Leveraging Temporal Constraints for Simplified Knit Representation

Knitting is a fabrication technique capable of producing incredibly complex shapes with a wide range of mechanical properties from a single, continous strand of yarn. This flexibility, however, also means that the underlying structure can be extremely complex, which makes reasoning about said structure equally difficult. While it is possible to describe the yarn geometry using knot theory, the difficulty of the knot equivalence problem means either the scale or the type of knit object must be limited to make computation on this representation tractable. To address this, our work seeks to leverage the temporal constraint inherent in the knitting process. By assuming the knitting process consumes yarn monotonically (a fact which holds true for the most common knit operations), we can establish an order on the loops produced by the knitting process. This allows each loop to be treated as a strand within a braid, a group that is much easier to compute equivalence on than knots. A simple representation would open the avenue for applications such as yarn level simulation and fast pattern validation.