Ambiguous Object

Joseph Kerns

M401

Assignment 3

Ambiguous Object

            Everyone has looked at an optical illusion before and thought, “how does that work?” With the advent of 3D printers, the world of optical illusions has opened up to including complex mathematical models. Using additive technology, we can construct sophisticated mathematical models and visualize them in virtual spaces, but then we can print them out and hold them in our hands. 

Kokichi Sugihara has written papers formulating how to construct 3-dimensional objects that appear differently than their reflection in a mirror. For our assignment, I relied heavily on his formulas to execute my design. Below you will see examples of Sugihara’s ambiguous objects, and then the designs that I made.

I decided to design a hexagon inscribed in a unit circle. In order to construct the figure, I utilized Wolfram Mathematica. The Piecewise[] function was an integral part of my construction, due to the nature of a hexagon. After the figure had been created, the next goal was to subtract the two functions from each other, and divide by 2. The goal is to “indent” one function on the other, so that as the viewing angle changes, the figure changes shape.