I agree the representation chosen in the SIGGRAPH lecture and the associated docs seems somewhat unnatural and counter-intuitive (why are points being represented as trivectors?).
Have you reached out to C. Gunn or S. De Keninck to ask what they think about the representation you propose in that blog post and the geometric product ⟑ and antiproduct ⟇ ? If the representations are equivalent and one is closer to concepts people already understand (e.g. points being (x,y,z,w), with w=1), then maybe adopting the simpler representation would lead to wider adoption of the ideas.
Alternatively, maybe they will point out some other reasons why points-as-trivectors representation is preferable.
I agree the representation chosen in the SIGGRAPH lecture and the associated docs seems somewhat unnatural and counter-intuitive (why are points being represented as trivectors?).
Have you reached out to C. Gunn or S. De Keninck to ask what they think about the representation you propose in that blog post and the geometric product ⟑ and antiproduct ⟇ ? If the representations are equivalent and one is closer to concepts people already understand (e.g. points being (x,y,z,w), with w=1), then maybe adopting the simpler representation would lead to wider adoption of the ideas.
Alternatively, maybe they will point out some other reasons why points-as-trivectors representation is preferable.