Curl Quantization for Automatic Placement of Knit Singularities

We develop a method for automatic placement of knit singularities based on curl quantization, extending the knit-planning frameworks of Mitra et al. [2024, 2023]. Stripe patterns are generated that closely follow the isolines of an underlying knitting time function, and has course and wale singularities in regions of high curl for the normalized time function gradient and its 90^◦ rotated field, respectively. Singularities are placed in an iterative fashion, and we show that this strategy allows us to easily maintain the structural constraints necessary for machine-knitting, e.g., the helix-free constraint, and to satisfy user constraints such as stripe alignment and singularity placement. Our more performant approach obviates the need for a mixed-integer solve [Mitra et al. 2023], manual fixing of singularity positions, or the running of a singularity matching procedure in post-processing [Mitra et al. 2024]. Our global optimization also produces smooth knit graphs that provide quick simulation-free previews of rendered knits without the surface artifacts of competing methods. Furthermore, we extend our method to the popular cut-and-sew garment design paradigm. We validate our method by machine-knitting and rendering yarn-based visualizations of prototypical models in the 3D and cut-and-sew settings.