  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.
