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.

中文翻译：

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使用螺旋支架对针织物进行几何建模

我们提出了一个双连续的最小表面（螺旋面）作为支架，在其上定义纬编织物中纱线的拓扑结构和几何形状。使用螺旋体建模提供了一种模拟物理制造过程的几何方法，该方法应生成适用于下游机械和有效性分析的几何模型。针织织物中纱线的中心线被指定为测地线路径，具有约束边界条件，沿螺旋线以固定距离运行。纱线中心线的形状是通过多段线上的优化过程产生的。折线顶点之间的距离缩短，排斥势使顶点与螺旋面保持指定距离。这些动作和约束被公式化为一个单一的“能量”函数，然后被最小化。纱线几何形状生成为围绕中心线的管。为半环定义的优化配置被复制、反射和移动，以产生构成织物的多个针迹的中心线。此外，螺旋面的参数可用于控制织物针迹的尺寸和形状。我们展示了螺旋形支架可用于定义针织和绗缝针迹，然后将它们组合起来以生产全针织、罗纹和吊袜带织物的模型。