hamish_todd

7 ms·

1.
by hamish_todd 3mo ago
You are correct and this is another failing of the article. Hestenes has very little relevance to the field today - the Atiyah/Penrose school, via Jon Selig, is much more influential. To be fair the article would have been correct ten
2.
by hamish_todd 3mo ago
You're certainly correct that it would be the done thing in physics (and I have written a draft for my blog). But note that Geometric Algebra is significantly a tool for graphics/game developers, who tend to prefer videos (even th
3.
by hamish_todd 3mo ago
Very sorry to hear about the brain fog, that's rough. Best of luck getting through it. > in some cases What cases do you have in mind? > why are these your operators in the first place? This is a perfectly reasonable question but
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by hamish_todd 3mo ago
Ah! If you do it would probably would need to be a followup rather than addendum
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by hamish_todd 3mo ago
If you want to learn physics from a geometric viewpoint, GA is brilliant. Here's a playlist of my stuff, which is aimed at computer graphics folks: https://youtube.com/playlist?list=PL9a8DfUJQcuA9AXqvjxYolq5-... Leadin
6.
by hamish_todd 3mo ago
In physics and especially computer graphics, yes. These are two fields that are culturally very different from algebraic geometry, in that mathematical techniques that appear at all "exotic" are "hard to sell", even if t
7.
by hamish_todd 3mo ago
The geometric product is transform composition. It plays the same role as matrix multiplication: if a group is represented by a set of matrices or multivectors then the GP will be group composition. For example Cl(4,2) can represent the spa
8.
by hamish_todd 3mo ago
He's distressingly wrong about this, the geometric product is transform composition (Apologies to folks who have seen me repeat this a million times; but it's very important folks be aware of it)
9.
by hamish_todd 3mo ago
Can do either! If your multivectors represent linear transformations then their products will also be linear transformations. If they're affine transformations then their products will be affine transformations. Euclidean, conformal, e
10.
by hamish_todd 3mo ago
The geometric product is transform composition. TRANSFORM COMPOSITION! (sorry, it's not your fault or even his that you didn't know this - GA textbooks should have it as the first thing they teach but they don't)
11.
by hamish_todd 3mo ago
I'm a GA researcher. I did this livestream of my reaction to the article https://m.twitch.tv/videos/2282548167 TLDR it is quite a bad article. One of the closest thing he has to a real argument is "I don&#x27
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AI's Non-Euclidean Geometry(youtube.com)
2 points by hamish_todd 1y ago|0 comments
13.
by hamish_todd 1y ago
Since Geometric Algebra == Clifford Algebra, Michael Atiyah, Roger Penrose, and Paul Dirac disagree with you.
14.
by hamish_todd 2y ago
You're making the word "some" do a lot of work in this comment. It's true that eg I would represent the inertia tensor with a matrix. But I would calculate it with GA... and I struggle to think of many other physics prob
15.
by hamish_todd 2y ago
The geometric product does transform composition. It has all the properties you want for multiplication in an algebra, or indeed a monoid or group. So it is like matrix multiplication, but for transforms represented as multivectors. Multive
16.
by hamish_todd 2y ago
There are ten thousand examples I want to give of why you're wrong. We have to start somewhere so here's a favourite, the "universal projection formula": (A.B)/B Projects any A onto any B, in any number of dimension
17.
by hamish_todd 2y ago
A quaternion is some amount of identity averaged with some amount of line reflection. You can visualize the line reflection as a pair of planar reflections at 90 degrees to each other. You can visualize the identity as a pair of planar refl
18.
by hamish_todd 2y ago
The second paragraph of the conclusion: "Nor should we be trying to make everything look more like complex numbers and quaternions. Those are already weird and confusing; we should be moving away from them!" It's also implici
19.
by hamish_todd 2y ago
I did two streams where I went through this article and explained the many places it is wrong. The second part of the article has more maths in it, so most of the content is there, you can watch it here: https://www.twitch.tv&#x2
20.
Visual Guide to Quaternions and Geometric Algebra for game programmers [video](youtube.com)
2 points by hamish_todd 2y ago|1 comments
21.
by hamish_todd 2y ago
Hey folks, here are two lectures by me on GA, at the Game Developer Conference: https://www.youtube.com/watch?v=en2QcehKJd8 https://www.youtube.com/watch?v=dSe7eg8Dj98 They include a visual code editor I wo
22.
by hamish_todd 3y ago
From that page: "When Euler Angles interpolation is used, Unity internally bakes the curves into the Quaternion representation used internally. This is similar to what happens when importing animation into Unity from external programs&
23.
by hamish_todd 3y ago
Where in the docs does it say that? Euler angle lerps, in the general case (eg none of the starts or ends are 0), look like complete shit. You need the log quat representation. Exp( T log(q1/q0) ) q0
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by hamish_todd 3y ago
Unity uses quats in its object transforms?
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by hamish_todd 3y ago
It's an extremely common misconception that because GPUs have matrix matrix and matrix vector products in the standard, that means GPU companies must be accelerating them. In fact, because it is SIMD across the shader cores already, yo
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by hamish_todd 3y ago
The mixed elements are the important ones! A quaternion with w=1, x,y,z=0 is just the identity. A quaternion with w=0, x=1, or perhaps w=0, x=y=0.7, those would only ever be rotations by 180 degrees. If you want arbitrary rotations, you nee
27.
by hamish_todd 3y ago
>"untyped" It's amazing because that's the diametric opposite of what I'd consider to be true this is what the non-GA approach does, and which we avoid! The modern approach to GA, eg https://en.wikipe
28.
by hamish_todd 3y ago
Seeing lots of discussion here! People with a game programming background might get something out of the talks I gave at the Game Developer Conference this year. The first one is on quaternions and and the advanced Geometric-Algebra-like us
29.
Pictogrammatic Programming Project(youtube.com)
1 points by hamish_todd 4y ago|0 comments
30.
Game about bayesian updating; watch murder mysteries together, bet on the ending(murdershebet.com)
2 points by hamish_todd 5y ago|0 comments

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