I have the following code:
\[Rho][c1_, R_, w_] := -((
c1 (R^4 + (4 + c1) R^2 w^2 - 3 (-1 + c1) w^4))/((-1 + c1) (R^2 +
w^2)^3));
Plot3D[\[Rho][23, R, w], {R, 0, 5}, {w, 0, 5},
PlotRange -> {Automatic, Automatic, {-10, 10}},
AxesLabel -> {"R", "w", "\[Rho]"},
MeshFunctions -> {(#/Sqrt[22] - #2) &}, MeshStyle -> {Thick, Red}]
It produces the correct plot, but gives too many mesh lines: I only want the one passing through $(0,0)$. How should I modify the code?
Contours -> {0} through {0,0}, we could set Mesh -> {{0}} to get the mesh line through {0,0}.f = (#/Sqrt[22] - #2) &;
ContourPlot[f[x, y], {x, 0, 5}, {y, 0, 5}, Contours -> {0},
ContourShading -> None]
f = (#/Sqrt[22] - #2) &;
Plot3D[ρ[23, R, w], {R, 0, 5}, {w, 0, 5},
PlotRange -> {Automatic, Automatic, {-10, 10}},
AxesLabel -> {"R", "w", "ρ"},
MeshFunctions -> {f}, Mesh -> {{0}},
MeshStyle -> {Thick, Red}]
{{0}} is almost self-documenting: Whatever valid mesh function f may be, then MeshFunctions -> {f}, Mesh -> {{f[0, 0]}} yields the mesh line(s) along which the function f has the same value as at (0, 0).
$\endgroup$
I solved the issue: I just had to modify the MeshFunction line as follows:
MeshFunctions -> {If[#/Sqrt[22] == #2,(#/Sqrt[22] - #2)] &}
Mesh -> {{0}}? $\endgroup$