摘要：This paper presents a new class of surfaces that give two quite different appearances when they are seen from two special viewpoints. The inconsistent appearances can be perceived by simultaneously viewing them directly and in a mirror. This phenomenon is a new type of optical illusion, and we have named it the ＂ambiguous cylinder illusion＂, because it is typically generated by cylindrical surfaces. We consider why this illusion arises, and we present a mathematical method for designing ambiguous cylinders.

摘要：There are many phenomena that generate polygonal tessellations on surfaces of 3D objects. One interesting example is the jackfruit, a multiple fruit found in the tropics. A recent study found the best-fit spherical Voronoi diagram from a photo of jackfruit skin, but the optimization was relative to the radius of the sphere and the height of the spikes. In this study, we propose a method for adjusting the position of the center of the sphere in addition to these parameters. Experiments were conducted using both ideal and real data. However, convergence with real data has not been confirmed due to relaxation of the convergence condition.

摘要：＂Hollow mask illusion＂ is an optical illusion and appears due to an error in the process of reconstructing the three-dimensional objects from our two-dimensional retinal image. In this paper, we present a computational method to create ＂Hollow mask＂ type new illusionary solid by calculating the hollow structure and its shading. The straight line Voronoi diagram for a given shape obtains the three-dimensional vertices of the hollow structure and the shading effect on each surface is calculated under the assumption that each surface has diffusely reflecting surface（Lambertian reflectance）. We also show two examples of our new illusionary solid works.