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DemetriSpanos
Oct 06, 2026
NOTimothyLottes
Oct 06, 2026
bonzajplc
Oct 06, 2026

ericlengyel

227 items with this tag.

Aug 28, 2026
EricLengyel
Mar 02, 2026
I've written a new blog post called "Dual Approaches to Projective Geometric Algebra".
Feb 06, 2026
When a is a vector and b is any multivector, the geometric product a ⟑ b decomposes as
Jan 23, 2026
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.
May 30, 2025
Generalizing to a convex polygon with n vertices, clipping against a single plane can increase the total vertex count by at most one.
May 23, 2025
I wrote a new blog post about something I'm calling the transwedge product.
Apr 22, 2025
What I ended up doing was transforming axis-aligned rectangles into a pair of overlapping pentagons arranged like this.
Mar 19, 2025
In the GDC bookstore.
Mar 04, 2025
Seriously?
Dec 30, 2024
Geometric algebra is linear algebra.
Dec 16, 2024
That would be highly dependent on how many Bézier curves are involved, whether you're using only fills or a mix of fills and strokes, what stroke features are used (cap, join, dashing), and how fast you're able to upload the output data to GPU-accessible memory.
Dec 15, 2024
This video shows the velocity buffer used to render motion blur during post-processing in the C4 Engine.
Dec 12, 2024
I was surprised to hear that many graphics people were surprised to learn that normals should be transformed with the adjugate transpose matrix.
Nov 27, 2024
Here's some video of the SSAO buffer as I run around in the C4 Engine.
Aug 21, 2024
Following up with 3D homogeneous coordinates.
Aug 11, 2024
A slice perpendicular to the null direction in the diagram about the observer horizon below looks exactly like this complement rotation I found in projective geometric algebra.
Aug 07, 2024
"The problem is that so long as there's sufficiently many crap-producers reviewing each other's crap, crap will continue to be produced."
Aug 02, 2024
The reason I have been giving talks about geometric algebra at NASA recently is that they (rightfully) found the so-called “plane-based” formulation clunky and unpalatable.
Jul 18, 2024
Did you know that quaternions have two different representations in homogeneous coordinates? They make up the special orthogonal group SO(3), but that's a subgroup of two larger complementary transformation groups.
Jul 02, 2024
In conformal geometric algebra, the dot product between two spheres s and t gives the product of their radii times the cosine of the angle 𝜙 between the tangent planes where they intersect.
May 04, 2024
A good programming language does not force you to write code in any specific way.
Apr 28, 2024
A common argument against the east coast metric signature (−+++) is that timelike magnitudes are negative.
Apr 19, 2024
This is a few years old, but holy crap, I can't believe a peer-reviewed journal actually published a paper claiming to have found an 8D associative division algebra.
Apr 15, 2024
There's a neat property about the quadratic formula that most people don't seem to be aware of.
Apr 10, 2024
Some people seem to think that all objects in exterior algebra or geometric algebra are represented in code by big 16-component entities.
Apr 09, 2024
After looking at the current state of Vulkan (the API, driver support, stability, etc.), I have concluded that I'm better off sticking with OpenGL for the time being when it comes to making a PC game.
Dec 11, 2022
Objects in conformal GA can have a real or imaginary radius.
Jan 17, 2022
One of the biggest misunderstandings I see about quaternions is their dimensionality.
Jan 17, 2022
@joonturbo Rotations in 3D space have 3 degrees of freedom.
Dec 26, 2021
It sure would be nice if we had a 100% common language syntax and function library instead of a bunch of random differences among GLSL, HLSL, and PSSL.
Dec 05, 2021
@FlohOfWoe @xgalaxy @CasualEffects @soylentgraham @MGDev91 The original glTF 2.0 spec did have the 4-influence limit.
Oct 03, 2021
So I was seeing inexplicable 100-200 ms frame times in my game, and I couldn't figure out what was going on.
May 03, 2021
Back in 1993, I was taking a number theory class, and there was a semester-long factorization contest that we could participate in.
Feb 17, 2020
How many people were taught that the formulas for the dot product (x₁x₂ + y₁y₂ + z₁z₂) and cross product (y₁z₂ − y₂z₁, z₁x₂ − z₂x₁, x₁y₂ − x₂y₁) are simply definitions and cannot be derived?
Dec 24, 2019
1/8 Every operation in Grassmann/geometric algebra has a dual, which is just as important.
Dec 21, 2019
@richgel999 @Atrix256 @guycalledfrank @PottuVoi The term “G-buffer” was already in use by the mid 90s.
Dec 05, 2019
I have written a draft proposal for a "disjoint" qualifier in C++.
Dec 05, 2019
@bdiamand I'm not convinced that casting to force disjoint should be allowed, but if it had to be there, something similar to const_cast<>() would do it.
Jan 07, 2019
@Atrix256 @paniq @arabek @kebby I have formal mathematical training, and I still think the arcane writings of asshole mathematicians is the #1 reason why a lot of important math isn't widely understood.
Oct 25, 2018
I think it's time to start a new gamedev conference that:
Aug 14, 2018
2018-08-14-thread
Jul 24, 2018
The final figure got even crazier.
Jul 04, 2018
I think it's safe to say that nowadays you should always be using an infinite projection matrix that maps camera-space depth [n,∞] to the reversed range [1,0] after perspective division.
Jun 28, 2018
User interface design rule #163:
Jun 23, 2018
Remember who you're talking to when evaluating a product.
Feb 02, 2018
No matter how expert you are, if another qualified person presents you with a new idea you haven't previously contemplated, take some time to objectively understand and respect its merits before becoming intransigently dismissive.
Dec 29, 2017
I know a lot of people are against software patents, but I believe they're appropriate when you've developed something of significant complexity that would be difficult for someone else to make, and the success of your business depends on you being able to sell products using it.
Nov 17, 2017
One advantage to not including any OS headers or standard C/C++ headers is that I get to enjoy blazing fast build times on my old-ish quad core.
Nov 13, 2017
I wrote down some thoughts about how a "transient" qualifier may have been a much better way to achieve move semantics in C++ compared to the awfulness of rvalue references.
Aug 17, 2017
The consensus so far is that world space, object space, camera space, etc., aren't taught correctly anywhere, and everyone's just guessing.
May 26, 2017
Needs repeating: You can always perform a signed integer range test with a single comparison.
Apr 13, 2017
The more I talk to people about other engine's editors, the more I realize everyone just accepts crashing all the time as normal.
Dec 15, 2016
@JesseRMeyer @casseveritt That would be taking the antiwedge product of two 3D antivectors to produce a homogeneous 2D point.
Oct 02, 2016
I love wasting time over driver bugs that clearly indicate that the functionality I'm trying to use was never tested even one time.
Feb 01, 2015
TextEdit just took 20 sec to open a 1 kB plain text file.
Dec 20, 2014
Remember that integer range checks can always be done with only one comparison: (unsigned) (x - min) <= (unsigned) (max - min)
Apr 05, 2014
I'd like a code editor that can recognize some kind of markup in comments and display it as formatted text with equations and diagrams.
Nov 14, 2013
Getting really sick of intellisense often not knowing the difference between a function declaration and its definition.
Sep 10, 2012
I've come to the conclusion that there's no respectable input device API included with any desktop OS.
Sep 19, 2011
@max_mcguire (1 << i) & 3 causes a microcode stall on Cell.
Jun 04, 2011
Cooked my own minimal Win32/DX header file.
Mar 03, 2026
thanks this interests me so much in relation also to the primary duals of Chaos/Random as essentially a shortening of flux wave from null horizon...
Mar 02, 2026
@EricLengyel A three dimensional drawing is by necessity a projective geometry.
Mar 02, 2026
@EricLengyel One pain behind point-based PGA is it's inconsistency with set theory and Boolean logic, given grades appear as literal bitcodes that you'd want to do Boolean logic on.
Feb 07, 2026
@EricLengyel So in the case of two vectors, the result of the geometric product would be a mixed grade bivector+scalar, right?
Feb 06, 2026
@EricLengyel Never could understand right or left contraction, still don't.
Jan 24, 2026
@EricLengyel Book ordered...
Jan 24, 2026
@EricLengyel @Jonathan_Blow wow, you are wrong on this point.
May 25, 2025
@EricLengyel I read your Foundation of Game Engine Development Volume 1 and Volume 2.
May 24, 2025
@EricLengyel Does this mean Geometric Algebra is metric independent?
Apr 22, 2025
@EricLengyel That moment when we witness an obscure piece of trivia being born in real time.
Mar 21, 2025
@EricLengyel Are these books about programming your own game engine?
Mar 20, 2025
@EricLengyel which should i start reading first?
Mar 20, 2025
@EricLengyel The covers look bootlegged, idk if that makes sense
Mar 20, 2025
@EricLengyel Wait… where that I didn’t see it?
Mar 20, 2025
@EricLengyel Do they also have the copy cats?
Mar 20, 2025
@EricLengyel Eye catcher : The Playful Undead and Video Games: Critical Analyses of Zombies and Gameplay😇😋
Mar 20, 2025
@EricLengyel wth how did you get a ticket
Mar 20, 2025
@EricLengyel wow nice, classics no doubt.
Mar 20, 2025
@EricLengyel
Mar 19, 2025
@EricLengyel Very nice, Eric! I need to order some copies for myself.
Mar 19, 2025
@EricLengyel Where I can buy digital copies?
Mar 19, 2025
@EricLengyel I would buy this book just because of the cover
Mar 19, 2025
@EricLengyel Huzzah!!! another big pile of books to add to my library 😍
Mar 19, 2025
@EricLengyel How many hours poured to write one ? Out of curiosity ? From the first letter typed on the keyboard to "ok i am done" ?
Mar 19, 2025
@EricLengyel I want them all 🥹😅😁
Mar 19, 2025
@EricLengyel Love your books 👍
Mar 19, 2025
@EricLengyel 3.
Mar 19, 2025
@EricLengyel 1.
Mar 19, 2025
@EricLengyel It must be thrilling for you to see it! Huge congratulations.
Mar 19, 2025
@EricLengyel Edge of the table could use some antialiasing
Mar 19, 2025
@EricLengyel 1 & 2 Sitting on my Amazon wishlist.
Mar 19, 2025
@EricLengyel Jeez, I want all of these🤩🫣
Mar 19, 2025
@EricLengyel What happened to the 3rd book?
Mar 19, 2025
@EricLengyel Are you self publishing? 👀
Mar 06, 2025
@EricLengyel Especially that [honest] authors hate being not-original / too close from something that already exist.
Mar 05, 2025
@EricLengyel Maybe make this a strategy for your next book titles, Eric:
Mar 05, 2025
@EricLengyel Probably the name was chosen by Packt.
Dec 16, 2024
@EricLengyel Don't use motion blur.
Dec 16, 2024
@EricLengyel it renders all velocities assuming your eye stares motionless so if your eye moves its all horribly wrong and looks like trash
Dec 15, 2024
@EricLengyel Finally the skeleton from the cover your 3Dmath book appears! Nice work on the engine so far!
Dec 13, 2024
@EricLengyel @SuppDiggyDawg You act like if we could actually read and shit 😅
Dec 13, 2024
@EricLengyel @SuppDiggyDawg I guess that...
Nov 27, 2024
@EricLengyel Yup.
Aug 17, 2024
@skdh @EricLengyel Thanks for sharing our pain.
Jul 21, 2024
@EricLengyel @Ancient_Geo Thank you!
Jul 02, 2024
@EricLengyel Spoilers! I havent gotten this far in the book yet haha
Jul 02, 2024
@EricLengyel My mind is too dirty for this graph.
May 06, 2024
@EricLengyel Imo statement of "good programming language makes it easy to use for anything" is contradictory.
May 05, 2024
@EricLengyel a good programming language could also be one that doesn't have you accidently leak memory
May 05, 2024
@EricLengyel No.
May 05, 2024
@EricLengyel Hmm but do you think Python ("preferably there should be one and only one way to do it") beat Perl (ten ways to do everything)?
May 05, 2024
@EricLengyel *my personal opinion without giving any proof*, *my personal opinion without giving any proof* because *my personal opinion without giving any proof* and that leads to conclusion that *my personal opinion without giving any proof* is the best programming language.
May 04, 2024
@EricLengyel I don’t agree.
May 04, 2024
@EricLengyel @Jonathan_Blow this is not accurate at all.
May 04, 2024
@EricLengyel Preferences are nice, but I don't like the "My way or the highway" language I see a lot.
May 04, 2024
@EricLengyel My ideal programming language would provide a way to specify things which are allowed or not in specific parts of the codebase: Freedom of design is good, but consistency is good as well, and it sucks when everybody does whatever they want in a large codebase, it gets messy.
May 04, 2024
@EricLengyel Which programming language do you consider a good one?
May 04, 2024
@EricLengyel I don't think "good" is really the word, both examples can be good programming languages, just for different people and intents
May 04, 2024
@EricLengyel The BCPL philosophy
May 04, 2024
@EricLengyel This is why I enjoy Lua.
May 04, 2024
@EricLengyel I think it depends whether you've built up taste for the problem space.
May 04, 2024
@EricLengyel I dont quite agree, while it's good that a language stays out of your way, for some things it's the other way around.
May 04, 2024
@EricLengyel This is only true in a world where there aren't junior/mid programmers.
May 04, 2024
@EricLengyel Ok but my design principles are that you ARE forced to write code in a specific way
May 04, 2024
@EricLengyel @Jonathan_Blow I agree, but specialization if languages is nothing bad.
May 04, 2024
@EricLengyel Speaking of languages, this was cute from four years ago.
May 04, 2024
@EricLengyel This is somewhat true.
May 04, 2024
@EricLengyel Minimise friction, maximise joy of programming.
May 04, 2024
@EricLengyel For what "ways"? Is C not good because it forces you to use types for every variable? I assume you don't mean something so fundamental, so where is the line of "coercion" and who is crossing it?
May 04, 2024
@EricLengyel @Jonathan_Blow Such a language might work for personal projects, but it just moves the responsibility of limiting personal expression to the management layer in teams and larger organizations (which usually fails and you get an unmaintainable mess)
Apr 29, 2024
@EricLengyel
Apr 20, 2024
@EricLengyel I wonder how much the problems with reliability of academic research have in common with the reliability of Amazon reviews.
Apr 16, 2024
@EricLengyel Wait…is completing the square somehow related to integrating? Trying to understand how I never noticed how the derivative of a quadratic “undoes” the outer operations in quadratic formula.
Apr 10, 2024
@EricLengyel + degenerate cases where a 0 value in one component would equivalently be a smaller type.
Dec 12, 2022
@EricLengyel @fatlimey ‘Complexity’ seems to work, sticking with the real/imaginary naming
Dec 12, 2022
@EricLengyel @fatlimey Imaginarity.
Dec 12, 2022
@EricLengyel @fatlimey Intuition tempts me to call it phase.
Dec 27, 2021
@EricLengyel It looks like a wrapper interface needs to be developed to smooth out the differences.
Dec 27, 2021
@EricLengyel IIRC, there is also a difference with saturate and clamp...
Dec 26, 2021
@EricLengyel WGSL (WebGPU) has its own story as well 🤦‍♂️
Oct 04, 2021
@EricLengyel I would’ve put money on Chrome
Oct 04, 2021
@EricLengyel Not enuf GPUs
Oct 03, 2021
@EricLengyel Okay, I'm super curious - what _was_ Photoshop doing?
May 07, 2021
@EricLengyel Serious applause and kudos!
May 04, 2021
@EricLengyel awesome!
May 04, 2021
@EricLengyel You sir are my hero
May 04, 2021
@EricLengyel
May 04, 2021
@EricLengyel @threadreaderapp please unroll
May 04, 2021
@EricLengyel Did the computer lab catch on?
May 04, 2021
@EricLengyel Macsbug was freaking work of genius imho @jdeamattson
May 04, 2021
@EricLengyel they let you win the contest cuz they felt sry 4 u staying in a computer lab all night instead of with friends
Feb 17, 2020
@EricLengyel When I was young my dad taught me to read multiplication as “of”.
Feb 17, 2020
@EricLengyel While I can't say I ever looked into into, introductory physics taught me that just about any formula complex enough can be derived
Feb 17, 2020
@EricLengyel I hope this a prelude for a tweetorial!
Feb 17, 2020
@EricLengyel @Atrix256 I learned the inner product in university but I had to wait another 10 years for me to deep dive into outer products on my own.
Feb 17, 2020
@EricLengyel Had to look up Grassman, but I remember the parallelogram-area as one of the key elements in the buildup towards Vector algebra.
Feb 17, 2020
@EricLengyel Derived in high school (higher level maths only).
Feb 17, 2020
@EricLengyel I was tought rather this way: dot product is linear.
Feb 17, 2020
@EricLengyel I saw them in a CS cursus, so we obviously didn't saw algebra behind it, but I remember a few way to retrieve them with some math, I'm not sure how it relates to other stuff.
Feb 17, 2020
@EricLengyel What's this supposed to mean - these _are_ basic definitions.
Feb 17, 2020
@EricLengyel In the absence of exterior algebra, you can also have students discuss why symmetry, bilinearity, and positivity are natural geometric properties for any inner product.
Feb 17, 2020
@EricLengyel We were taught these in geometric terms.
Feb 17, 2020
@EricLengyel Yup, in high school and college.
Feb 17, 2020
@EricLengyel I don’t even know how to answer a question like this.
Feb 17, 2020
@EricLengyel Unfortunately, I was.
Feb 17, 2020
@EricLengyel People were taught things like this in secondary/high school??
Dec 25, 2019
@EricLengyel My problem with the anti wedge product is that it needs an arbitrary pseudoscalar to be defined.
Dec 25, 2019
@EricLengyel precisely the reason I bought FGED1! looking forward to 3!
Dec 25, 2019
@EricLengyel When you say GA community do you mean that abstractly or are you on a mailing list? Is there a better book than the Kaufman series Geometric Algebra for computer science that covers this? I really want to get into GA
Dec 25, 2019
@EricLengyel Yes please!
Dec 21, 2019
@richgel999 @PottuVoi Huh! What was its GBuffer like?
Dec 05, 2019
@EricLengyel @bdiamand I imagine there might be some use cases for a disjoint_cast<>() for the implementation of custom allocators.
Jan 14, 2019
@EricLengyel @Atrix256 @paniq @arabek @kebby This "knowledge obfuscation" is the worst.
Jan 13, 2019
@EricLengyel @TMFAshrafEassa @Atrix256 @paniq @arabek @kebby “What one fool can do, another can”
Jan 08, 2019
@EricLengyel @Atrix256 @paniq @arabek @kebby A lot of it isn't even necessarily arcane.
Jan 07, 2019
@Atrix256 @paniq @kebby I seriously need to update my knowledge.
Jan 07, 2019
@EricLengyel @Atrix256 @paniq @kebby @EricLengyel makes me feel less stupid.
Jan 07, 2019
@paniq @Atrix256 @kebby maybe some day we'll reach levels of star trek's idgaf about money utopia.
Jan 07, 2019
@paniq @Atrix256 @kebby wasn't cryptography deemed to be doomed with the dawn of quantum computing?
Jan 07, 2019
@paniq I call a strawman.
Jan 07, 2019
@paniq It totally does though.
Aug 16, 2018
@EricLengyel Very good, I wish more people used this chart! (and yes, I just used it)
Aug 15, 2018
@EricLengyel What if I do *not* know what I'm talking about? :)
Jun 28, 2018
@EricLengyel Same goes for pressing Delete when the rest of the line is all deleted.
Jun 28, 2018
@EricLengyel Someone somewhere is sweating “oh boy, that was close - at least we can still override the arrow keys on our regon specific number input field”
Jun 28, 2018
@EricLengyel It’s the first thing I turn off in any terminal or VIM setup
Feb 03, 2018
@tom_forsyth @EricLengyel @joeludwig I suppose it depends on how it's said but variants of "why don't/didn't you..X?" I might mean as "This is probably obvious but why dismiss X?"
Jan 03, 2018
@EricLengyel Software patents are evil.
Dec 29, 2017
@EricLengyel Software is math.
Dec 29, 2017
@EricLengyel Let's get back to the original intent.
Dec 29, 2017
@EricLengyel If software patents applied for a much shorter time (say 3-5 years), I'd be right there with you.
Dec 29, 2017
@EricLengyel If it's something of significant complexity wouldn't that already protect your work? Wouldn't that be enough?
Nov 17, 2017
@EricLengyel I think often it's good enough to not include system headers in your own headers, but only .cpp where needed (and maybe own headers that are only used in a few .cpp's)
Nov 17, 2017
@EricLengyel A lot of that comes down to proper usage of C++.
Nov 17, 2017
@EricLengyel on the other hand it is sad what is considered blazing fast in C++ compiler world.
Nov 17, 2017
@EricLengyel Just curious, what is the build system involved?
Aug 18, 2017
@EricLengyel Everyone had this "If I negate this or that value, rendering looks ok"-moment in his life.
Aug 18, 2017
@EricLengyel I know what they mean.
Aug 18, 2017
@EricLengyel Then hurry up and release FGED2!!!
Aug 18, 2017
@EricLengyel I mean, it's a hierarchy right.
May 27, 2017
@EricLengyel @Atrix256 One of my favs.
May 26, 2017
@EricLengyel @dsuoch Yeah, this is one of the things coworkers hate me for
May 26, 2017
@EricLengyel Otherwise UB if hi == INT_MAX and lo == INT_MIN
May 26, 2017
@EricLengyel Shouldn't that be `unsigned(x)-unsigned(lo) <= unsigned(hi)-unsigned(lo)`
Apr 14, 2017
@EricLengyel We do take Unreal editor crashes seriously, not acceptable!
Apr 14, 2017
@EricLengyel @sehurlburt Yeah, what's up with that? Why do people have such a low bar of quality for internal tools?
Apr 14, 2017
@EricLengyel @waddlesplash that goes for graphics drivers as well.
Apr 13, 2017
@EricLengyel Even Maya crashes far too often for a pro tool.
Apr 13, 2017
@EricLengyel So very true...
Apr 13, 2017
@EricLengyel In my experience, that has been the case for every single tool ever made (not just editors) since forever :/
Apr 13, 2017
@EricLengyel @sehurlburt After reading @Code_Analysis's PVS-Studio blog I wonder how the hell anything works on my PC :D More should use it, tiny typos can be fatal.
Apr 13, 2017
@EricLengyel see also: 3D modelers, video editors, audio editors 😭
Dec 15, 2016
@EricLengyel @JesseRMeyer Antivectors sound evil.
Oct 03, 2016
@EricLengyel the story of my life lately.
Oct 02, 2016
@EricLengyel smells a little bit like the world I live in lol
Oct 02, 2016
@EricLengyel It was tested and worked, but later changes in other bits broke it, and they didn't have automated test coverage.
Oct 02, 2016
@EricLengyel yuuup
Feb 01, 2015
@EricLengyel I was snarking about VC++'s start-up speed in 1999.
Dec 20, 2014
@EricLengyel @ben_nuttall Gives me the heebie jeebies since overflow is undefined behaviour in C.
Apr 05, 2014
@ericlengyel Oh yes ! +1
Apr 05, 2014
.
Apr 05, 2014
@EricLengyel Sounds like Knuth's literate programming.
Apr 05, 2014
@EricLengyel well XML commenting can do something like that.
Sep 11, 2012
@EricLengyel then just do it BY yourself for every single OS and then share it with us
Sep 11, 2012
@EricLengyel XInput is good for what it's supposed to do.
Sep 10, 2012
@EricLengyel Windows Joystick API is really simple & clean

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