The help for ContourPlot3D starts with this example
ContourPlot3D[x^3 + y^2 - z^2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
This returns a Plots of the surface $x^2 + y^2 - z^2 = 0$:
.
Now I have a function, and I would like to know how this function behaves on this surface. For example, take
f[x_,y_,z_] := {x^3 - 2 x y + z^2 x - 5 z^2 y^2 - 4 x y z,
Sin[10x] + Cos[5y] + Cos[20z]}
I was thinking of making a list with some of the point that lie on this surface. Then it is easy to evaluate the function on these points. The way I would like to generate the list is to click with the mouse on a few points that I think are interesting. Is that possible?
What are the alternatives to using the mouse? There most be some list available with all points that were used to draw this graph. How can I take some point of that list and add them as point to the 3D plot to visualize them?
Update
The methods of Szabolcs and Heike work fine on the example $x^3 + y^2 - z^2 =0$. Now I try to apply the same to
$$ 2316 a^{12} c^6+500 a^{11} b c^5+10296 a^{10} b^2 c^4+1624 a^{10} c^5+656 a^9 b^3 c^3- \\ - 3856 a^9 b c^4+41 a^8 b^4 c^2+808 a^8 b^2 c^3+784 a^8 c^4+a^7 b^5 c+24 a^7 b^3 c^2- \\ - 176 a^7 b c^3+2 a^6 b^4 c+16 a^6 b^2 c^2+32 a^6 c^3 = 0 $$
f[a_, b_, c_] := 2 a^6 b^4 c + a^7 b^5 c + 16 a^6 b^2 c^2 + 24 a^7 b^3 c^2
+ 41 a^8 b^4 c^2 + 32 a^6 c^3 - 176 a^7 b c^3 + 808 a^8 b^2 c^3
+ 656 a^9 b^3 c^3 + 784 a^8 c^4 - 3856 a^9 b c^4
+ 10296 a^10 b^2 c^4 + 1624 a^10 c^5 + 500 a^11 b c^5 + 2316 a^12 c^6
pts = {};
Substituting this function into Heike's solution does not work. Clicking does not result in points on the surface. Also Szabolcs's FindInstance does not work. What goes wrong here?
.
Tooltip
does work, so there's some support. But the mouse coordinates can only be retrieved in 2D while this time you want the coordinates in 3D, on the surface. +1. $\endgroup$f
while ColorFunction does a better job with its second component, which is rapidly varying; using PlotPoints -> 20 helps.) $\endgroup$