Robert Lipshitz

Professor of Mathematics, University of Oregon

Mathematical Line Drawings in Blender

Blender is a software package for 3D graphics. It also has the capacity to produce line drawings (via its "Freestyle" and "Grease Pencil" features). So, it is potentially useful for drawing figures in topology research papers. Here are some experiments along those lines. I have included both Blender's 3D rendering and its line drawing. In some cases, I cleaned up the line drawing Blender produced, using Adobe Illustrator.

Since some web browsers don't render .svg files reliably, I have included both .jpg and .svg version of the line drawings. Click on any of the images for a larger one (or, for the .svg files, to download just that file). I have not formatted this page to render well on cell phones -- try a computer or tablet.

Description Rendered image Line drawing (.jpg) Line drawing (.svg)
A saddle cobordism, from a forthcoming expository paper with M. Khovanov. 3D rendered image of a saddle cobordism Line drawing of a saddle cobordism Line drawing of a saddle cobordism
Another cobordism, from a "Homotopy functoriality for Khovanov spectra" 3D rendered image of a another tangle cobordism Line drawing of another tangle cobordism Line drawing of another tangle cobordism
A ribbon knot, used as a cover graphic for some talks I gave.
3D rendered image of a ribbon disk Line drawing of a ribbon disk Line drawing of a ribbon disk
A bordered Heegaard diagram, from an NSF proposal.
3D rendered image of a bordered Heegaard diagram Line drawing of a bordered Heegaard diagram Line drawing of a bordered Heegaard diagram
A 2-periodic diagram of the trefoil, from a talk.
3D rendered image of a 2-periodic diagram of the trefoil Line drawing of a 2-periodic diagram of the trefoil Line drawing of a 2-periodic diagram of the trefoil
A (4,7) torus knot, from a movie illustrating a free period of it, from a talk.
3D rendered image of a freely periodic diagram of T(4,7) Line drawing of a freely periodic diagram of T(4,7) Line drawing of a freely periodic diagram of T(4,7)
A piece of a Heegaard diagram, from a talk.
3D rendered image of a piece of a Heegaard diagram Line drawing of a piece of a Heegaard diagram Line drawing of a piece of a Heegaard diagram