The model shows the neighbourhood of a hyperbolical point P with the normal of the surface and the two corresponding principal circles of curvature. Their centres are located on the normal of the surface, with P lying between them.

At the same time the portrayed figure represents that in a general parabolic point P osculating vertex paraboloid (a hyperbolic paraboloid, saddle roof). Indeed the real parallel intersections to the tangential plane in the point P have the appearance of a half of the Dupian indicatrix in P (a pair of conjunctive hyperbolas) . The tangent plane intersects the HP-surface after two generatrices and at the same time the asymptote in P.

Surface areas with solely hyperbolic surface points are called double inverse curved or saddle-shaped. The Gaussian curvature is negative.