Machine knitted textiles are complex multi-scale material structures increasingly important in many industries, including consumer products, architecture, composites, medical, and military. Computational modeling, simulation, and design of industrial fabrics require efficient representations of the spatial, material, and physical properties of such structures. We propose a process-oriented representation, TopoKnit, that defines a foundational data structure for representing the topology of weft-knitted textiles at the yarn scale. Process space serves as an intermediary between the machine and fabric spaces, and supports a concise, computationally efficient evaluation approach based on on-demand, near constant-time queries. In this paper, we define the properties of the process space, and design a data structure to represent it and algorithms to evaluate it. We demonstrate the effectiveness of the representation scheme by providing results of evaluations of the data structure in support of common topological operations in the fabric space.

中文翻译：

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TopoKnit：面向过程的表示形式，用于对纬编纺织品中的纱线拓扑进行建模

机织纺织品是复杂的多尺度材料结构，在许多行业中变得越来越重要，包括消费品，建筑，复合材料，医疗和军事。工业织物的计算建模，模拟和设计需要有效表示此类结构的空间，材料和物理特性。我们提出了一个面向过程的表示形式TopoKnit，它定义了一个基本的数据结构来表示纬纱针织织物在纱线规模上的拓扑。进程空间充当机器空间和结构空间之间的中介，并支持基于按需，接近恒定时间查询的简洁，计算高效的评估方法。在本文中，我们定义了过程空间的属性，并设计一个数据结构来表示它并评估它的算法。我们通过提供数据结构评估结果来证明表示方案的有效性，以支持结构空间中的常见拓扑操作。