Single-Cycle Plain-Woven Objects

—It has recently been shown that if we twist an arbitrary subset of edges of a mesh on an orientable surface, the resulting extended graph rotation system (EGRS) can be used to induce a cyclic weaving on the surface. In extended graph rotation systems, an edge is viewed as a paper strip that can be twisted. The sides of the paper strips provide “two strands” to construct weaving structures. Either these strands are “parallel” to the mesh edge for an “untwisted edge”, or they both cross over the edge and over each other for a “twisted edge”. If an arbitrary subset of edges of a mesh on an orientable surface is twisted in the same helical sense, then the EGRS induces a cyclic plain-weaving on the surface, which consists of cycles that cross other cycles (or themselves) by alternatingly going over and under. In this paper, we show that it is always possible to create a single-cycle plain-weaving starting from a mesh on an arbitrary surface, by selecting an appropriate su...

• Type: Journal
• Year: 2010
• Where: SMI
• Authors: Qing Xing, Ergun Akleman, Jianer Chen, Jonathan L. Gross
• Keywords: Extended Graph Rotation, Image Analysis, Mesh, Single-cycle Plain-woven Objects, SMI 2010