Optical Illusion - Star and Full Moon

This ambiguous cylinder object is created for Math 401: Mathematics through 3D Printing at George Mason University under course instructor Dr. Evelyn Sander. We focus on the idea of optical illusion and projection of the object to the perpendicular plane. We use the angle of 45 degrees as assumption to viewer looking down from point <0,1,1> in the direction <0, -1, -1>.

For this assignment, the 3D printed object was inspired by Professor Sugihara, a famous Japanese mathematician who is known for his three-dimensional optical illusions. This ambiguous cylinder creates a visual effect from being a circle to a four-pointed star and vice versa. I have used Mathematica to produce the object by creating functions for the star and circle and combine them in respect to their corresponding intervals. Adding and subtracting the two functions in taking account of the 45 angles would create a single object that creates eye and mirror view.

One lesson that I have learned from coding this object is that Piecewise function does not work well with ParametricPlot3D in Mathematica. It caused the 3D object to have a gap which would not hold it together. To solve this issue, I decomposed the objects into smaller pieces of functions with respect to the divided intervals and then combine them into one as my last step.

This optical illusion object was printed on Ultimaker S5 using ABS Orange filament and took approximately 5hrs to complete. Brim support was used but with Green PLA filament. The object dimension is around 42.5 x 58.6 x 50.2 mm with thickness of 3mm.

http://www.isc.meiji.ac.jp/~kokichis/ambiguousc/ambiguouscylindere.html