**comp.graphics.algorithms**

## Subject: **Re: General flat-flat intersection**

Kaba wrote:

> 1) What is "Geometric algebra" and how it relates to Clifford algebra

> and Grassmann algebra?

>

Geometric algebra is a term invented almost a hundred years ago by

Artin (as far as I remember). It is a branch of math covering (but not

limited to): Clifford algebras (Plural! It is not just one Clifford

algebra. Even if we fix a dimension we have a number of possible

signatures to choose from.), quaternion algebra(s) (being a special case

of Clifford algebras), Brauer-Wall group(s) and so on.

Recently it gained interest from CG and animation comunity.

In our FAQ, Ken wrote a page on it:

http://cgafaq.info/wiki/Geometric_algebra

I started to write another page almost a year ago, but never had

time to finish it:

http://cgafaq.info/wiki/Clifford_Algebra

In the section 'external links' there you can find much more stuff.

> 2) I am also reading on tensors at the moment. I have a feeling tensors

> are somehow connected to the Clifford algebra. Is there a connection and

> if there is, what is it?

>

Well, yes there is. But in fact you can connect tensors to

many areas of algebra, anyway. In a nut shell, one way to

define Clifford algebras is via tensor algebras. More modern

treatments, usually define Clifford algebras axiomatically, but

the way through tensor algebras is IMHO more intuitive. And

even with the more abstract approach, to show the existence we

revert to tensor algebras anyway (although sometimes they are

kept hidden inside more advanced structures :)

Przemek

--

"Beauty is the first test: there is no permanent place

in the world for ugly mathematics." G.H. Hardy

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