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.