[at_compile_time]

Geometric algebra was, for me, an easier on-ramp to more advanced topics in mathematics, leveraging the geometric intuition built into these objects. I learned vector algebra in university, so extending the idea of a direction with magnitude and orientation into areas and volumes with direction and magnitude was a manageable step. Projective algebras similarly allow the construction of points, lines, and planes with orientation and magnitude. Learning that you can generate transformations by dividing one object by another was also really neat. Then you can take the logarithm of that transformation to perform linear interpolation. Geometric algebra is a tool that I use to manipulate geometric objects as easily as I would manipulate real numbers.

The hard part was getting there amidst a host of confusing and conflicting source materials, as this post highlights, and as its author helps proliferate. I used Eric Lengyel's materials a lot in my journey, but I really dislike his decision to represent points as vectors. Notice how every transformation in his poster [1] uses the antigeometric product and antireverse? These operations are only necessary because he's defined everything in the point-based dual space and has to bring everything back to the plane-based space to perform transformations. But he has a wiki and posters, and I'm just here doing my own thing, so I guess that's that.

Alan MacDonald's two books [2] were great, and I would recommend them as an introduction to geometric algebra. Work through the examples and you will learn the material.

[1] - http://projectivegeometricalgebra.org/projgeomalg.pdf

[2] - http://www.faculty.luther.edu/~macdonal/index.html#geometric...