# Plotting the domain of a 3d surface found implicitly with ContourPlot3D

I obtained a surface defined by $$f(x,y,z) = 0$$ using ContouPlot3D. How can I plot the domain of this surface in the $$(x,y)$$ plan? In other words I am looking for the projection of the surface onto the $$(x,y)$$ plan. Note that I am not trying to have the surface and its projection on the same figure like in here, only a 2d region of the domain. Thanks in advance!

If you name your plot (Graphics3D-object )

plt=ContourPlot3D[x^3 + y^2 - z^2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]


you can change the points to x,y (2D) and use the Graphicsstructure:

plot[[1]] /.GraphicsComplex[p_List, rest__] :>GraphicsComplex[Map[Most[#] &, p], rest];
Graphics[%]


or change the viewpoint of your 3D-Plot

Show[plot, ViewPoint -> {0, 0, Infinity}]

• "Comments are used to ask for clarification or to point out problems in the post. Outdated comments may get deleted." Still, I can't help writing to say thank you! – Namsaknoi Jul 2 '19 at 18:25
• Now, could you please help me doing the same thing, i.e finding the 2d domain of a surface lying in a 3d space, but when my surface in not defined by $f(x,y,z)=0$ anymore, but rather as the intersection of a volume obtained using RegionPlot3D, called vol, with a surface obtained via ContourPlot3D, let's call it surf? – Namsaknoi Jul 5 '19 at 13:21