Cyclic Plain-Weaving on Polygonal Mesh Surfaces with Graph Rotation Systems We show that graph rotation systems with twisted edges can represent links.

04/21/23 19:54

Cyclic Plain-Weaving on Polygonal Mesh Surfaces with Graph Rotation Systems

We show that graph rotation systems with twisted edges can represent links and knots, in addition to manifold meshes.

ERGUN AKLEMAN JIANER CHEN QING XING – JONATHAN GROSS

04/21/23 19:54

Plain-weaving consists of threads that are interlaced so that a traversal of each thread alternately goes over and under the other threads (or itself) as it crosses them.

To model a plain-weaving pattern on a surface, we construct an alternating projection of a link.

We prove that it is possible to create such a plain-weaving pattern for any given manifold mesh by twisting all of the edges of a related orientable manifold mesh.

Cyclic Plain-Weaving on Polygonal Mesh Surfaces

04/21/23 19:54

We have developed a new method that converts plain-weaving cycles to 3D thread structures.

Projection Method

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Our method provides both sparse and dense plain-weaving.

We also formally classify plain-weaving patterns.

Classification