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Siggraph2019 Geometric Algebra

Bivector

5.7K subscribers • 1 video on Hallway

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  • Recommended by 9 people: 8 on Hacker News and 1 on Lobsters.
  • Presented by Steven De Keninck

Intermediate. Assumes working knowledge.

87K views6 years ago9 recommendations

Graphics and audioComputer scienceRenderingMath for programmers

Steven De Keninck and Charles Gunn introduce geometric algebra for computer graphics programmers, demonstrating its elegance and efficiency with live code examples.

**Programmer focused part** starts at Try the examples here enkimute.github.io/ganja.js/examples/coffeeshop.html The Geometric Algebra course at Siggraph 2019. Intro : Charles Gunn ( - ) Course : Steven De Keninck ( - end) Course notes, slides, software, discourse and discord at bivector.net

Why it's here

9 people recommend this

What people say. Highly recommended as an intuitive, developer-friendly introduction to geometric algebra and its advantages over traditional vector math in graphics.

Moments people linked to

friendlysockon Lobsters • Recommends

Geometric Algebra
13View on Lobsters

crubieron Hacker News • Recommends

On “Let's remove quaternions from every 3D engine (2018)”

Ok look just watch this mind blowing video: link to this video After that, you can’t argue that geometric algebra is not THE right way to do geometry. Projective geometry (in any dimension) is a subset of geometric algebra. Please watch it.
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cs702on Hacker News • Recommends

On “Ask HN: What are you learning?”

The following video has a good, developer-friendly introduction to the subject that should answer your question. Take a look in particular at the code snippets that are sprinkled throughout the video and notice how much cleaner, shorter, simpler, less computationally costly, and "universal"/"exception-free" the code becomes: link to this video
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aabajianon Hacker News • Recommends

On “4D Toys: how objects bounce and roll in 4D – paper accepted to SIGGRAPH 2020”

If you like this, then checkout the presentation on Geometric Algebra from 2019 SIGGRAPH: link to this video You can then play around with objects in 3D, 4D, and beyond: link
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aabajianon Hacker News • Recommends

On “Ask HN: What startup/technology is on your 'to watch' list?”

Geometric algebra: link to this video It makes a lot of hard physics problems (Maxwell's equations, relativity theory, quantum mechanics) much more understandable and (I'm told) unifies them in a common framework. I think it will help your average developer become comfortable with these areas of physics.
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adamnemecekon Hacker News • Recommends

On “Intuitive Guide to Maxwell's Equations”

It's one equation in geometric algebra. link Also there is a new community for geometric algbera people link . Check out the demo link Watch the SIGGRAPH talk link to this video Join the discord link
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ivan_ahon Hacker News • Recommends

On “Geometric Algebra for Python”

Here is a video link to this video and the associated HN thread link that provide some more background on GA and its applications. I think you're generally right that GA is a rebranding of concepts we already knew about, however representing them in a uniform manner seems like a useful thing to do. The at t=4083 in the video they show some interesting examples of projections, rotations, and other geometric operations that can be done quite simply link to this video
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adamnemecekon Hacker News • Recommends

On “All Hail Geometric Algebra”

You should check out the bivector community link . Check out a demo link Join the discord link . Enki (the guy behind bivector) also gave a talk on GA at SIGGRAPH 2019 link to this video
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adamnemecekon Hacker News • Recommends

On “Vanishing zeroes for geometric algebra in Rust”

You should check out the bivector community dedicated to geometric algebra link . Check out a demo link Join the discord link . Enki (the guy behind bivector) also gave a talk on GA at SIGGRAPH 2019 link to this video
View on Hacker News

adamnemecekon Hacker News • Recommends

On “Ganja.js: Geometric Algebra Generator for JavaScript, C++, C#, Rust, Python”

You should check out the bivector community dedicated to geometric algebra link . Check out a demo link Join the discord link . Enki (the guy behind bivector) also gave a talk on GA at SIGGRAPH 2019 link to this video
View on Hacker News

these_are_not_ton Hacker News • Recommends

On “Ganja.js: Geometric Algebra Generator for JavaScript, C++, C#, Rust, Python”

…eal line: when encountered for the first time, it is not simple in any way, but it offers a clean solution to many (originally real valued) problems (perhaps by the fact that it is algebraically closed?). NB: the author of this library also made a very interesting presentation of geometric algebra (using this library as vehicle) for SIGGRAPH 2019: link to this video It has been posted a few times on HN before.…
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adamnemecekon Hacker News • Recommends

On “Quaternion Quantum Mechanics [video]”

Reasoning about space and time is just so much nicer in geometric algebra. There's a new cool community on geometric algebra link The founder (Steven De Keninck aka enki) gave a talk at Siggraph2019 link to this video You should join the discord link
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javajoshon Hacker News • Recommends

On “Manim: An animation engine for explanatory math videos”

…9 2 that explains why this algebra is better than matrices, tensors, vectors, complex numbers. Of particular interest (to me anyway) is the 2D projective geometry. I don't want to oversell it, but ganja is fucking amazing and there is a great deal I want to do with it. For one, I'd like to recapitulate my physics degree with it. 1 link 2 link to this video…
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adamnemecekon Hacker News • Recommends

On “Quaternions”

You should check out the bivector community dedicated to geometric algebra link . Check out a demo link Join the discord link . Enki (the guy behind bivector) also gave a talk on GA at SIGGRAPH 2019 link to this video
View on Hacker News

orlpon Hacker News • Recommends

On “Exponentially Better Rotations”

…ing this with rotations without suffering gimbal locks already brings you to quaternions. Are quaternions 'convoluted'? The fact that all objects are native to the algebra means they're composable. Take for example this slide of the formula of a 4D torus in coordinates, and in 4D PGA: link The talk in general has a bunch of example applications: link to this video Questions such as "the intersection of this line and this plane", "the line through two points" "the circle where these two spheres intersect", "the point at the intersection of three planes", "the projection of this line on this plane" and such are trivial, native (the resulting object is part of the algebra) and exception-free in geometri…
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jiggawattson Hacker News • Mentions

On “Why is Maxwell's theory so hard to understand? (2007) [pdf]”

Maxwell's theory is hard to understand because it's based on an almost-but-not-quite-appropriate algebra. It's like stringly-typed programming. It works , but it's messy and hard to understand. Maxwell's set of coupled differential vector electromagnetic equations simplify to a hilariously short single equation in Geometric Algebra. A random Google turned up this paper comparing classic EM and the GA formulation. It's not even the simplest possible representation, because that uses natural units and a 4D GA to basically condense the entire set of EM theory into about 4 characters worth of equation that is fully relativistic for free: link It's almost a joke. To me it's reminiscent of looki…
View on Hacker News