Set $A = \{f(\mathbf{v}) | \mathbf{v} \in B, \mathbf{v} \in \Bbb{R}^n \}$, $A \subset \Bbb{R}^2$. Domain of $f$ is defined as $B = \prod_{i=1}^{n} [x_{i,\rm min},x_{i,\rm max}]$ (values are limited by their projection to axes).
Is there any method for finding boundary $bd(A)$ as an analytic function (maybe in an implicit form) or for finding an approximation function for it, at least for some simple $f$?
Update: If you don't have an exact answer, I'm glad to get any reference that can help me to figure out by myself.