Geometric modeling of knitted fabrics using helicoid scaffolds

Abstract

We present a bicontinuous, minimal surface (the helicoid) as a scaffold on which to define the topology and geometry of yarns in a weft-knitted fabric. Modeling with helicoids offers a geometric approach to simulating a physical manufacturing process, which should generate geometric models suitable for downstream mechanical and validity analyses. The centerline of a yarn in a knitted fabric is specified as a geodesic path, with constrained boundary conditions, running along a helicoid at a fixed distance. The shape of the yarn’s centerline is produced via an optimization process over a polyline. The distances between the vertices of the polyline are shortened and a repulsive potential keeps the vertices at a specified distance from the helicoid. These actions and constraints are formulated into a single “energy” function, which is then minimized. The yarn geometry is generated as a tube around the centerline. The optimized configuration, defined for a half loop, is duplicated, reflected, and shifted to produce the centerlines for the multiple stitches that make up a fabric. In addition, the parameters of the helicoid may be used to control the size and shape of the fabric’s stitches. We show that helicoid scaffolds may be used to define both knit and purl stitches, which are then combined to produce models of all-knit, rib, and garter fabrics.

TopoKnit : A Process-Oriented Representation for Modeling the Topology of Yarns in Weft-Knitted Textiles

“…The under-development CONNECTED TO algorithm would provide the connections between the contacts needed to compute flow over the whole fabric. We also intend to integrate TopoKnit's topology and yarn ordering information with the work of Wadekar et al [30] to extend their yarnlevel geometric models to complex knitted fabrics. These models support rapid evaluation of the mechanical properties of knitted fabrics.…”

“…Duhovic and Bhattacharyya [27] simulated the knitting process in order to understand how each of a yarn's deformation mechanisms contribute to the overall deformation energy/behavior of a yarn in a knitted fabric. In recent work, Knittel, Wadekar et al [28,29,30,31] investigated helicoid scaffolds as a framework within which to study the structure of knitted fabrics.…”

Isogonal piecewise-linear embeddings of 1-periodic knots and links, and related 2-periodic chain-link and knitting patterns

“…Knitting patterns (e.g. Wadekar et al, 2020) are related. Particularly in 'circular' (a better term would be 'helical') knitting there is strictly just one thread.…”

Review on the 3-D simulation for weft knitted fabric

“…The thickness and undulation effect of weft knitted fabric is simulated. Wadekar et al 17 proposed the application that a geometric approach to simulating a physical manufacturing process is offered by modeling with helicoids, and this way ought to generate geometric models which apply for downstream mechanical and validity analyses. Specify the centerline of a yarn in a knitted fabric as a geodesic path, and the boundary conditions are constrained to extend at a fixed distance along the helicoid.…”