Geometric modeling of complex knitting stitches using a bicontinuous surface and its offsets

Helicoids have been utilized as a scaffold on which to define the topology and geometry of yarns in a weft-knitted fabric. The centerline of a yarn in the fabric is specified as a geodesic path, with constrained boundary conditions, running along a helicoid at a fixed distance. The properties and constraints of the yarn are formulated into a single energy function, which is then minimized to produce the desired resulting models. We present improvements to this approach that address the deficiencies of the original work and extend its capabilities to more complex stitches, such as transfer, tuck and miss. A single bicontinuous surface is described, which replaces discrete helicoids and produces higher quality, continuous yarn models. A new computational method is employed that significantly speeds up the optimization computations. Including offset surfaces with the scaffold, as well as removing sections of the scaffold, allow for the modeling of complex stitches. The improved approach produces superior geometric results, consisting of complex knitting stitches, at a fraction of the computational cost of the previous method. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The helicoids are used as a scaffold to define the topology and geometry of yarns in a weft-knitted fabric. An energy function is formulated for the properties and constraints of the yarn, which is then minimized to produce desired models. Improvements have been made to the approach to address deficiencies and extend capabilities to more complex stitches, with a new computational method that speeds up optimization calculations significantly.