The window "Domain" displays a domain (as a
wireframe) and a point (u_{0}, v_{0}) in the domain.

The window "Surface
X(u,v)" shows the plane X(u,v) = (u, v, 0), the point X(u_{0},
v_{0}), and the
tangent vectors X_{u}(u_{0},v_{0}) and X_{v}(u_{0},v_{0})
with
their tails at that point.

The window "Projection" displays the projection of
the surface X(u,v) onto the tangent plane at X(u_{0}, v_{0}).

The
control
window displays the four elements of the matrix g associated to the
first fundamental form. Note that g_{11} gives the square of
the length of
X_{u}(u_{0},v_{0}) (the red vector), g_{22}
gives
the square of the
length of
X_{v}(u_{0},v_{0}) (the green vector), and g_{12}
and g_{21} give the dot
product of
X_{u}(u_{0},v_{0}) and X_{v}(u_{0},v_{0}),
which equals the product
of the lengths of the
two vectors times the cosine of the angle between them. It is possible
to change u_{0} and v_{0} in the control window.