Siggraph2019 Geometric Algebra

What people said

crubier · 2020-02 · Strong recommendation

Ok look just watch this mind blowing video: [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.

Read the original HN comment ↗

orlp · 2022-04 · Recommendation

> Quite bluntly, this all sounds like an attempt to reinvent euclidean geometry following a convoluted way. I mean, what does all this buy you that applying a subset of affine transformations (scaling, translation, rotation) to an orthogonal coordinate system doesn't give you already? It is attempting to reinvent Euclidean geometry, yes. I don't think it's convoluted though. To give a prime example, take the article we're commenting on: interpolating rotations. Or more generally: interpolating transformations. Just doing 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: [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 geometric algebra. E.g. two planes always intersect, it just happens that the intersection is a line at infinity if they're parallel. The exact same code used to translate and rotate a point around the origin can be used to translate and rotate a line, or a plane around the origin. Al

Read the original HN comment ↗

adamnemecek · 2021-12 · Recommendation

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 [VIDEO]

Read the original HN comment ↗