Dual Overlapping Cylinders

Jean-Marc Daviau-Williams

For the print this week, we made ambiguous objects where when viewed from a 45 degree angle is seen as one shape, but when viewed from the opposite direction is seen as another.  My object was a dual, overlapping cylinder where they look like diamond cylinders with one side over the other and elliptical/circular cylinders from the opposite direction with the other side over.  The process of making this print was a learning experience, but came out well.

First, I had to greater familiarize myself with Mathematica, understanding how the function for creating the 3d model interacts with the mathematical functions put through it.  I started with the function ParametricPlot3D[], with the boilerplate code provided with the assignment.  Next, I copied the arguments, shifted them by plus or minus 1, and pasted them as additional arguments in the same function.  This created the initial plan of the two shapes, ensuring the optical illusion could be achieved.  

Next, I had to use the same ParametricPlot3D[] function to create the full 3d model to print.  This added an additional layer of complexity, as the code required many more nested, curly-bracket arguments.  After some playing around with the values, I was able to get my cylinders positioned one over the other and overlapping in the x direction.  Overall, this took the most effort in the whole process.

Finally was the process of printing the actual object.  During my print slot, the only printer available was the makerbot as the ultimaker and lulzbot were experiencing technical difficulties, which is common for cutting-edge technology.  With the .stl file I exported from Mathematica, it was sliced on the makerlab computer and took x hours to print.

This assignment was an important learning experience.  Many 3d objects that are hard to visualize are only possible to create through the use of mathematical functions in cartesian, polar, or spherical coordinates in software like Mathematica.  This will be even more apparent in the next assignment, where I am to print a visual representation of the discontinuity of a surface, differentiable in the x and y directions but non-differentiable itself.