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 –
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
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).