isolines on a (different) surface

Question

I have two surfaces $f_1(x,y)$ and $f_2(x,y)$. I want to plot the isolines of $f_2$, i.e. the points such that $f_2(x,y)=C$ with $C$ a constant, on the surface 3D plot of $f_1(x,y)$.

A similar problem is here solved with density plots, but I want a 3D plot.

Answer 1

You can use the options MeshFunctions and Mesh with Plot3D as follows:

ClearAll[f1, f2]
f1[x_, y_] := Sin[x + y^2]
f2[x_, y_] := (x^2 + y) Cos[x^2 + 2 y]

c = .5;

Plot3D[f1[x, y], {x, -3, 3}, {y, -2, 2}, 
 MeshFunctions -> {f2[#, #2] &},
 Mesh -> {{c}}, 
 MeshStyle -> Directive[Thick, Blue]]