Hestenes' Geometric Algebra

[Rick Jarosh]

I have downloaded a lot of papers by David Hestenes and others on
geometric algebra and am reading the book Clifford Algebra to
Geometric Calculus by Hestenes,but I am still looking for some
pratical examples of calculations done using this system of geometric
algebra.Does anyone know of any examples?

[Tim Sweeney]

> algebra. Does anyone know of any examples?

Hello,

In writing 3D graphics code in C++, I've used geometric algebra to
represent points (3D vectors), planes (3D bivectors), and quaternions
(3D spinors, the sum of a bivector and a scalar). This approach works
quite well, though I haven't yet found any fundamental improvements in
using geometric algebra over more traditional matrix approaches.

Hestenes presets the basis-free nature of geometric algebra as one of
its biggest strengths, but if you're a computer guy, the first thing
you'll do in writing a geometric algebra library is to make the basis
explicit.

-Tim

[Patrick Reany]

Basis-free programming is possible with computer algebra systems, such as Axiom, Maple or Mathematica.

Patrick

[Lee Rudolph]

>Hestenes presets the basis-free nature of geometric algebra as one of
>its biggest strengths, but if you're a computer guy, the first thing
>you'll do in writing a geometric algebra library is to make the basis
>explicit.

32 years ago (plus or minus a year), I heard Mike Artin proclaim
"Daddy and his friends put all that effort into getting bases out
of linear algebra, and now when we want to do anything we just
put them right back in!" (Exact words not guaranteed, sentiment
correctly transcribed.)

Lee Rudolph