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An interactive introduction to rotors from geometric algebra (2018)
- dang 1y agoRelated. Others? Let's remove Quaternions from every 3D Engine (2018) - https://news.ycombinator.com/item?id=29512302 https://news.ycombinator.com/item?id=29512302 - Dec 2021 (38 comments) Let's remove quaternions from every 3D engine (2018) - https://news.ycombinator.com/item?id=22200260 https://news.ycombinator.com/item?id=22200260 - Jan 2020 (326 comments) Let's remove Quaternions from every 3D Engine - https://news.ycombinator.com/item?id=18365433 https://news.ycombinator.com/item?id=18365433 - Nov 2018 (175 comments)
- kjeetgill 1y agoI'm pretty soft on this subject but one thing that's always bugged me when I see bivectors represented as a parallelograms is that different coplanar parallelograms of the same area are the same bivector algebraically but visually very different. It just feels confusing when you're trying to learn what it "is".
- nh23423fefe 1y agoIsn't that just inherent in binary operations? I feel like you are saying the same thing as: What is 0 sometimes people write 1-1 or 3-3 or -10+10. by the linearity of ^, B = a^b = 1 * a^b = x*(x^-1) a^b = xa ^ (x^-1)b So the bivector is the "hyperbola" of all touching parallelograms just like 0 is the set of all oppositely directed arrows of equal magnitude. But the parallelograms only become a bivector after you wedge them. not before.