shape and complex surfaces means that these techniques can be pushed beyond conventional craft-based limits towards novel applications across disciplines [1][2].
Figure 1: Minimal surface, woven version. Planar Enneper’s. Woven paper, 2025.
References
[1] Alison Martin. “Smooth Triaxial Weaving with Naturally Curved Ribbons.” Physics Review Letters, vol. 127, no. 10, 2021. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.104301 [2] Alison Martin. “3D Weaving with Curved Ribbons.” ACM Transactions on Graphics, vol. 40, no. 4, pp. 1-15. https://dl.acm.org/doi/10.1145/3450626.3459788