Overview on Mathematical Illustration in Blender

A line art cube

Wed, 13 Sep 2023 00:00:00 +0000

A line art cube#

At the end of this tutorial we will have made the following line art image:

Working through this tutorial takes 15 to 30 minutes.

Getting started with Blender#

We’ll start with a very quick introduction to Blender. If you have used it before, skip to the next section. If you haven’t used it before, I strongly recommend working through an hour or so of a more general introduction to blender, such as this one (which is newer but which I haven’t used) or this older one (which I have).

Add-ons

Wed, 13 Sep 2023 00:00:00 +0000

Some convenient add-ons#

Blender has many add-on features which are not enabled by default. Here are a few which are useful for mathematical drawings. There are probably others that would also be useful but which I have not explored. (This tutorial is less tutorially than the others.)

Installing add-ons#

There are three kinds of add-ons: ones that are included with Blender but simply not enabled by default, ones in Blender’s online extension library, and ones you can download and install. Most of the add-ons discussed here are from the second category. (Blenderkit, discussed briefly at the end, is in the third category.)

Curve basics

Wed, 13 Sep 2023 00:00:00 +0000

Curve basics#

In this tutorial, we will create a couple of diagrams for the trefoil: a sloppy one, and then a tidier one that witnesses several of its symmetries:

We will then create a diagram for the knot 9₄₆, and from it, a cable of 9₄₆:

(Click for .svg versions.)

Curve scripting

Mon, 01 Jul 2024 00:00:00 +0000

Curve Scripting#

In this tutorial, we will create a family of fibers of the Hopf fibration, lying over a great circle in $S^2$:

We will use Blender Python, and assume some familiarity with (ordinary) Python. Working through this tutorial takes about 20 minutes, though understanding it might take longer. There is explanation of how the code works and some other sample code at the end.

Mesh scripting

Mon, 01 Jul 2024 00:00:00 +0000

Mesh Scripting#

This curve has three parts. In the first part, we will create some contact planes, by just adding, rotating, and translating mesh plane objects. In the second, we will build a small mesh by hand, to understand the format. In the third, we will warp Blender’s default monkey. There is also sample code at the end for creating tube plots. Like the Curve Scripting tutorial, this tutorial assumes some familiarity with Python. This tutorial does not assume you have gone through the Curve Scripting tutorial, but is a little terser than that one.