For my lectures I need to visualize mapping from R^n to R^m. I would like to use Wolfram Mathematica but I do not have an idea how to do it using Plot3D. For example, we have a domain in R^2 with coordinates (u,v) how can we visualize a map x=x(u,v), y=y(u,v), z=z(u,v)? It is clear how to do it in a paper and how to do it when we know equations of domains' boundary. But probably it is possible to do visualization of mapping when we put a domain in R^n, for example, square with vertices (0,0), (0,1), (1,1), (1,0) and obtain a map to R^3 by some rules, for example, helicoid x=u Cos[v], y=u Sin[v], z=v?
