Graph/Knot Theoretical Analysis and Generation for Impossible Figures

An algorithm to represent impossible multibar figures and their subclass of torus figures is proposed based on graph and knot theory. A multibar type graph, which is an abstract concept of multibar figures, is defined by the junction graph that represents the connections of the lines. It is shown that the junction graph is able to characterize multibar figures where this characterization is realized according to the type of the multibar type graph. An automatic drawing system of torus figures is also presented by analyzing junction graphs that construct the shapes of corners of torus figures. The proposed method aims a basic tool for experiments in visual psychology and possible/impossible figures generation.