An isolated singularity of a function is a singularity at a point at which the surface is not differentiable and with no other singularity in a sufficiently small enough neighborhood of . Different types of singularities have been studied and classified; see [1].

[2] S. Holzer and O. Labs, "Illustrating the Classification of Real Cubic Surfaces," Algebraic Geometry and Geometric Modeling, Mathematics and Visualization, Berling: Springer, 2006 pp. 119–134.