Topology-disturbing objects: a new class of 3D optical illusion

Abstract

A new class of objects, called topology-disturbing objects, is presented. These objects appear to disturb the topological properties when they are seen from two specific viewpoints; for example, two objects appear to be separated when seen from one viewpoint while they appear to be intersecting when seen from the other viewpoint. This cannot happen physically, but due to the phenomenon of an optical illusion, it can be perceived to occur. A general method for designing this class of objects is presented and examples are given. These objects might provide a new resource for arts and entertainment.