Dupin indicatrix

In differential geometry, the Dupin indicatrix is a method for characterising the local shape of a surface. Draw a plane parallel to the tangent plane and a small distance away from it. Consider the intersection of the surface with this plane. The shape of the intersection is related to the Gaussian curvature. The Dupin indicatrix is the result of the limiting process as the plane approaches the tangent plane. The indicatrix was introduced by Charles Dupin.

Equivalently, one can construct the Dupin indicatrix at point p, by first rotating and translating the surface, so that p is at origin, and the tangent plane is the xy-plane. Now the contour plot of the surface are the Dupin indicatrices.