Hyperboloid of One Sheet

thingiverse

A 3-D rendering of a hyperboloid of one sheet ("basket" surface) forms part of my "Gallery of Quadric Surfaces." The design begins in Sage, then exports to X3D (resulting file included), followed by importing X3D into Blender. In Blender, I edit out artifacts left behind by Sage, such as a cube of lines surrounding the figure, and thicken the surface so that Cura recognizes it as a solid object: select Properties -> Modifiers (wrench icon) -> Add Modifier -> Solidify; set Thickness to 0.1 and click Apply; then export to STL, and import STL into Cura. In Cura, I scale the figure (graph units in Sage become millimeters in Cura) and position it on the print platform, followed by exporting STL again to form the STL thing file here. The Sage code that generates the figure reads: u,v=var('u,v'); parametric_plot3d([sqrt(1+v^2)*cos(u), sqrt(1+v^2)*sin(u), v], (u,0,2*pi), (v,-3,3), aspect_ratio=1). Since Sage is Python-based, I verify line breaks. Note that the surface is defined parametrically and plotted using the parametric_plot3d() method.