The Lovely Fancy Fish

thingiverse

The Lovely Fancy Fish Victor Guzman Duran October 12th, 2021 George Mason University Math 401: Mathematics Through 3D Printing This project had me working with optical illusions and how viewing an object from a certain side or angle can alter what we perceive. First off, this phenomenon of seeing different objects has to do with how we see and process what we see – this process can be tricked by using different heights and curves to mask a hidden meaning within the design. This concept is not new and in fact, goes back in history as far as the Greeks since they used these geometrical ideas in order to build their architecture; the most famous being the Parthenon (Barnes, 2011). My design has the idea of changing into 3 different well-known and easy-to-recognize objects as you view them from different angles. From the article written by Dave Richeson, we can parametrize the curves that we use to create the object by using this equation (Richeson, 2016): r(t) = <0.5[f(t)+g(t)], 0.5[g(t)-f(t)]. When working on my code I made sure to think about this equation along with the tutorials that we had on ambiguous objects and just how I could go about combining these concepts together. When looking at my Mathematica code and using the Viewpoint command I was able to create 3 different objects – a fish from the top view, a heart from the front view, and a bowtie from the back view. I have added screenshots of this down below in a separate section, so please ask that you scroll down to see what I am talking about. Using two separate functions that combine into one – an absolute value function and a transcendental (sine and cosine) function allows the design to have sharp edges as well as curves. Combining both functions helped to create the illusions within the design as from the different views the functions playoffs each other. For example, when looking from the top view you will think that the entire top of the shape is curved in the center yet when starting to lower the angle of incidence, we can see that there are sharp edges coming from the absolute value function near the curves. Another cool example happens when looking through the back view, the bowtie shape with the triangles furthest back look like they are higher than the middle curves, yet the curves are always a small amount bigger than the absolute value function. Much of the inspiration for this design comes from wanting to do something different and even though the shapes created by Sugihara are cool, I wanted to create something like the Roy Lichtenstein House Illusion that we saw in class. So, I had to think of something that could look one way but change if viewed from a different angle or side and thanks to the class lectures I was able to continue with my Tutorial B assignment and use the functions I made for that assignment. I also was able to get more knowledge about how optical illusions work on the human mind and the term “forced perspective” which Adou defines as, “misleading photographs of someone holding a building like the Eiffel Tower” (Adou, 2020). I printed my design on the Monoprice Mini V1 in the George Mason University MIX Lab since I was not able to make it to my set print time slot. I used a raft as recommended by the employees and there were no supports as there were no hanging components. The print took about 2.5 hours and there were no issues during the print process. I decided to use a white-colored filament as I think this would be able to show off the most about how the design changes under different viewpoints and angles. I will admit this has been the toughest project so far, but also the most rewarding as I truly enjoyed my final product.