Thickness design for ambiguous cylinder illusion

Abstract

This paper proposes methods for giving as uniform a thickness as possible to a class of illusion solids called ambiguous cylinders. Ambiguous cylinders are solids that have two quite different appearances when seen from two specific viewpoints, and thus create the impression of impossible objects. In order to realize them as physical objects, we have to give them thickness. However, it is impossible to give a completely uniform thickness despite this being desirable. Instead we have to content ourselves with second-best methods. For this purpose, this paper proposes three alternative strategies for creating objects as uniform as possible. Each strategy has its own merits and demerits, and hence users can choose their method according to their priorities for the visual effects which they want to emphasize.