Given two spaces $X$ and $Y$ with uniformly spaced coordinate system, I can produce a mapping where the new coordinates are non-uniformly spaced.
As a simple example, let $X$ = sin($\pi$x) = $Y$, and $Z=X\times Y=\{ \sin(\pi x)\times \sin(\pi x):0\leq x \leq 1\}$ with $Z \in [0, 1]\times[0,1]$. Attached is an image of $Z$: Figure: Z
Now imagine I only know the original sinusoids exist but do not have access to them (for instance, their coordinates are given in scrambled, albeit matching, combinations). Instead, I only have a straight line to fit on $Z$, and know that the rate of change of this function is dependent on these inaccessible sinusoids. Ideally, I would want a map that can simply transform any such straight line $Z$ into $Z'$: a straight line with uniformly spaced points.
I'm trying to understand how this type of problem relates to preceding literature. I have a lot of candidate terms I've been researching, including: uniform spaces, bounded distances, isometric mapping, rates of change; but I'm not sure which language best suits this context. I've also considered that there may be some other function I need to project $Z$ onto (akin to the idea of a stereographic projection) to retrieve the proper distances between points.
If anyone could point me in the right direction (proper terminology, internet article, chapters in a textbook, etc), I would be absolutely delighted. Thank you for your time and interest.