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I thought this was called projective geometric algebra. Is the projective part optional? Or it refers to a specific thing. Why would there be a bivector commun

by iamwil 6y ago

I thought this was called projective geometric algebra. Is the projective part optional? Or it refers to a specific thing. Why would there be a bivector community? Is it something relatively new, so there's a sense of "we're convinced, but other people aren't yet?"

adamnemecek 6y ago
It’s a community dedicated to discussion and promotion of geometric algebra.
fanf2 6y ago
Geometric algebra is very general: it can model straight Euclidean space, non-Euclidean geometry, projective geometry (the familiar homogeneous coordinate system) and also conformal geometry. Some of the earlier applications of geometric algebra to computer graphics were based on conformal geometry (eg https://rjw57.github.io/phd-thesis/rjw-thesis.pdf https://rjw57.github.io/phd-thesis/rjw-thesis.pdf) because it can model more interesting things than projective geometry, but it is more computationally expensive than projective geometry. WRT community, the https://bivector.net https://bivector.net web site has a discussion forum for people interested in geometric algebra. I’m still a newbie so I don’t know the territory very well, but it is still fairly hard to get to grips with geometric algebra: there isn’t a lot of tutorial material and there’s still a lot of variation in details of notation and choice of basic operators, which is confusing for a beginner. I have been collecting links recently: see https://dotat.at/:/?q=geometric+algebra https://dotat.at/:/?q=geometric+algebra
tsuru 6y ago
As a beginner, these are questions that lead to a big rabbit hole for me. 1. Yes, it seems Projective Geometric Algebra is new enough that the terminology and symbols are still being debated. 2. Yes, people who "get" it seem pretty convinced. I think the newish PGA is attractive for convincing real-time graphics software engineers and hardware engineers. For example, it has 16 floats in R(3,0,1) too. 3. The community is there to help spread the knowledge and to help as you start finding out about all the other Geometric Algebras. And overcoming the Euclidean mindset is tough. This is the first bit of higher-than-Calc math I've worked at in a long while and it feels like it's bending my mind in a good way, like Lisp did.

by iamwil 6y ago

adamnemecek 6y ago

It’s a community dedicated to discussion and promotion of geometric algebra.

fanf2 6y ago

Geometric algebra is very general: it can model straight Euclidean space, non-Euclidean geometry, projective geometry (the familiar homogeneous coordinate system) and also conformal geometry. Some of the earlier applications of geometric algebra to computer graphics were based on conformal geometry (eg https://rjw57.github.io/phd-thesis/rjw-thesis.pdf https://rjw57.github.io/phd-thesis/rjw-thesis.pdf) because it can model more interesting things than projective geometry, but it is more computationally expensive than projective geometry. WRT community, the https://bivector.net https://bivector.net web site has a discussion forum for people interested in geometric algebra. I’m still a newbie so I don’t know the territory very well, but it is still fairly hard to get to grips with geometric algebra: there isn’t a lot of tutorial material and there’s still a lot of variation in details of notation and choice of basic operators, which is confusing for a beginner. I have been collecting links recently: see https://dotat.at/:/?q=geometric+algebra https://dotat.at/:/?q=geometric+algebra

tsuru 6y ago

As a beginner, these are questions that lead to a big rabbit hole for me. 1. Yes, it seems Projective Geometric Algebra is new enough that the terminology and symbols are still being debated. 2. Yes, people who "get" it seem pretty convinced. I think the newish PGA is attractive for convincing real-time graphics software engineers and hardware engineers. For example, it has 16 floats in R(3,0,1) too. 3. The community is there to help spread the knowledge and to help as you start finding out about all the other Geometric Algebras. And overcoming the Euclidean mindset is tough. This is the first bit of higher-than-Calc math I've worked at in a long while and it feels like it's bending my mind in a good way, like Lisp did.