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Eric Lengyel
Personal blog · terathon.comgamesmathprogramming
Eric Lengyel's personal blog at terathon.com covers games, math and programming. Since 2013, 40 different Hacker News readers have linked it 47 times, most often “Slug Text Rendering Algorithm Dedicated to Public Domain”. It is still writing: the last post was on 2026-04-12, and you can follow it by feed.
Most-linked posts?
- Slug Text Rendering Algorithm Dedicated to Public Domain5 people · 5 mentions · first linked 2026-03-17
- Projective Geometric Algebra Done Right4 people · 4 mentions · first linked 2020-01-24
- So you want to write a technical book3 people · 3 mentions · first linked 2021-10-15
- /blog/symmetries-in-projective-geometric-algebra/2 people · 2 mentions · first linked 2020-11-30
- Poor Foundations in Geometric Algebra2 people · 2 mentions · first linked 2024-08-24
- The Development of Radical Pie2 people · 2 mentions · first linked 2025-11-01
- GPU – Centered Font Rendering Directly from Glyph Outlines [pdf]2 people · 2 mentions · first linked 2018-05-26
- GPU-Friendly Font Rendering Directly from Glyph Outlines [pdf]2 people · 2 mentions · first linked 2017-03-28
- /gdc12_lengyel.pdf2 people · 2 mentions · first linked 2020-01-26
What Hacker News says?
For people interested in this topic, here's a good set of slides going over Grassman/Clifford/Geometric algebra concepts: http://www.terathon.com/gdc12_lengyel.pdf And another good site: https://mattferraro.dev/posts/geometric-algebra
Comment linking /gdc12_lengyel.pdf
on “Look, ma, no matrices”Submitted Poor Foundations in Geometric Algebra as a story · 229 points
HN discussionHe posts to his blog about GA too: http://terathon.com/blog/projective-geometric-algebra-done-r... And, he has a website dedicated to PGA: http://projectivegeometricalgebra.org
Comment linking /blog/projective-geometric-algebra-done-right/
on “All Hail Geometric Algebra”Submitted Projective Geometric Algebra Done Right as a story · 137 points
HN discussionThanks for sharing this blog post and the cheat sheet http://terathon.com/pga_lengyel.pdf I agree the representation chosen in the SIGGRAPH lecture and the associated docs seems somewhat unnatural and counter-intuitive (why are points being represented as trivectors?). Have you reached out to C. Gunn or S. De Keninck to ask what they think about the representation you propose in that blog post and the geometric prod…
Comment linking /pga_lengyel.pdf
on “Siggraph2019 Geometric Algebra (2019) [video]”Submitted So you want to write a technical book as a story · 131 points
HN discussionHere is an informative critique of this video along with an improved application of geometric algebra to computer geometry: http://terathon.com/blog/projective-geometric-algebra-done-r...
Comment linking /blog/projective-geometric-algebra-done-right/
on “Siggraph2019 Geometric Algebra (2019) [video]”Submitted A Mathematical Keyboard Layout (2018) as a story · 76 points
HN discussionHe filed in 2018-02-01, after publishing in 2017. What do you think breaks in the patent system with such an approach? https://terathon.com/blog/decade-slug.html
Comment linking /blog/decade-slug.html
on “SDF vs. MSDF vs. Slug: GPU Text Rendering”Submitted C4 game engine drops Linux support citing frustrations with desktop Linux as a story · 44 points
HN discussionThe details are in Eric's post here: https://terathon.com/blog/decade-slug.html The timeline basically checks out, maybe it simply took the patent office over a year to process the patent application?
Comment linking /blog/decade-slug.html
on “SDF vs. MSDF vs. Slug: GPU Text Rendering”Submitted GPU-Friendly Font Rendering Directly from Glyph Outlines [pdf] as a story · 19 points
HN discussionAnother poster has already linked [1] and [2]. That's what I was getting at as well: A bias towards the wedge/'join' and against the 'anti-wedge'/'meet' crops in via the geometric product, when the situation should be symmetric due to Hodge duality. This leads to constructions I find rather unnatural. [1] http://terathon.com/blog/projective-geometric-algebra-done-r... [2] http://terathon.com/blog/symmetries-in-proje…
Comment linking /blog/symmetries-in-projective-geometric-algebra/
on “Geometric Algebra (2012)”Submitted The Transwedge Product as a story · 11 points
HN discussion> Also, why the need o a dual(e12, e02, e01) to represent a point when in vector it's just a (e0, e1, e2). This is just counterinuitive. It seems like it isn't needed, but it hasn't all been wrapped up into an easy to understand package yet: http://terathon.com/blog/projective-geometric-algebra-done-r... http://terathon.com/blog/symmetries-in-projective-geometric-...
Comment linking /blog/symmetries-in-projective-geometric-algebra/
on “Geometric Algebra (2012)”Submitted The Return of Forgotten Math in Computer Graphics [pdf] (2012) as a story · 5 points
HN discussionWhat you wrote has nothing to do with Eric's geometric antiproduct. Eric calls the dual vectors in a geometric algebra (or Grassmann algebra as he calls it) antivectors . See his presentation from GDC2012 around the middle: >Instead of saying (n−1)-vector, we call these “antivectors” http://www.terathon.com/gdc12_lengyel.pdf (also: https://youtu.be/WZApQkDBr5o?t=1673 ) So e.g. in 3D bivectors would be antivectors, i…
Comment linking /gdc12_lengyel.pdf
on “Projective Geometric Algebra Done Right”Submitted So you want to write a technical book as a story · 5 points
HN discussionPretty good overview of what you asked about - https://medium.com/@evanwallace/easy-scalable-text-rendering... Other links https://developer.nvidia.com/gpugems/gpugems3/part-iv-image-... https://jcgt.org/published/0006/02/02/ Also ( https://terathon.com/i3d2018_lengyel.pdf ) Which was developed into a product IIRC. Another GPU text renderer https://github.com/hypernewbie/VEFontCache There's been other development an…
Comment linking /i3d2018_lengyel.pdf
on “Why are 2D vector graphics so much harder than 3D? (2019)”Submitted Geometric Algebra Books as a story · 3 points
HN discussionSee also Eric Lengyel's take on this which he calls the Transvoxel Algorithm: http://www.terathon.com/voxels/
Comment linking /voxels/
on “Generating Complex Procedural Terrains Using the GPU (2008)”Submitted Projective Geometric Algebra done right as a story · 3 points
HN discussionSo You Want to Write a Technical Book http://terathon.com/blog/so-you-want-to-write-a-technical-bo...
Comment linking /blog/so-you-want-to-write-a-technical-book/
on “Advice to Prospective Book Authors (2003)”Submitted The Development of Radical Pie as a story · 2 points
HN discussionIndeed, the most recent example I've seen of this is the slug library: http://sluglibrary.com/ Presentation slides: http://terathon.com/i3d2018_lengyel.pdf A paper: http://jcgt.org/published/0006/02/02/
Comment linking /i3d2018_lengyel.pdf
on “Introducing the Distance Field Generator”Submitted Wedge Products, Dot Products, Scalars, and Norms as a story · 2 points
HN discussionI agree in general, but can think of at least one counterpoint: https://terathon.com/blog/decade-slug.html Actually novel implementation is protected, paid the author's bills, and was dedicated to the public domain recently - no massive corp involved.
Comment linking /blog/decade-slug.html
on “Mistral Patent for "Code implemented tool calls"”Submitted Wedge and Dot Products Involving Scalars as a story · 2 points
HN discussionI like how you gloss over the "needed libraries". But seriously, let's take a quick look (here)[ http://www.terathon.com/architecture.php ] and think, what might be a clear pain point in Linux, even if the "needed libraries" worked perfectly with all the hardware and all distros and the blobs were perfect. Did I hear someone say "Linux sound support"? Yes, that is a correct answer. Sound in Linux is a know clusterfu…
Comment linking /architecture.php
on “C4 game engine drops Linux support citing frustrations with desktop Linux”Submitted GPU Font Rendering: Current State of the Art (2018) [pdf] as a story · 2 points
HN discussion
