Trefoil Knot

thingiverse

A 3-D rendering of a trefoil knot is achieved by taking a parametric path representation and thickening it to form a solid, without making the knot self-intersect. The design starts in Sage, where it's exported to X3D, resulting in a file included here for reference. This file is then edited in Blender to remove artifacts left behind by Sage, such as a cube of lines around the figure. After editing, the file is exported to STL, imported into Cura, scaled because graph units in Sage become millimeters in Cura, and situated on a print platform. The STL file is then exported again to form the STL thing file here. The Sage code used to generate the figure is as follows: t = var('t'); parametric_plot3d([sin(t)+2*sin(2*t), cos(t)-2*cos(2*t), -1*sin(3*t)],(t,0,2*pi), thickness=50, aspect_ratio=1) Since Sage is Python-based, it's essential to check line breaks. The surface is defined parametrically and plotted using the parametric_plot3d() method with a large enough "thickness" setting to make the knot substantial. A nod of appreciation goes to artist M.C. Escher for his iconic work: http://www.mcescher.com/Gallery/recogn-bmp/LW444.jpg