Quadratic Surfaces – Hyperboloid of Two Sheets

The last quadratic surface I printed was a hyperboloid of two sheets.

Screen Shot 2015-07-20 at 1.25.54 PM For the hyperboloid of two sheets I created the entire object from scratch in Cinema 4D using the same process I used to create the cone and other similar objects. For this surface I used the same formula spline as the hyperboloid of one sheet \(x(t)=cosh(t), y(t)=sinh(t), z(t)=0\), and then rotated it to the correct orientation. I then used the lathe tool and rotated this spline 180 degrees since this was all it needed. Because of this I needed to use only 30 rotation segments for a total of 60 all around the object. 

Screen Shot 2015-07-20 at 1.25.32 PMI also had to reverse the normals on half of the object to make sure they were all aligned with the other half before I extruded the surface. I optimized the polygons to be sure the edges joined up into one object. I then extruded the surface to create my hyperboloid of two sheets. I copied this and put equations through one of them. I also made sure to Boole the edges of the hyperboloid to make them flat for printing. 

FullSizeRender 5 copy 2


Here is a picture of the final object! It can be found on Thingiverse here.