- #1
chasehusky
- 2
- 0
Howdy everyone,
I'm on a quest for something that is proving a bit elusive at the moment: a Cartesian to polar transform (along with its inverse) for \mathbb{R}^4. I'm well aware of how to derive the transform for both \mathbb{R}^2 and \mathbb{R}^3, as it is just a matter of looking at the angles made, with respect to the origin and appropriate coordinate axes, for the vector in question; e.g., for the \mathbb{R}^3 case: x = r \sin(\theta)\cos(\psi), y = r \sin(\theta)\sin(\psi), z = r \cos(\theta). Unfortunately, as with all high-dimensional spaces, visualizing these angles becomes much trickier. If anyone can help me with this, I'd greatly appreciate it.
I'm on a quest for something that is proving a bit elusive at the moment: a Cartesian to polar transform (along with its inverse) for \mathbb{R}^4. I'm well aware of how to derive the transform for both \mathbb{R}^2 and \mathbb{R}^3, as it is just a matter of looking at the angles made, with respect to the origin and appropriate coordinate axes, for the vector in question; e.g., for the \mathbb{R}^3 case: x = r \sin(\theta)\cos(\psi), y = r \sin(\theta)\sin(\psi), z = r \cos(\theta). Unfortunately, as with all high-dimensional spaces, visualizing these angles becomes much trickier. If anyone can help me with this, I'd greatly appreciate it.
