SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2457-2480, January 2020.
Recent advances in the computer graphics of woven images in 3-space motivate the development of a model for weavings on arbitrary surfaces of higher genus. Our paradigm differs markedly from what Grünbaum and Shepard have provided for the plane. In particular, we induce our weavings from graph imbeddings on surfaces in 3-space. Additionally, we show that the two most frequently invoked subdivision algorithms in computer graphics, the Catmull--Clark and Doo--Sabin algorithms, correspond nicely to topological surgery operations on the induced weavings. The inherently topological formulation of our model permits a graphic designer to superimpose strand colors and geometric attributes---distances, angles, and curvatures---that conform to manufacturing or artistic criteria.

中文翻译：

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拓扑上完整的编织理论

SIAM离散数学杂志，第34卷，第4期，第2457-2480页，2020年1月。
在3空间中机织图像的计算机图形学方面的最新进展推动了在较高属的任意表面上进行编织的模型的开发。我们的范例与Grünbaum和Shepard为飞机提供的范例截然不同。特别是，我们通过在3空间表面上的图形嵌入来进行编织。此外，我们证明了计算机图形学中最常调用的两种细分算法Catmull-Clark和Doo-Sabin算法与诱导编织上的拓扑外科手术非常吻合。我们的模型具有固有的拓扑结构，允许图形设计师叠加符合制造或艺术标准的线色和几何属性（距离，角度和曲率）。