I’m at Virginia Tech again this week to speak in the math career connections series. I’ll be telling students all about what I’ve been doing with my VT math degrees over the past 30 years.

I posted an unusual entry in my blog that reminisces about my first professional software engineering job before I entered the games industry in the mid-90s.

Bespoke Software for Oscillating Bob Viscometry
terathon.com/blog/viscome...

Porting to the Mac (without MS Word integration) would actually be rather straightforward. It's deploying on the Mac that's difficult.

Several non-Windows users have now told me that they bought a Windows machine just so they could run Radical Pie. Pretty cool!
radicalpie.com

NASA's Artemis II Live Mission Coverage (Official Broadcast) YouTube video by NASA

NASA has a live stream of the Artemis II mission that will run for the entire duration:
www.youtube.com/watch?v=m3kR...

Yes, it is. Just log into your account, and you can download the new version.

Radical Pie 1.8 was released today, and it includes the ability to parse LaTeX. If you have a big equation already written in LaTeX, then you can just copy/paste the plain text into the editor, and Radical Pie will lay it out visually.
radicalpie.com

Thor, the dog of thunder.

Currently working on fur rendering for Chapter 15 in FGED3. Thor, the dog of thunder, is helping with some real-world BRDF references.

New blog post: A Decade of Slug
This talks about the evolution of the Slug font rendering algorithm, and it includes an exciting announcement: The patent has been dedicated to the public domain.
terathon.com/blog/decade-...

The equation editor called Radical Pie that I developed throughout 2025 has been getting a lot of nice feature updates over the four months since its initial release. We're already up to version 1.7. Free trial available on radicalpie.com.

I've written a new blog post called "Dual Approaches to Projective Geometric Algebra".
terathon.com/blog/dual-pg...

I wrote a short blog post about the special mathematical / scientific font included with the Radical Pie equation editor.
terathon.com/blog/radical...

At some point, you neglect infinitesimals. The notion of equality changes from something exact to something that's infinitely close.

Then 1 − 1 = 1 + (−1) = 000...001 + 111...111 = 000...000.000...001, which is the smallest representable number. Now let n be arbitrarily large, and this smallest number looks like an infinitesimal. If you want to see something neat, sum 2^n terms of Grandi's series like this.

Imagine an n.n-bit fixed-point number representation where addition is defined as usual for two's complement values, but any carryout on the left of the whole part wraps around to the far right of the fractional part.

Yes, there are algebras in which a − a is essentially an infinitesimal and not exactly zero. My favorite is this:

Here, ^★ and _★ are the right and left Hodge duals.

The expression b ∨ (a^★) is the definition of the right contraction, sometimes written b ⌊ a. Likewise, (a_★) ∨ b is the left contraction a ⌋ b.

When a is a vector and b is any multivector, the geometric product a ⟑ b decomposes as

a ⟑ b = a ∧ b + b ∨ (a^★),

and b ⟑ a decomposes as

b ⟑ a = b ∧ a + (a_★) ∨ b.

If a and b are both vectors, these both reduce to

a ⟑ b = a ∧ b + a ⋅ b.

Whoa, the SIGGRAPH exhibit floor is tiny this year. This used to be a huge show! What the heck is going on?
maps.goeshow.com/acm/siggraph...

This might be the first year since 1999 that I don't attend GDC.

This is a reminder that every diagram from my book Projective Geometric Algebra Illuminated is available on Wikimedia Commons under the CC-BY-4.0 license. They can be freely used in slides, papers, books, Wikipedia articles, etc., with proper attribution.
commons.wikimedia.org/wiki/User:Er...

Thanks!!

I wrote a very thorough answer to that question here:
www.amazon.com/dp/B0CXY8C72...

Lengyel's conventions. Fuck yeah.

I feel very honored, and you can imagine the deep sense of satisfaction and justification this provides for me. The images above are from a recent NASA paper and a new textbook in aerospace engineering.

Pose Estimation in the Geometric Algebra G(3,0,1) by Russell Carpenter.

Fundamentals of Spacecraft Optical Navigation by John Christian.

I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism. The results of my efforts are now being adopted by prominent scientists and engineers in various fields.

It's got lots of great stuff with two big chapters covering mathematics (including Grassmann / geometric algebra) and another chapter covering things like radiometry, reflectance models, scattering, and ray tracing. There's substantial overlap between this field and computer graphics.

John Christian's new book Fundamentals of Spacecraft Optical Navigation arrived today.

I was recently considering this same question for the purpose of fitting horizontal strokes in a glyph to the pixel grid. I didn't find a satisfying solution.

I added LaTeX output to the latest version of Radical Pie, which was released today. It can't handle everything that Radical Pie can do, but it tries its best to faithfully reproduce equations that can be written in basic LaTeX code without requiring obscure packages.