Extended graph rotation systems as a model for cyclic weaving on orientable surfaces

We present an extension of the theory of graph rotation systems, which has been a widely used model for graph imbeddings on topological surfaces. The extended model is quite beyond what is needed to specify graph imbeddings on surfaces, and it can be used to represent and generate link structures immersed on surfaces. Since link structures immersed on surfaces can be viewed as woven images in 3D space, the extended graph rotation systems provide a well-formulated mathematical model for developing a topologically robust graphics system with strong interactive operations for the design of woven images in 3D mesh-modeling and computer-aided sculpting.