I was just wondering if there were any "obvious" resources, papers, or textbooks I should look into regarding the nyquist-criterion in higher dimensions. For example, this would be relevant if there is some curve that is i.e. not 1-to-1 w.r.t. time: $f: t \in \mathbb{R}^1 \rightarrow f(t) \in \mathbb{R}^1 $, but instead for some other parameterization $(u,v) \in \mathbb{R}^2 \rightarrow \big(t(u,v),\tilde f(u,v)\big) \in \mathbb{R}^2$, it is 1-to-1, but your independent variables are no longer single dimensional.

Then I'd like to know what sampling scheme I need to be able to recreate the curve through reconstruction. Using this approach, you could use nyquist's theorem for general spatial surfaces and manifolds as well.

This might be a math question, so I can migrate this. But I figured some experts on this sub-stack might know.

EDIT: several small edits for clarity/correctness.