A Graph Model and a Layout Algorithm for Knitting Patterns (2406.13800v1)

Abstract: Knitting, an ancient fiber art, creates a structured fabric consisting of loops or stitches. Publishing hand knitting patterns involves lengthy testing periods and numerous knitters. Modeling knitting patterns with graphs can help expedite error detection and pattern validation. In this paper, we describe how to model simple knitting patterns as planar graphs. We then design, implement, and evaluate a layout algorithm to visualize knitting patterns. Knitting patterns correspond to graphs with pre-specified edge lengths (e.g., uniform lengths, two lengths, etc.). This yields a natural graph layout optimization problem: realize a planar graph with pre-specified edge lengths, while ensuring there are no edge crossings. We quantitatively evaluate our algorithm using real knitting patterns of various sizes against three others; one created for knitting patterns, one that maintains planarity and optimizes edge lengths, and a popular force-directed algorithm.