Visualising the torus as a level set

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The following picture shows the level set of the function \(f : \mathbb{R}^3 \rightarrow \mathbb{R}\) given by \[ f(x, y, z) = \left( R - \sqrt{x^2 + y^2} \right)^2 + z^2 . \] The two black circles represent the intersection of the torus with the \(xz\)-plane, from which you can see that the torus is the rotation of these circles around the \(z\)-axis.

By moving the sliders for \(r\) and \(R\), you can see that the surface degenerates to a circle in the \(xy\)-plane as \(r \rightarrow 0\), and that a critical point appears at the origin as \(r \rightarrow R\).