Level curve ($f(x,y)=c$)

A level curve is the planar level set of a scalar function. Where the gradient does not vanish, the implicit function theorem makes it locally a smooth curve. At a critical point, branches may cross, narrow into a cusp or shrink to a point, so a plot should be interpreted with the local critical-point analysis.

A contour plot displays several level curves of a real-valued function of two variables, usually with labels indicating their values. It represents a surface's height on a flat page. Closely spaced level curves indicate a large change per unit distance only when the gaps between their labeled values are comparable.