Umbilic Torus

thingiverse

A three-dimensional rendering of an umbilic torus begins in Sage. The design is then exported to X3D, with the resulting file included. From there, it's imported into Blender for editing. In Blender, any artifacts left behind by Sage are removed, such as a cube of lines around the figure. Next, it's exported to STL and then imported into Cura. In Cura, the figure is scaled because graph units in Sage become millimeters in Cura. The figure is also situated on the print platform before being exported again as an STL thing file here. Here is the Sage code to generate this figure: u, v = var('u, v') parametric_plot3d([sin(u)*(7+cos(u/3-2*v)+2*cos(u/3+v)), sin(u/3-2*v)+2*sin(u/3+v), cos(u)*(7+cos(u/3-2*v)+2*cos(u/3+v))], (u,-pi,pi), (v,-pi,pi), aspect_ratio=1) Since Sage is Python-based, be sure to check line breaks. The surface is defined parametrically and plotted using the parametric_plot3d() method. This surface is closed, so Cura already recognizes the STL as representing a solid without any need to "thicken" the surface in Blender. With an obligatory nod to sculptor Helaman Ferguson: http://helasculpt.com/gallery/?album=3&gallery=66