4Dspace wrote:Thank you, quickfur. I can't describe how very much I value your input
I don't know how much value I'm giving you. Half is stuff you obviously disagree with, and the other half is just pointing you to other sources which you might have found on your own. *shrug* Well, I tried.
So, I was thinking about this plane that is the result of cross product in 4D. Does it have chirality? Cause the structure I have in mind is dynamic. Lines have directions and planes have chirality.
How does vector/matrix notation differs from a static plane to plane with chirality? It was a long way for me, besides, in CGI courses i never had to deal with chirality So, I don't know. But I know that the result of a cross product in 3D is a vector and not just a line. So, what about this plane? Which way it turns? And if it does not, can chirality be simply assigned to it?
http://en.wikipedia.org/wiki/Cross_product#Generalizations
Specifically, look for "wedge product".
Also, see Chirality (mathematics).