Use of Crossing-State Equivalence Classes for Rapid Relabeling of Knot-Diagrams Representing 2 1 / 2 D Scenes

In previous research, we demonstrated a sophisticated computer-assisted drawing program calledDruid, which permits easy construction of 21/2D scenes . A 21/2D scene is a representation of surfaces that is fundamentally two-dimensional, but which also represents the relative depths of those surfaces in the third dimension. This paper greatly improves Druid’s efficiency by exploitating a topological constraint on 2 1/ D scenes which we call a crossing-state equivalence class . This paper describes this constraint and how it is used by Druid.