plotting – If the level set of real valued function f(x,y,z) is a curve then will ContourPlot3D fail to plot points?

I have the function $f(x,y,z)=frac{x^2}{2}+x y+frac{y^2}{2}+z^2$. The solution set to the equation $f(x,y,z)=0$ is the line parametrized as $(t,-t,0)$. When I use ContourPlot3D on f=0 I get an empty graph. I begin to suspect that ContourPlot3D only works for level sets that are surfaces. Is this correct?