I have 100 points scattered in the 3D space along the $z$ coordinate axis. The points appear to lie on a curve. Is it possible to find an (implicit) curve that fit these points and option to insert coordinate $z$ and get the pair $(x,y)$ from the fitting curve equation.
2026-04-03 03:02:53.1775185373
Implicit Curve Fitting
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If your goal is to get $(x,y)$ in terms of $z$, then I think you should fit curve that has $(x,y)$ as functions of $z$. Using the least squares fit, this problem splits into two: fitting $(z,x)$ pairs to a curve $x=f(z)$ and fitting $(z,y)$ pairs to a curve $y=g(z)$. (Indeed, the square of deviation is the sum of squares of $x$-deviation and $y$-deviation.) Then $(f(z),g(z))$ gives what you wanted.
If for some reason you need a specialized curve fitting method, it's more likely to be found at Statistics.SE.