Is curl defined in higher dimensions?
Is the direction of the resulting vector then just giving the change in direction of the function at u?
The example of curl on the following slides seems to be in 2D. How would you visualize/use curl with three dimensions?
What would we use curls for in practice? What meaningful information does it give that's applicable to graphics?
I know curl is used to determine how much a vector "rotates/circles" around a specific point. I can imagine it being used for things like modeling fluids or other objects that flow. Does it have another application besides this or is curl not even used for fluid dynamics?
Curl turns out to be scaler values in 2D vector field but 3D vectors in 3D vector field. Isn't it not well-defined? Is it because that cross product is not well defined in nD spaces?
In a higher dimension, what will the curl look like?
So is curl in 3 dimensions a vector while in 2 dimensions it is a scalar?
In graphics, in what scenario would using curl be useful and in what scenario would using divergence is more so?
In relations to actually visualizing something graphics, will we be determining the curl of a vector space in order to map some visualization on to it in this class?