# Quadratic Surfaces – Hyperbolic Paraboloid

The quadratic surface that gave me the most trouble was the hyperbolic paraboloid. This surface could not be created in Cinema 4D and had to be imported from Mathematica. When I imported the surface from Mathematica the center of the saddle had hundreds of little polygons that overlapped, which became a huge problem when I tried to extrude them to give the surface thickness.

I had to spend a long time experimenting to find the lowest number of plot points I could use in Mathematica and still get an accurate object. Once I had done this I did the same thing with the optimize tool in Cinema 4D to see how big I could make the polygons before the surface started to lose accuracy. The first time I went through all these steps the hyperbolic paraboloid I had chosen just didn’t work correctly. So, I went back to the beginning and created a new Mathematica file of a hyperbolic paraboloid, and spent some time deciding where to cut it off to create edges that were as straight as possible.

Once I had done this and imported the surface into Mathmatica I optimized the surface as much as it would allow and extruded it. Finally I had a surface I could print! I then added the hyperbolic paraboloid’s equation to the surface. Instead of just imprinted the equation, since the surface was so thin I punched it all the way through.

In order to print this surface I used the FormLabs liquid printer. When the object came out of the printer it looked great and only had a few minor flaws to fix after this first print. One of the issues was the size of the object; it was just a little too small. The other issue was that the 2 in the exponent of the equation didn’t quite form correctly because it was too small. The final issues was that the equation had a $$+$$ sign where there should have been a $$–$$ sign (oops). The equation was little too long with a 0 that was missing its center.  To fix these problems I rearranged the equation (and fixed the sign issues) in Adobe Illustrator and then punched it through the surface again. The second print on the liquid printed I made 1.4 times larger than the last print.

The final print still had issues with the formula but otherwise worked out well. We are currently looking into changing the font to see if that helps with this issue. This model can be found on Thingiverse here.

Using my experiences building this and the other quadratic surfaces, I’ve put together a set of instructions on how to build quadratic surfaces using Mathematica and Cinema 4D. This can be found here.