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Visualizing the cross product between two vectors
- Jach 13y agoBoo cross products. http://www.av8n.com/physics/clifford-intro.htm#hi-stamp http://www.av8n.com/physics/clifford-intro.htm#hi-stamp
- gfodor 13y agowell, i just discovered a new thing. thanks! any recommended texts/papers on this subject (geometric algebra) as applied to computer graphics? I see there are basically 3 books on amazon.
- defen 13y agoI've had good luck with this one: http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425 http://www.amazon.com/Geometric-Algebra-Computer-Science-Rev... They definitely explain why the cross product is an ugly hack :) The authors have a website - geometricalgebra.net - where you can download a program which will display all the diagrams from the book and allow you to manipulate them. You can also render arbitrary low-dimensional geometric algebra constructions which helps tremendously with improving your intuition about how things work. I'd say it's at a middle ground of mathematical sophistication - it's a good mix of proofs and practical usage. It's almost entirely dedicated to applying geometric algebra to computer graphics, so you won't get as much out of it if you're interested in applications to physics, or just pure mathematics. If nothing else, I finally know what a quaternion really is after going through this book.
- mbq 13y agoMaths people always complain about the fact that cross product is reasonable only in 3D, but from a physical point of view this may be an argument why the universe has 3 spatial dims (;
- sp332 13y agoWhy does theta θ look so weird in that font?
- Zikes 13y agoAccording to the wikipedia page[1] that's a valid way of displaying lowercase theta. [1] http://en.wikipedia.org/wiki/Theta http://en.wikipedia.org/wiki/Theta
- United857 13y agoI've always found the parallelogram-area interpretation to be the easiest to intuit about: http://en.wikipedia.org/wiki/Cross_product#Geometric_meaning http://en.wikipedia.org/wiki/Cross_product#Geometric_meaning