Optical illusions - mixed pentagon

thingiverse

Math 401-001 Assignment 4: Optical illusions Sang Hyun Yun This ambiguous cylinder object was developed for George Mason University's Math 401: Mathematics through 3D Printing class, taught by Dr. Evelyn Sander. This object belongs to the Reflexively Fused Objects class of optical illusions discovered by Kokichi Sugihara (RFO). RFOs are identified by their appearance when seen at a 45-degree angle on a horizontal mirror. Because of the difference in viewing angles between the direct and mirrored views, this is conceivable. Because both viewpoints are 90 degrees apart, the form depicts both of them at the same time. It should be impossible to make a quadrilateral in this way, yet the picture of a quadrilateral is formed by adjusting the edges such that they appear different from different views. This object was created in Mathematica. I generated two functions based on the image that I provided. one for the quadrilateral's front and one for the quadrilateral's back. It's worth noting that these two functions operate on the same time interval. I created the object in Mathematica by defining functions for the two quadrilaterals and combining them with respect to their respective intervals. Taking into account the 45 degrees, calculating the two functions would result in a single object. I discovered that I must be aware of the object's border. I wanted to make two shapes that went in opposite directions. Because both viewpoints are 90 degrees apart, the shape presents both views at the same time, causing the 3D item to have a gap that would not hold it together. The top and bottom functions do not cover the same interval. By adjusting small amounts, I was able to solve the problem. This optical illusion object was printed on Ultimaker with green filament (40 mm across, 40mm hight).