The window "Domain" displays a domain and a point (u0, v0) in the domain.

The window "Surface: X(u, v)" shows the hyperbolic paraboloid X(u, v) = (u, v, u2 – v2) and the images of (u0, v0) and the colored subset of the domain on this surface (with each point in the domain mapped to a point of the same color).

The window "Normal Image" shows the surface produced by mapping each point on the surface X(u,v) to its unit normal vector, preserving the coloring from the "Surface" window.

It is possible to change the point (u0, v0) and the colored subset of the domain by clicking and dragging the points shown in the "Domain" window.

In this demo, we indicate a surface and its tangent plane at p, and, in a separate window, the tangent plane at p viewed perpendicular to the unit normal vector at p. We may select a vector A in the tangent plane and the demonstration shows the image vector dnp(A).