I'm working on a project in which I need to somehow define oriented solid angle in Cartesian coordinate system, similar to how "regular" oriented angle is defined. And well, I have no idea how to do it. I thought about some plane with one point fixed at $O=(0,0,0)$ but i don't feel if it even is reasonable. So the question is how should I define it and how should I define a negative solid angle with such a definition? I'm looking for some ideas and concepts to consider because my mind is completly blank at the moment.
2026-03-13 09:00:14.1773392414
Orienting a solid angle
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How about just the vector and half angle?